the polynomial 10x³ + 35x² - 4x - 14 is factored by grouping. 10x³ + 35x² - 4x - 14 5x²(____) - 2(____) what…
the polynomial 10x³ + 35x² - 4x - 14 is factored by grouping. 10x³ + 35x² - 4x - 14 5x²(____) - 2(____) what is the common factor that is missing from both sets of parentheses? -2x - 7 2x + 7 -2x² + 7 2x² + 7
Answer
Answer:
B. (2x + 7)
Explanation:
Step1: Group the polynomial terms
(10x^{3}+35x^{2}-4x - 14=(10x^{3}+35x^{2})+(-4x - 14))
Step2: Factor out the GCF from each group
For (10x^{3}+35x^{2}), GCF is (5x^{2}), so (10x^{3}+35x^{2}=5x^{2}(2x + 7)); for (-4x - 14), GCF is (-2), so (-4x - 14=-2(2x + 7))
Step3: Identify the common factor
The common factor in (5x^{2}(2x + 7)-2(2x + 7)) is (2x + 7)