PSAT: Advanced Math - Equivalent expressions

Posljednje ažuriranje 3 months ago

PSAT: Advanced Math - Equivalent expressions

Posljednje ažuriranje 3 months ago

Which expression is equivalent to $(9x^3 + 5x + 7) + (6x^3 + 5x^2 - 5)$?

$15x^6 + 5x^2 - 5x - 35$

$15x^3 + 10x^2 + 2$

$15x^6 + 5x^2 + 5x + 2$

$15x^3 + 5x^2 + 5x + 2$

Which expression is equivalent to $(2x^2 - 4) - (-3x^2 + 2x - 7)$?

$5x^2 - 2x + 3$

$5x^2 + 2x - 3$

$-x^2 - 2x - 11$

$-x^2 + 2x - 11$

Which expression is equivalent to $(m^{4}q^{4}z^{-1})(mq^{5}z^{3})$, where $m$, $q$, and $z$ are positive?

$m^{4}q^{20}z^{-3}$

$m^{5}q^{9}z^{2}$

$m^{6}q^{8}z^{-1}$

$m^{20}q^{12}z^{-2}$

The functions $g$ and $h$ are defined by the equations shown.
$g(x) = \frac{3}{5}x + \frac{7}{6}$
$h(x) = 6x - 5$
Which expression is equivalent to $g(x)\cdot h(x)$?

$\frac{18x^{2}}{5} - \frac{35}{6}$

$\frac{18x^{2}}{5} + \frac{27x}{11} - \frac{35}{6}$

$\frac{18x^{2}}{5} - 4x - \frac{35}{6}$

$\frac{18x^{2}}{5} + 4x - \frac{35}{6}$

Which expression is equivalent to $23x^3 + 2x^2 + 9x$?

$23x(x^2 + 2x + 9)$

$9x(23x^3 + 2x^2 + 1)$

$x(23x^2 + 2x + 9)$

$34(x^3 + x^2 + x)$

$\left(\frac{1}{2}x+\frac{3}{2}\right)\left(\frac{3}{2}x+\frac{1}{2}\right)$
The expression above is equivalent to $ax^{2}+bx+c$, where $a$, $b$, and $c$ are constants. What is the value of $b$?

$(2x + 3) - (x - 7)$
Which of the following is equivalent to the given expression?

$x - 4$

$3x - 4$

$x + 10$

$2x^2 + 21$

Which expression is equivalent to $(8yz)(y)(7z)$?

$56y^2z^2$

$56y^2z$

$56yz$

$16yz$

One of the factors of $2x^3 + 42x^2 + 208x$ is $x + b$, where $b$ is a positive constant. What is the smallest possible value of $b$?

Which of the following is equivalent to $2x^3 + 4$?

$4(x^3 + 4)$

$4(x^3 + 2)$

$2(x^3 + 4)$

$2(x^3 + 2)$

The expression $(3x - 23)(19x + 6)$ is equivalent to the expression $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants. What is the value of $b$?

In the expression $3(2x^2 + px + 8) - 16x(p + 4)$, $p$ is a constant. This expression is equivalent to the expression $6x^2 - 155x + 24$. What is the value of $p$?

$-3$

$7$

$13$

$155$

Which of the following is equivalent to the expression above?

-1/6 x + 8

-1/6 x - 2

-1/3 x^2 + 1/2 x + 15

-1/3 x^2 - 9/2 x - 15

Which of the following is an equivalent form of $(1.5x - 2.4)^2 - (5.2x^2 - 6.4)$?

$-2.2x^2 + 1.6$

$-2.2x^2 + 11.2$

$-2.95x^2 - 7.2x + 12.16$

$-2.95x^2 - 7.2x + 0.64$

Which expression is equivalent to $(x^2 + 11)^2 + (x - 5)(x + 5)$?

$x^4 + 23x^2 - 14$

$x^4 + 23x^2 + 96$

$x^4 + 12x^2 + 121$

$x^4 + x^2 + 146$

Which expression is equivalent to $(8x^3 + 8) - (x^3 - 2)$?

$8x^3 + 6$

$7x^3 + 10$

$8x^3 + 10$

$7x^3 + 6$

Which of the following expressions is equivalent to $2a^2(a+3)$?

$5a^3$

$8a^5$

$2a^3+3$

$2a^3+6a^2$

Which of the following expressions is equivalent to $8x^{10} - 8x^9 + 88x$?

