Match each polynomial expression with its completely factored form.

$x^2 - 25$ $(x - 5)(x + 5)$
$4x^2 + 8x$ $4x(x + 2)$
$x^2 + 7x + 10$ $(x + 2)(x + 5)$
$x^2 - 3x - 10$ $(x - 5)(x + 2)$

Answer

The correct matches pair each polynomial with its fully factored equivalent using difference of squares, greatest common factor, and basic trinomial factoring rules.

Each correct pairing applies fundamental algebraic factoring rules: recognizing special binomial products like the difference of squares, pulling out the greatest common factor (GCF) from terms, and finding appropriate numerical binomial factors for quadratic trinomials.

Step-by-Step Solution

Analyze each polynomial to determine the applicable factoring method.

Identified difference of squares, GCF, and two basic quadratic trinomials.

Different polynomial structures require specific factoring techniques.

Factor the difference of squares:

x^2 - 25

Matched with

(x - 5)(x + 5)

The pattern

a^2 - b^2

factors into

(a - b)(a + b)

Factor out the greatest common factor for

4x^2 + 8x

Matched with

4x(x + 2)

Both terms share a maximum common factor of

4x

Factor the trinomial

x^2 + 7x + 10

Matched with

(x + 2)(x + 5)

The numbers

2

and

5

multiply to positive

10

and add to positive

7

Factor the trinomial

x^2 - 3x - 10

Matched with

(x - 5)(x + 2)

The numbers

-5

and

2

multiply to negative

10

and add to negative

3

Key Concept

Factoring Polynomials

Question

Answer

Step-by-Step Solution

Key Concept

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