How do you factor x2 minus 10x plus 24?

Answer 1

x^(2) - 10x + 24

Since the coefficient of 'x^(2)' is '1', ; number not shownl we look at the constant '24'.

Write down all the factors of '24'. They are 1,2,3,4,6,8,12,& 24.

From this list we need to select two numbers that add to '10' and multiply to '24'.

The possibilities of addition ARE 4 + 6, 2+ 8 , & 12 -2.

However, only 4 + 6 = 10 & -4 x -6 = 24 , but -12 X 2 = -24 (Not +24).

So the only pair are '4' & '6'.

Set up factor brackets;)

(x 4)(x 6)

Since ;24; is positive (+) then the signs in the brackets are both the same. They can be either '+' or '-' .

Since the coefficient of 'x' is '-10' , then the signs are negative(-).

So fully factored it is

( x - 4)(x - 6)

Answer 2

what two numbers multiply to 24 and add to -10? -4 and -6 look good, so:

(x - 4)(x - 6)

x = 4 or 6