# Thread: Can you help me factor out these polynomials the complete way

1. ## Can you help me factor out these polynomials the complete way

What I mean by the complete way is this example:
x^2 - 12x + x - 12
x^2 - 12x + x - 12
x (x - 12) - 1(x - 12)
(x - 12) (x + 1)
x^2 - x + 12x - 12
x^2 + 11x - 12

These are the problems that I'm stuck on:

1. 5x^2 - 80
2. x^2 - 100
3. x^3 - 3x^2 + 4x
4. 81x^2 - 1
5. x^2 + 13x - 30

2. ## Re: Can you help me factor out these polynomials the complete way

Originally Posted by AmberxRebecca
What I mean by the complete way is this example:
x^2 - 12x + x - 12
x^2 - 12x + x - 12
x (x - 12) - 1(x - 12)
(x - 12) (x + 1)
x^2 - x + 12x - 12
x^2 + 11x - 12

These are the problems that I'm stuck on:

1. 5x^2 - 80
2. x^2 - 100
3. x^3 - 3x^2 + 4x
4. 81x^2 - 1
5. x^2 + 13x - 30
1. You need to use the Difference of Two Squares: \displaystyle \begin{align*} a^2 - b^2 = (a - b)(a + b) \end{align*}

\displaystyle \begin{align*} 5x^2 - 80 &= 5\left(x^2 - 16\right) \\ &= 5\left(x^2 - 4^2\right) \end{align*}

2. See 1.

3. \displaystyle \begin{align*} x^3 - 3x^2 + 4x &= x\left(x^2 - 3x + 4\right) \end{align*}

Now factorise the Quadratic as you normally would.

4. See 1.

5. The two numbers you are looking for are 15 and -2.