$x(7x^{10} - 7x^9 + 87x)$

$x(8^{10} - 8^9 + 88)$

$8x(x^{10} - x^9 + 11x)$

$8x(x^9 - x^8 + 11)$

Which expression is equivalent to $12x + 27$?

$12(9x + 1)$

$27(12x + 1)$

$3(4x + 9)$

$3(9x + 24)$

If $k - x$ is a factor of the expression $-x^2 + \frac{1}{29}nk^2$, where $n$ and $k$ are constants and $k > 0$, what is the value of $n$?

$-29$

$-\frac{1}{29}$

$\frac{1}{29}$

$29$

Which expression is equivalent to $13x^2 - 7x^2$?

$-91x^2$

$6x^2$

$20x^2$

$40x^2$

Which of the following is equivalent to the sum of $3x^4 + 2x^3$ and $4x^4 + 7x^3$?

$16x^{14}$

$7x^8 + 9x^6$

$12x^4 + 14x^3$

$7x^4 + 9x^3$

Which of the following is equivalent to the expression above?

4x^2 + 21x + 33

4x^2 + 21x + 29

4x^2 + x + 29

4x^2 + x + 33

Which of the following expressions is(are) a factor of $3x^2 + 20x - 63$?
I. $x - 9$
II. $3x - 7$

I only

II only

I and II

Neither I nor II

Which of the following is equivalent to $\left(a + \frac{b}{2}\right)^2$?

$a^2 + \frac{b^2}{2}$

$a^2 + \frac{b^2}{4}$

$a^2 + \frac{ab}{2} + \frac{b^2}{2}$

$a^2 + ab + \frac{b^2}{4}$

If $a = c + d$, which of the following is equivalent to the expression $x^2 - c^2 - 2cd - d^2$?

$(x + a)^2$

$(x - a)^2$

$(x + a)(x - a)$

$x^2 - ax - a^2$

Which of the following expressions has a factor of $x + 2b$, where $b$ is a positive integer constant?

$3x^{2} + 7x + 14b$

$3x^{2} + 28x + 14b$

$3x^{2} + 42x + 14b$

$3x^{2} + 49x + 14b$

Which expression is equivalent to $4(x^2 + 6)$?

$4x^2 + 24$

$4x^2 + 10$

$4x^2 + 6$

$4x^2 - 2$

$(2x^3 + 3x)(x^3 - 2x)$
Which of the following is equivalent to the expression above?

$x^3 + 5x$

$3x^3 + x$

$2x^6 - x^4 - 6x^2$

$3x^6 - x^4 - 6x^2$

Which expression is equivalent to $\dfrac{h^{15}q^{7}}{h^{5}q^{11}}$, where $h > 0$ and $q > 0$?

$\dfrac{h^{10}}{q^{14}}$

$\dfrac{h^{3}}{q^{3}}$

$h^{10}q^{14}$

$h^{3}q^{3}$

Which expression is equivalent to $6x^8y^2 + 12x^2y^2$?

$6x^2y^2(2x^6)$

$6x^2y^2(x^4)$

$6x^2y^2(x^6 + 2)$

$6x^2y^2(x^4 + 2)$

$4a^2 + 20ab + 25b^2$
Which of the following is a factor of the polynomial above?

$a + b$

$2a + 5b$

$4a + 5b$

$4a + 25b$

Which expression is equivalent to $5x^5 - 6x^4 + 8x^3$?

$x^4(5x - 6)$

$x^3(5x^2 - 6x + 8)$

$8x^3(5x^2 - 6x + 1)$

$6x^5(-6x^4 + 8x^3 + 1)$

$0.36x^2 + 0.63x + 1.17$
The given expression can be rewritten as $a(4x^2 + 7x + 13)$, where $a$ is a constant. What is the value of $a$?

Which expression is equivalent to $5x^2 - 50xy^2$?

$5x(x - 10y^2)$

$5x(x - 50y^2)$

$5x^2(10xy^2)$

$5x^2(50xy^2)$

Which expression is equivalent to $9x^2 + 5x$?

$x(9x + 5)$

$5x(9x + 1)$

$9x(x + 5)$

$x^2(9x + 5)$

Which expression is equivalent to $(7x^3 + 7x) - (6x^3 - 3x)$?

