Question

factor.
3x^2 - 2x - 21

Explanation:

Step1: Multiply leading - coefficient and constant

Multiply 3 and - 21, getting - 63. We need two numbers that multiply to - 63 and add up to - 2. The numbers are - 9 and 7 since (-9)×7=-63 and - 9 + 7=-2.

Step2: Rewrite the middle term

Rewrite - 2x as - 9x+7x. So, 3x² - 2x - 21 becomes 3x² - 9x+7x - 21.

Step3: Group the terms

Group the terms: (3x² - 9x)+(7x - 21).

Step4: Factor out the GCF from each group

From 3x² - 9x, factor out 3x to get 3x(x - 3). From 7x - 21, factor out 7 to get 7(x - 3).

Step5: Factor out the common binomial factor

We have 3x(x - 3)+7(x - 3). Factor out (x - 3) to get (x - 3)(3x + 7).

Answer:

(x - 3)(3x + 7)