Question

Can someone help me with these algebraic expressions? And can you please EXPLAIN OR SHOW YOUR WORK!

Answer 1

Answer:

1.  (3x - 2)(x + 5).

2. 2(x + 4)(x - 2).

3. (2x - 9)(2x + 9).

Step-by-step explanation:

1. f(x) = 3x^2 +13x -10

Try to factor by the ac method:

3 * -10 = -30

We need 2 numbers whose product is -30 and whose sum is + 13.

They are -2 and +15, so we write:

3x^2 + 15x - 2x - 10       Factor by grouping:

= 3x(x + 5) - 2(x + 5)

= (3x - 2)(x + 5).

2.  f(x) = 2x^2+4x-16

= 2(x^2 + 2x - 8)

Now we need 2 numbers whose product is -8 and whose sum is + 2.

They are +4 and -2. So:

= 2(x + 4)(x - 2).

3. 4x^2 - 81    This is the difference of 2 squares so the factors are:

(2x - 9)(2x + 9).