Factor completely. 96-6x^(2)=

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms in the expression 96 - 6x^2. The GCF of 96 and 6x^2 is 6.Factor out GCF: Factor out the GCF from the expression. 96 - 6x^2 = 6(16 - x^2)Recognize difference of squares: Recognize that the expression inside the parentheses is a difference of squares. 16 - x^2 can be written as 4^2 - (x)^2, which is in the form a^2 - b^2.Apply difference of squares formula: Apply the difference of squares formula to factor the expression inside the parentheses. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Therefore, 16 - x^2 = (4 - x)(4 + x).Write fully factored form: Write the fully factored form of the original expression by including the GCF. 96 - 6x^2 = 6(4 - x)(4 + x)

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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96-6x^{2}=

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms in the expression $96 - 6x^2$ . $\newline$ The GCF of $96$ and $6x^2$ is $6$ .
Factor out GCF: Factor out the GCF from the expression. $96 - 6x^2 = 6(16 - x^2)$
Recognize difference of squares: Recognize that the expression inside the parentheses is a difference of squares. $16 - x^2$ can be written as $4^2 - (x)^2$ , which is in the form $a^2 - b^2$ .
Apply difference of squares formula: Apply the difference of squares formula to factor the expression inside the parentheses. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Therefore, $16 - x^2 = (4 - x)(4 + x)$ .
Write fully factored form: Write the fully factored form of the original expression by including the GCF. $\newline$ $96 - 6x^2 = 6(4 - x)(4 + x)$