Factor completely. 5x^(2)-320=

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms in the expression 5x^2 - 320. The GCF of 5x^2 and 320 is 5.Factor out GCF: Factor out the GCF from the expression. 5x^2 - 320 = 5(x^2 - 64)Recognize difference of squares: Recognize that the expression inside the parentheses is a difference of squares. x^2 - 64 can be written as x^2 - 8^2, 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). So, x^2 - 8^2 = (x - 8)(x + 8).Write fully factored form: Write the fully factored form of the original expression by including the GCF. 5x^2 - 320 = 5(x - 8)(x + 8)

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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5x^{2}-320=

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms in the expression $5x^2 - 320$ . $\newline$ The GCF of $5x^2$ and $320$ is $5$ .
Factor out GCF: Factor out the GCF from the expression. $5x^2 - 320 = 5(x^2 - 64)$
Recognize difference of squares: Recognize that the expression inside the parentheses is a difference of squares. $x^2 - 64$ can be written as $x^2 - 8^2$ , 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 $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ So, $x^2 - 8^2 = (x - 8)(x + 8)$ .
Write fully factored form: Write the fully factored form of the original expression by including the GCF. $\newline$ $5x^2 - 320 = 5(x - 8)(x + 8)$