Factorise: 2x^2+2x-364
Answers
Answer:
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
STEP
1
:
Equation at the end of step 1
(2x2 + 2x) - 364 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
2x2 + 2x - 364 = 2 • (x2 + x - 182)
Trying to factor by splitting the middle term
3.2 Factoring x2 + x - 182
The first term is, x2 its coefficient is 1 .
The middle term is, +x its coefficient is 1 .
The last term, "the constant", is -182
Step-1 : Multiply the coefficient of the first term by the constant 1 • -182 = -182
Step-2 : Find two factors of -182 whose sum equals the coefficient of the middle term, which is 1 .
-182 + 1 = -181
-91 + 2 = -89
-26 + 7 = -19
-14 + 13 = -1
-13 + 14 = 1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -13 and 14
x2 - 13x + 14x - 182
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-13)
Add up the last 2 terms, pulling out common factors :
14 • (x-13)
Step-5 : Add up the four terms of step 4 :
(x+14) • (x-13)
Which is the desired factorization
Equation at the end of step
3
:
2 • (x + 14) • (x - 13) = 0
STEP
4
:
Theory - Roots of a product
4.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
2x2+2x-364=0
Taking 2 as a common factor we get,
x2+x-182=0
x2 – 13x + 14x – 182=0
x(x-13) + 14(x-13)=0
(x+14) (x-13)=0
(x+14) (x-13) are the factors of equation 2x2+2x-364=0