Question

factor completely. 35k² + 14k - 21

Explanation:

Step1: Find GCF of coefficients

The coefficients are 35, 14, -21. GCF of 35,14,21 is 7.
$$35k^2 + 14k - 21 = 7(5k^2 + 2k - 3)$$

Step2: Factor quadratic trinomial

Factor \(5k^2 + 2k - 3\). Find two numbers \(a,b\) such that \(a\times b = 5\times(-3)= -15\) and \(a + b = 2\). The numbers are 5 and -3.
$$5k^2 + 5k - 3k - 3 = 5k(k + 1) - 3(k + 1) = (5k - 3)(k + 1)$$

Step3: Combine factors

Substitute back the factored quadratic into the expression from Step1.
$$7(5k - 3)(k + 1)$$

Answer:

\(7(5k - 3)(k + 1)\)