IXL - Factor using a quadratic pattern (Algebra 1 practice)

Factor

completely.

All factors in your answer should have integer coefficients.

ref_doc_title.

Learn with an example

question

Factor

completely.

All factors in your answer should have integer coefficients.

key idea

An expression in quadratic form can be written as

where

and

are numbers with

≠

and

is some expression in

Factor

Theorem:

The binomial

–

is a linear factor of the polynomial

(

)

if and only if

is a zero (or root) of

(

)

solution

Try writing the polynomial in quadratic form by substituting

for an expression in

A good choice is

Then, factor the quadratic expression in

(

)

Substitute

Factor

(

)

Factor

Substitute

(

)

Substitute

The quadratic

has no real roots. By the Factor Theorem, it does not have any linear factors with real coefficients. The polynomial factors completely as:

(

)

Looking for more? Try these:

Lesson: Factoring expressions

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X.5Factor quadratics with leading coefficient 1

Lesson: Factoring expressions

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