Q.Factorize by splitting the middle term. @. 2x²+11x+14
Answers
Step-by-step explanation:
The first term is, 2x2 its coefficient is 2 .
The middle term is, -11x its coefficient is -11 .
The last term, "the constant", is +14
Step-1 : Multiply the coefficient of the first term by the constant 2 • 14 = 28
Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is -11 .
-28 + -1 = -29
-14 + -2 = -16
-7 + -4 = -11 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -4
2x2 - 7x - 4x - 14
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-7)
Add up the last 2 terms, pulling out common factors :
2 • (2x-7)
Step-5 : Add up the four terms of step 4 :
(x-2) • (2x-7)
Which is the desired factorization
Step-by-step explanation:
2x²+11x+14=0
2x²+2x+7x+14=0
2x(x+2)+7(x+2)=0
(2x+7)(x+2)=0
2x+7=0. x+2=0
2x=-7. x=-2
x=-7/2