QuestionFind the factored form of $x^{3}+343$ . Choose from: a. $(x+7)^{3}$ , b. $(x+7)(x^{2}+49)$ , c. $(x+7)(x^{2}+7x+49)$ , d. $(x+7)(x^{2}-7x+49)$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $x^{3}+343$ . We need to find the factored form of the equation

STEP 2

We know that 343 =7^. So, we can rewrite the equation as $x^{}+7^{}$

STEP 3

The expression $x^{3}+7^{3}$ is a sum of cubes. The sum of cubes can be factored using the formula $(a^3 + b^3) = (a + b)(a^2 - ab + b^2)$

STEP 4

In our case, $a = x$ and $b =7$ . So, we can rewrite the equation as $(x+7)(x^{2}-7x+49)$ So, the factored form of the equation $x^{3}+343$ is $(x+7)(x^{2}-7x+49)$ .
Therefore, the correct answer is option d.

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