Factor completely if the polynomial is not factorable write prime also state the methods used to factor the polynomial.

1. x^2-12x+36

2. r^3-81r

3. 35x^3y^4-60x^4y

4. 6mn+18m+n+3

5. 8c^3-g^3

6. (12az - 6bz - 6cz) + (10ax-5bx-5cx)

For question 1

x²-12x+36

An easy and efficient way to remember how to factor is to see the different parts of the polynomial.

If the last number (in this case 36) has the multiples which add up to the middle number (12), then the polynomial is factorable. 36 has the multiples (6,6) which add up to 12.

Now check the symbols, if the symbol before the last number is a +, that means the two factors have the same symbol. Now see the symbol before the middle number. If its a negative, the factors would be minus as well.

x²-12x+36

(x) (x)

(x-) (x-) Same symbol as (-) 12x

(x-6) (x-6) Multiples of the last number (36)

x²-12x+36 = (x-6) (x-6)