How to factor these

Question

1. -63p^3-72p^2-90
2. b^2-7b+6
3. v^3+11+28
4. 4n^2-1
5. 9n^2-30n+25

Answer 1

-63p^3-72p^2-90

Identify the greatest common factor of the coefficients (-63, -72 and -90)

Determine what the GCF needs to be multiplied by to obtain each term in the expression.

Write the factored expression as the product of the GCF and the sum of the terms we need to multiply by.

b^2-7b+6

This is a trinomial of the form ax^2 + bx + c.

To factor, find two integers x and y whose product is 6 and whose sum is -7

Factoring will be (b+x)(b+y)

v^3+11+28

This trinomial is already prime.

4n^2-1

This polynomial is the difference of two square (2n squared - 1 squared).

The difference of two squares a^2 - b^2 is factored as (a+b)(a-b)

9n^2-30n+25

This polynomial is a perfect square (a^2 - 2ab + b^2, where a = 3, b = 5)

A perfect square factors as (a-b)^2