Question

Write the expression 5x(x+9) -7(x+9) in complete factored form.​

Answer 1

5x^2 + 45 - 7x - 63 which simplifies to 5x^2 -7x -18?

Answer 2

Answer:

(5x-7)(x-9)

Step-by-step explanation:

Factoring is the inverse of the distributive property. This means that we want to find the factors, not the product.

Partial Factoring

The expression we are given has already been factored to an extent. Both terms are split into 2 different factors. This was done by factoring out the greatest common factor (GCF) from both terms. In the first term, the GCF was 5x, and in the second, the GCF was -7.

Complete Factoring

Even though it was partially factored, we can factor it more. When given the situation:

• a(x + y) - b(x + y)

The expression can be factored into:

• (a - b)(x + y)

You can add (subtract in this case because 7 is negative) the values from outside the parentheses together. This term can then be multiplied by the value within the parentheses.

Thus, 5x(x+9) -7(x+9) can be factored into:

• (5x-7)(x-9)

Remember this trick only works when both terms share a factor like (x-9).