$x^3 + 10x$

$-13x^3 + 10x$

$-13x^3 + 4x$

$x^3 + 4x$

Which expression is equivalent to $(2x^2 + x - 9) + (x^2 + 6x + 1)$?

$2x^2 + 7x + 10$

$2x^2 + 6x - 8$

$3x^2 + 7x - 10$

$3x^2 + 7x - 8$

Which of the following is equivalent to the expression above?

x - 23y

2x^2 - xy - 3y^2

2x^2 + 24xy + 36y^2

2x^2 - 49xy + 69y^2

Which expression is equivalent to $19(x^2 - 7)$?

$19x^2 - 133$

$19x^2 - 26$

$19x^2 - 7$

$19x^2 + 12$

Which expression is equivalent to $16(x + 15)$?

$16x + 31$

$16x + 240$

$16x + 1$

$16x + 15$

Which expression is equivalent to $256w^2 - 676$?

$(16w - 26)(16w - 26)$

$(8w - 13)(8w + 13)$

$(8w - 13)(8w - 13)$

$(16w - 26)(16w + 26)$

Which of the following expressions is equivalent to the sum of $(r^3 + 5r^2 + 7)$ and $(r^2 + 8r + 12)$?

$r^5 + 13r^3 + 19$

$2r^3 + 13r^2 + 19$

$r^3 + 5r^2 + 7r + 12$

$r^3 + 6r^2 + 8r + 19$

$5x + 15$
Which of the following is equivalent to the given expression?

$5(x + 3)$

$5(x + 10)$

$5(x + 15)$

$5(x + 20)$

Which expression is equivalent to $20w - (4w + 3w)$?

$10w$

$13w$

$19w$

$21w$

If $4^{8c} = \sqrt[3]{4^7}$, what is the value of $c$?

Which expression is equivalent to $34x + 34y$?

$34xy$

$34(x + y)$

$68y$

$68x$

The expression $2x^2 + ax$ is equivalent to $x(2x + 7)$ for some constant $a$. What is the value of $a$?

Which expression is equivalent to $(d - 6)(8d^2 - 3)$?

$8d^3 - 14d^2 - 3d + 18$

$8d^3 - 17d^2 + 48$

$8d^3 - 48d^2 - 3d + 18$

$8d^3 - 51d^2 + 48$

$(7532 + 100y^2) + 10(10y^2 - 110)$
The expression above can be written in the form $ay^2 + b$, where $a$ and $b$ are constants. What is the value of $a + b$?

PSAT: Advanced Math - Equivalent expressions

PSAT: Advanced Math - Equivalent expressions

Which expression is equivalent to $(9x^3 + 5x + 7) + (6x^3 + 5x^2 - 5)$?

Which expression is equivalent to $(2x^2 - 4) - (-3x^2 + 2x - 7)$?

Which expression is equivalent to $(m^{4}q^{4}z^{-1})(mq^{5}z^{3})$, where $m$, $q$, and $z$ are positive?

The functions $g$ and $h$ are defined by the equations shown.$g(x) = \frac{3}{5}x + \frac{7}{6}$$h(x) = 6x - 5$Which expression is equivalent to $g(x)\cdot h(x)$?

Which expression is equivalent to $23x^3 + 2x^2 + 9x$?

$\left(\frac{1}{2}x+\frac{3}{2}\right)\left(\frac{3}{2}x+\frac{1}{2}\right)$The expression above is equivalent to $ax^{2}+bx+c$, where $a$, $b$, and $c$ are constants. What is the value of $b$?

$(2x + 3) - (x - 7)$Which of the following is equivalent to the given expression?

Which expression is equivalent to $(8yz)(y)(7z)$?

One of the factors of $2x^3 + 42x^2 + 208x$ is $x + b$, where $b$ is a positive constant. What is the smallest possible value of $b$?

Which of the following is equivalent to $2x^3 + 4$?

The expression $(3x - 23)(19x + 6)$ is equivalent to the expression $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants. What is the value of $b$?

In the expression $3(2x^2 + px + 8) - 16x(p + 4)$, $p$ is a constant. This expression is equivalent to the expression $6x^2 - 155x + 24$. What is the value of $p$?

Which of the following is equivalent to the expression above?

Which of the following is an equivalent form of $(1.5x - 2.4)^2 - (5.2x^2 - 6.4)$?

Which expression is equivalent to $(x^2 + 11)^2 + (x - 5)(x + 5)$?

