Question

What is the factorization of the polynomial below? 2x2 + 28x + 98 A. (x + 7)(x + 2) B. (x + 7)(x + 14) C. (2x + 7)(x + 7) D. 2(x + 7)(x + 7)

Answer 1

2x^2 + 28x + 98 =
2(x^2 + 14x + 49) =
2(x + 7)(x + 7) <==

Answer 2

2(x+7)(x+7)

Explanation:

Greetings,

The first thing to bear in mind:

2x²+28x+98

We need to find two Integer Numbers which product is 2*98=196

and a Sum between those two must be 28

Prime Factorize 196

196 | 2

98 | 2

49 | 7

7 | 7

1

So P(x) = ( 14 ) * (14 ) = 196

And S(x) = ( 14 ) + ( 14 ) = 28

2x²+28x+196x+98

Groupping it:

(2x²+28x)+(196x+98)

x(2x+1)+98(2x+1)

(2x+1)(x+98)

We can make it even simpler since 98=2*7² and we have 1 on the first parenthesis

Therefore,

2(x+7)(x+7) = (2x+1)(x+98) = 2x²+28x+98