Lesson 4.4 Factor Polynomials

Instructions

Learning Goal: I can use factoring to write a polynomial as the product of polynomials of lesser degree

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Function Operations

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Factoring a polynomial involves finding factors of lesser degree that can be multiplied together to produce the polynomial. You have already factored polynomials of degree 2, as in the example below.

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In a similar fashion, factor the following,

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Not all polynomials can be factored over the integers.

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When a polynomial is factored, the degree of each factor is less than the degree of the polynomial. While the goal is to rewrite the polynomial as a product of linear factors, this is not always possible. A factor of degree 2 or greater that cannot be factored further is an irreducible factor.

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Use Special Factoring Patterns to factor the following.

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FACTOR BY GROUPING
If you can group together pairs of terms of a polynomial that have a common factor, you may be able to use a method called factoring by grouping to factor the polynomial.

1

FACTOR BY GROUPING
If you can group together pairs of terms of a polynomial that have a common factor, you may be able to use a method called factoring by grouping to factor the polynomial.

2

Factor the polynomial over the integers or identify it as irreducible.

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Factor the polynomial over the integers or identify it as irreducible.

2

Factor the polynomial over the integers or identify it as irreducible.

2

Factor the polynomial over the integers or identify it as irreducible.

2

Factor the polynomial over the integers or identify it as irreducible.

3

Factor the polynomial over the integers or identify it as irreducible.

3

Factor the polynomial over the integers or identify it as irreducible.

3

Factor the polynomial over the integers or identify it as irreducible.

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Factor the polynomial over the integers or identify it as irreducible.

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The manufacturer of a wooden feeding trough for farm animals makes the sides and bottom of the trough 1 foot thick. The outer height and outer width of the trough are the same, and the outer length is twice the outer height and outer width. What should the outer dimensions of the trough be if the trough is to hold 36 cubic feet of feed?

Lesson 4.4 Factor Polynomials

Function Operations

Factoring a polynomial involves finding factors of lesser degree that can be multiplied together to produce the polynomial. You have already factored polynomials of degree 2, as in the example below.

In a similar fashion, factor the following,

Not all polynomials can be factored over the integers.

When a polynomial is factored, the degree of each factor is less than the degree of the polynomial. While the goal is to rewrite the polynomial as a product of linear factors, this is not always possible. A factor of degree 2 or greater that cannot be factored further is an irreducible factor.

Use Special Factoring Patterns to factor the following.

FACTOR BY GROUPINGIf you can group together pairs of terms of a polynomial that have a common factor, you may be able to use a method called factoring by grouping to factor the polynomial.

FACTOR BY GROUPINGIf you can group together pairs of terms of a polynomial that have a common factor, you may be able to use a method called factoring by grouping to factor the polynomial.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Function Operations

Factoring a polynomial involves finding factors of lesser degree that can be multiplied together to produce the polynomial. You have already factored polynomials of degree 2, as in the example below.

In a similar fashion, factor the following,

Not all polynomials can be factored over the integers.

When a polynomial is factored, the degree of each factor is less than the degree of the polynomial. While the goal is to rewrite the polynomial as a product of linear factors, this is not always possible. A factor of degree 2 or greater that cannot be factored further is an irreducible factor.

Use Special Factoring Patterns to factor the following.

FACTOR BY GROUPINGIf you can group together pairs of terms of a polynomial that have a common factor, you may be able to use a method called factoring by grouping to factor the polynomial.

FACTOR BY GROUPINGIf you can group together pairs of terms of a polynomial that have a common factor, you may be able to use a method called factoring by grouping to factor the polynomial.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

Factor the polynomial over the integers or identify it as irreducible.

FACTOR BY GROUPING
If you can group together pairs of terms of a polynomial that have a common factor, you may be able to use a method called factoring by grouping to factor the polynomial.

FACTOR BY GROUPING
If you can group together pairs of terms of a polynomial that have a common factor, you may be able to use a method called factoring by grouping to factor the polynomial.

FACTOR BY GROUPING
If you can group together pairs of terms of a polynomial that have a common factor, you may be able to use a method called factoring by grouping to factor the polynomial.

FACTOR BY GROUPING
If you can group together pairs of terms of a polynomial that have a common factor, you may be able to use a method called factoring by grouping to factor the polynomial.