Question

Factorise : x² - 21x + 90 .​

Answer 1

(x - 15)(x - 6)

Explanation:

Hi! Our task is to factorize
`\sf{x^2-21x+90}`.

Our first step is to think of two numbers that:

• Multiply to make 90
• Add to make -21

It would be helpful to take a look at the factors of 90. We could get 90 by multiplying the following numbers:

1 * (90) <- We rule that out, because that does not add up to -21, no matter what you do

2 * (45) <- This can also be ruled out

3 * (30) <- And this too

5 * (18) <- this doesn't add up to -21 either

6 * (15) <-

These can only add up to -21 when they're both negative; in that case, they would also multiply to 90.

So far, we have:

(x - ___)(x - ____)

The numbers 15 and 6 go in the blanks.

So, we end up with:

(x - 15)(x - 6)