Question

Juanita begins to factor an expression as shown. x2 + 3x – 18 = (x + )(x – ) The numbers that should be placed in the boxes, from left to right, are .

Answer 1

The question is asking us to factor the expression :

$x^{2}+3x-18.$

To factor the expression we need to split the middle term +3x in two terms.For that we need to find two numbers such that the numbers on addition will give us the middle term that is 3 and the same numbers on multiplication should give us -18.We look at the factors of -18 .+6 and -3 are the two numbers .+6-3=+3 and +6x3=-18.

Splitting the middle term 3x = +6x-3x we have:

$x^{2}+3x-18=x^{2}+6x-3x-18.$

Taking common factors of the two pairs we have:

=x(x+6)-3(x+6) =(x+6)(x-3).

The numbers that should be placed in the boxes, from left to right, are +6 and -3.