Which expression is equivalent to $(8x^3 + 8) - (x^3 - 2)$?

Which of the following expressions is equivalent to $2a^2(a+3)$?

Which of the following expressions is equivalent to $8x^{10} - 8x^9 + 88x$?

Which expression is equivalent to $12x + 27$?

If $k - x$ is a factor of the expression $-x^2 + \frac{1}{29}nk^2$, where $n$ and $k$ are constants and $k > 0$, what is the value of $n$?

Which expression is equivalent to $13x^2 - 7x^2$?

Which of the following is equivalent to the sum of $3x^4 + 2x^3$ and $4x^4 + 7x^3$?

Which of the following is equivalent to the expression above?

Which of the following expressions is(are) a factor of $3x^2 + 20x - 63$?I. $x - 9$II. $3x - 7$

Which of the following is equivalent to $\left(a + \frac{b}{2}\right)^2$?

If $a = c + d$, which of the following is equivalent to the expression $x^2 - c^2 - 2cd - d^2$?

Which of the following expressions has a factor of $x + 2b$, where $b$ is a positive integer constant?

Which expression is equivalent to $4(x^2 + 6)$?

$(2x^3 + 3x)(x^3 - 2x)$Which of the following is equivalent to the expression above?

Which expression is equivalent to $\dfrac{h^{15}q^{7}}{h^{5}q^{11}}$, where $h > 0$ and $q > 0$?

Which expression is equivalent to $6x^8y^2 + 12x^2y^2$?

$4a^2 + 20ab + 25b^2$Which of the following is a factor of the polynomial above?

Which expression is equivalent to $5x^5 - 6x^4 + 8x^3$?

$0.36x^2 + 0.63x + 1.17$The given expression can be rewritten as $a(4x^2 + 7x + 13)$, where $a$ is a constant. What is the value of $a$?

Which expression is equivalent to $5x^2 - 50xy^2$?

Which expression is equivalent to $9x^2 + 5x$?

Which expression is equivalent to $(7x^3 + 7x) - (6x^3 - 3x)$?

Which expression is equivalent to $(2x^2 + x - 9) + (x^2 + 6x + 1)$?

Which of the following is equivalent to the expression above?

Which expression is equivalent to $19(x^2 - 7)$?

Which expression is equivalent to $16(x + 15)$?

Which expression is equivalent to $256w^2 - 676$?

Which of the following expressions is equivalent to the sum of $(r^3 + 5r^2 + 7)$ and $(r^2 + 8r + 12)$?

$5x + 15$Which of the following is equivalent to the given expression?

Which expression is equivalent to $20w - (4w + 3w)$?

If $4^{8c} = \sqrt[3]{4^7}$, what is the value of $c$?

Which expression is equivalent to $34x + 34y$?

The expression $2x^2 + ax$ is equivalent to $x(2x + 7)$ for some constant $a$. What is the value of $a$?

Which expression is equivalent to $(d - 6)(8d^2 - 3)$?

$(7532 + 100y^2) + 10(10y^2 - 110)$The expression above can be written in the form $ay^2 + b$, where $a$ and $b$ are constants. What is the value of $a + b$?

Which expression is equivalent to $(9x^3 + 5x + 7) + (6x^3 + 5x^2 - 5)$?

Which expression is equivalent to $(2x^2 - 4) - (-3x^2 + 2x - 7)$?

Which expression is equivalent to $(m^{4}q^{4}z^{-1})(mq^{5}z^{3})$, where $m$, $q$, and $z$ are positive?

The functions $g$ and $h$ are defined by the equations shown.$g(x) = \frac{3}{5}x + \frac{7}{6}$$h(x) = 6x - 5$Which expression is equivalent to $g(x)\cdot h(x)$?

Which expression is equivalent to $23x^3 + 2x^2 + 9x$?

$\left(\frac{1}{2}x+\frac{3}{2}\right)\left(\frac{3}{2}x+\frac{1}{2}\right)$The expression above is equivalent to $ax^{2}+bx+c$, where $a$, $b$, and $c$ are constants. What is the value of $b$?

$(2x + 3) - (x - 7)$Which of the following is equivalent to the given expression?

Which expression is equivalent to $(8yz)(y)(7z)$?

One of the factors of $2x^3 + 42x^2 + 208x$ is $x + b$, where $b$ is a positive constant. What is the smallest possible value of $b$?

Which of the following is equivalent to $2x^3 + 4$?

