Question

What is the factorization of the polynomial 2x^2+28x+98

Answer 1

Option B. $2(x+7)(x+7)$ is the factorization of the polynomial $2x^{2} + 28x+98.$

Step-by-step explanation:

Step 1:

To determine which of the following options is the factor for the polynomial we can expand the given options and see which matches the given polynomial $2x^{2} + 28x+98.$

So we expand the four given options.

Step 2:

Option A. $(2x+7)(x+7) = 2x^{2} +14x + 7x + 49 = 2x^{2} +21x+49.$

Option B. $2(x+7)(x+7) = 2 (x^{2} +14x+49) = 2x^{2} + 28x + 98.$

Option C. $(x+7)(x+2) = x^{2} +2x+7x+14= x^{2} +9x+14.$

Option D. $(x+7)(x+14)= x^{2} +14x + 7x + 98 = x^{2} +21x+98.$

Only option B matches the given polynomial $2x^{2} + 28x+98.$ So option B is the factorization of the polynomial $2x^{2} + 28x+98.$