Question

Use the Distributive Property to write each expression in factored form. DO NOT determine the answer.

11) 6x2+ 6x3
12) -6x 2 + (-6) x3
13) 5x - 8x

Answer 1

11) 6x^2+ 6x^3 = 6.x.x+6.x.x.x

12) -6x^2 + (-6) x^3 = -6.x.x + (-6).x.x.x

13) 5x - 8x = 5.x -8.x

Explanation:

Let us solve the question one by one.

11) 6x^2+ 6x^3

In order to convert the polynomial in the factored form, we see which factors are common in all terms in the polynomial.

`6x^2 = 6.x.x\\6x^3 =6.x.x.x`

The factored form is:

`= 6.x.x+6.x.x.x`

12) -6x^2 + (-6) x^3

Similarly, as 11

`-6x 2 =-6.x.x\\-6x^3=-6.x.x.x`

The factored form is:

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

13) 5x - 8x

We can clearly see that there is only one common factor in both terms which is x

`5x = 5.x\\8x = 8.x`

The factored form is:

`=5.x-8.x`

Hence,

11) 6x^2+ 6x^3 = 6.x.x+6.x.x.x

12) -6x^2 + (-6) x^3 = -6.x.x + (-6).x.x.x

13) 5x - 8x = 5.x -8.x