Math, asked by khushi02022010, 6 months ago

Factorise: 2x^2+2x-364​

Answers

Answered by vk8091624
1

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.

Answered by Anonymous
6

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

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