Match each polynomial expression on the left with its completely factored equivalent on th… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each polynomial expression on the left with its completely factored equivalent on the right.

$x^2 - 3x - 10$ $(x - 5)(x + 2)$
$2x^2 - 18$ $2(x - 3)(x + 3)$
$3x^2 - 6x$ $3x(x - 2)$
$x^2 - 10x + 25$ $(x - 5)^2$

Answer

The correct matches pair each polynomial with its completely factored form by applying techniques such as factoring out the greatest common factor (GCF), recognizing difference of squares, and factoring trinomials.

Each polynomial is completely factored by extracting any Greatest Common Factors and correctly applying fundamental algebraic patterns, including the difference of squares, perfect square trinomials, and standard quadratic trinomial factoring.

Step-by-Step Solution

Analyze the first polynomial:

x^2 - 3x - 10

It factors to

(x - 5)(x + 2)

This is a basic trinomial where we need factors of -10 that add up to -3.

Analyze the second polynomial:

2x^2 - 18

It factors to

2(x - 3)(x + 3)

Factoring out the GCF of 2 leaves

x^2 - 9

, which is a difference of squares and factors further into

(x - 3)(x + 3)

Analyze the third polynomial:

3x^2 - 6x

It factors to

3x(x - 2)

The two terms share a common factor of

3x

. Extracting this GCF directly yields the factored form.

Analyze the fourth polynomial:

x^2 - 10x + 25

It factors to

(x - 5)^2

This matches the perfect square trinomial pattern

a^2 - 2ab + b^2 = (a - b)^2

with

a=x

and

b=5

Key Concept

Factoring Polynomials

Question

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Step-by-Step Solution

Key Concept

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