The expression $(3x - 23)(19x + 6)$ is equivalent to the expression $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants. What is the value of $b$?

In the expression $3(2x^2 + px + 8) - 16x(p + 4)$, $p$ is a constant. This expression is equivalent to the expression $6x^2 - 155x + 24$. What is the value of $p$?

Which of the following is equivalent to the expression above?

Which of the following is an equivalent form of $(1.5x - 2.4)^2 - (5.2x^2 - 6.4)$?

Which expression is equivalent to $(x^2 + 11)^2 + (x - 5)(x + 5)$?

Which expression is equivalent to $(8x^3 + 8) - (x^3 - 2)$?

Which of the following expressions is equivalent to $2a^2(a+3)$?

Which of the following expressions is equivalent to $8x^{10} - 8x^9 + 88x$?

Which expression is equivalent to $12x + 27$?

If $k - x$ is a factor of the expression $-x^2 + \frac{1}{29}nk^2$, where $n$ and $k$ are constants and $k > 0$, what is the value of $n$?

Which expression is equivalent to $13x^2 - 7x^2$?

Which of the following is equivalent to the sum of $3x^4 + 2x^3$ and $4x^4 + 7x^3$?

Which of the following is equivalent to the expression above?

Which of the following expressions is(are) a factor of $3x^2 + 20x - 63$?I. $x - 9$II. $3x - 7$

Which of the following is equivalent to $\left(a + \frac{b}{2}\right)^2$?

If $a = c + d$, which of the following is equivalent to the expression $x^2 - c^2 - 2cd - d^2$?

Which of the following expressions has a factor of $x + 2b$, where $b$ is a positive integer constant?

Which expression is equivalent to $4(x^2 + 6)$?

The functions $g$ and $h$ are defined by the equations shown.
$g(x) = \frac{3}{5}x + \frac{7}{6}$
$h(x) = 6x - 5$
Which expression is equivalent to $g(x)\cdot h(x)$?

$\left(\frac{1}{2}x+\frac{3}{2}\right)\left(\frac{3}{2}x+\frac{1}{2}\right)$
The expression above is equivalent to $ax^{2}+bx+c$, where $a$, $b$, and $c$ are constants. What is the value of $b$?

$(2x + 3) - (x - 7)$
Which of the following is equivalent to the given expression?

Which of the following expressions is(are) a factor of $3x^2 + 20x - 63$?
I. $x - 9$
II. $3x - 7$

$(2x^3 + 3x)(x^3 - 2x)$
Which of the following is equivalent to the expression above?

$4a^2 + 20ab + 25b^2$
Which of the following is a factor of the polynomial above?

$0.36x^2 + 0.63x + 1.17$
The given expression can be rewritten as $a(4x^2 + 7x + 13)$, where $a$ is a constant. What is the value of $a$?

$5x + 15$
Which of the following is equivalent to the given expression?

$(7532 + 100y^2) + 10(10y^2 - 110)$
The expression above can be written in the form $ay^2 + b$, where $a$ and $b$ are constants. What is the value of $a + b$?

The functions $g$ and $h$ are defined by the equations shown.
$g(x) = \frac{3}{5}x + \frac{7}{6}$
$h(x) = 6x - 5$
Which expression is equivalent to $g(x)\cdot h(x)$?

$\left(\frac{1}{2}x+\frac{3}{2}\right)\left(\frac{3}{2}x+\frac{1}{2}\right)$
The expression above is equivalent to $ax^{2}+bx+c$, where $a$, $b$, and $c$ are constants. What is the value of $b$?

$(2x + 3) - (x - 7)$
Which of the following is equivalent to the given expression?

Which of the following expressions is(are) a factor of $3x^2 + 20x - 63$?
I. $x - 9$
II. $3x - 7$

$(2x^3 + 3x)(x^3 - 2x)$
Which of the following is equivalent to the expression above?

$4a^2 + 20ab + 25b^2$
Which of the following is a factor of the polynomial above?

$0.36x^2 + 0.63x + 1.17$
The given expression can be rewritten as $a(4x^2 + 7x + 13)$, where $a$ is a constant. What is the value of $a$?

$5x + 15$
Which of the following is equivalent to the given expression?

$(7532 + 100y^2) + 10(10y^2 - 110)$
The expression above can be written in the form $ay^2 + b$, where $a$ and $b$ are constants. What is the value of $a + b$?