Factor completely. 28-7x^(2)=

Identify common factor: Identify the common factor in the terms 28 and -7x^2. Both terms have a common factor of 7. Factor out the 7: 28 - 7x^2 = 7(4 - x^2)Factor out the common factor: Recognize the expression 4 - x^2 as a difference of squares. 4 can be written as 2^2 and x^2 is already a perfect square. So, 4 - x^2 can be expressed as (2)^2 - (x)^2Recognize difference of squares: Apply the difference of squares formula to factor 4 - x^2. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Using this formula, we get (2)^2 - (x)^2 = (2 - x)(2 + x).Apply difference of squares formula: Combine the factored form of 4 - x^2 with the common factor we factored out in Step 1. The complete factored form is 7(2 - x)(2 + x).

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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28-7x^{2}=

Identify common factor: Identify the common factor in the terms $28$ and $-7x^2$ . $\newline$ Both terms have a common factor of $7$ . $\newline$ Factor out the $7$ : $28 - 7x^2 = 7(4 - x^2)$
Factor out the common factor: Recognize the expression $4 - x^2$ as a difference of squares. $\newline$ $4$ can be written as $2^2$ and $x^2$ is already a perfect square. $\newline$ So, $4 - x^2$ can be expressed as $(2)^2 - (x)^2$
Recognize difference of squares: Apply the difference of squares formula to factor $4 - x^2$ . $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Using this formula, we get $(2)^2 - (x)^2 = (2 - x)(2 + x)$ .
Apply difference of squares formula: Combine the factored form of $4 - x^2$ with the common factor we factored out in Step $1$ . $\newline$ The complete factored form is $7(2 - x)(2 + x)$ .