Question

factorise this:- -a square+2a+35​

Answer 1

Answer:

Factoring a2-2a-35

The first term is, a2 its coefficient is 1 .

The middle term is, -2a its coefficient is -2 .

The last term, "the constant", is -35

Step-1 : Multiply the coefficient of the first term by the constant 1 • -35 = -35

Step-2 : Find two factors of -35 whose sum equals the coefficient of the middle term, which is -2 .

-35 + 1 = -34

-7 + 5 = -2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 5

a2 - 7a + 5a - 35

Step-4 : Add up the first 2 terms, pulling out like factors :

a • (a-7)

Add up the last 2 terms, pulling out common factors :

5 • (a-7)

Step-5 : Add up the four terms of step 4 :

(a+5) • (a-7)

Which is the desired factorization

Equation at the end of step

1

:

(a + 5) • (a - 7) = 0

STEP

2

:

Theory - Roots of a product

2.1 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.