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Factor completely. $4 x^{2}-64 x+252$
Answer Attempt 1 out of 2

Studdy Solution

STEP 1

1. The expression $4x^2 - 64x + 252$ is a quadratic polynomial.
2. We need to factor the quadratic expression completely.
3. Factoring involves finding two binomials that multiply to give the original quadratic expression.

STEP 2

1. Identify and factor out the greatest common factor (GCF) from the expression.
2. Factor the resulting quadratic expression completely.

STEP 3

Identify the greatest common factor (GCF) of the coefficients in the expression $4x^2 - 64x + 252$ .
The GCF of $4$ , $64$ , and $252$ is $4$ .
Factor out the GCF from the expression:
$4(x^2 - 16x + 63)$

STEP 4

Now, focus on factoring the quadratic expression inside the parentheses: $x^2 - 16x + 63$ .
Look for two numbers that multiply to $63$ (the constant term) and add up to $-16$ (the coefficient of the linear term).
These numbers are $-9$ and $-7$ .
Rewrite the quadratic expression using these numbers:
$x^2 - 16x + 63 = (x - 9)(x - 7)$

STEP 5

Combine the factored terms with the GCF factored out earlier:
$4(x - 9)(x - 7)$
This is the completely factored form of the original expression.
The completely factored expression is:
$\boxed{4(x - 9)(x - 7)}$

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