Match each polynomial expression with its completely factored algebraic form.

$9x^2 - 16y^2$ $(3x - 4y)(3x + 4y)$
$x^2 - 8x + 15$ $(x - 3)(x - 5)$
$3x^2 + 12x - 36$ $3(x - 2)(x + 6)$
$2x^2 + 5x - 12$ $(2x - 3)(x + 4)$

Answer

The expressions correctly match their completely factored forms by applying the rules for difference of squares, perfect trinomials, extracting a greatest common factor, and factoring by grouping.

Each polynomial must be analyzed to find its unique factors. Recognizing perfect squares, extracting common factors first, and finding the correct binomial number pairs based on sum and product rules lead to the correct matches.

Step-by-Step Solution

Identify the structure of each polynomial to determine the correct factoring technique.

Categorize the expressions into difference of squares, monic trinomials, GCF + trinomial, and non-monic trinomials.

Applying the correct initial technique is essential to fully factoring the polynomial.

Apply the corresponding factoring method to break down the polynomial into its most basic prime factors.

Each expression is rewritten as a product of binomials and, if applicable, a constant scalar.

This verifies that the polynomial is factored completely, revealing the correct match.

Key Concept

Factoring Polynomials

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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