Option B. [tex]2(x+7)(x+7)[/tex] is the factorization of the polynomial [tex]2x^{2} + 28x+98.[/tex]
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 [tex]2x^{2} + 28x+98.[/tex]
So we expand the four given options.
Step 2:
Option A. [tex](2x+7)(x+7) = 2x^{2} +14x + 7x + 49 = 2x^{2} +21x+49.[/tex]
Option B. [tex]2(x+7)(x+7) = 2 (x^{2} +14x+49) = 2x^{2} + 28x + 98.[/tex]
Option C. [tex](x+7)(x+2) = x^{2} +2x+7x+14= x^{2} +9x+14.[/tex]
Option D. [tex](x+7)(x+14)= x^{2} +14x + 7x + 98 = x^{2} +21x+98.[/tex]
Only option B matches the given polynomial [tex]2x^{2} + 28x+98.[/tex] So option B is the factorization of the polynomial [tex]2x^{2} + 28x+98.[/tex]
