Factor completely. 3x^(2)-147=

Identify common factor: Identify a common factor in the terms 3x^2 and -147. Both terms are divisible by 3.Factor out GCF: Factor out the greatest common factor (GCF) from the expression. GCF of 3x^2 and -147 is 3. 3x^2 - 147 = 3(x^2 - 49)Recognize difference of squares: Recognize that x^2 - 49 is a difference of squares. x^2 = x * x = (x)^2 49 = 7 * 7 = 7^2 So, x^2 - 49 = (x)^2 - 7^2Use difference of squares formula: Use the difference of squares formula to factor x^2 - 49. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). (x)^2 - 7^2 = (x - 7)(x + 7)Combine factored form with GCF: Combine the factored form of x^2 - 49 with the GCF that was factored out. 3(x^2 - 49) = 3(x - 7)(x + 7)

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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3x^{2}-147=

Identify common factor: Identify a common factor in the terms $3x^2$ and $-147$ . $\newline$ Both terms are divisible by $3$ .
Factor out GCF: Factor out the greatest common factor (GCF) from the expression. $\newline$ GCF of $3x^2$ and $-147$ is $3$ . $\newline$ $3x^2 - 147 = 3(x^2 - 49)$
Recognize difference of squares: Recognize that $x^2 - 49$ is a difference of squares. $\newline$ $x^2 = x \times x = (x)^2$ $\newline$ $49 = 7 \times 7 = 7^2$ $\newline$ So, $x^2 - 49 = (x)^2 - 7^2$
Use difference of squares formula: Use the difference of squares formula to factor $x^2 - 49$ . $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ $(x)^2 - 7^2 = (x - 7)(x + 7)$
Combine factored form with GCF: Combine the factored form of $x^2 - 49$ with the GCF that was factored out. $\newline$ $3(x^2 - 49) = 3(x - 7)(x + 7)$