1st Question:
Our problem is [tex]-2x^2 - 10x + 100[/tex]
We have a common factor between the three terms, -2. So:
[tex]-2x^2 - 10x + 100[/tex]
[tex]-2(x^2 + 5x -50)[/tex]
We can factor further. What two numbers add up to 5 and multiply to -50? Our answer would be positive 10 and -5. Therefore:
[tex]-2(x^2 + 5x -50)[/tex]
[tex]-2(x +10)(x-5)[/tex]
2nd Question:
The problem is [tex]3x^3 + 9x^2 - 54x[/tex]
Like the first question, we can factor out a constant. In this case, we factor out a 3.
[tex]3x^3 + 9x^2 - 54x[/tex]
[tex]3(x^3 + 3x^2 - 18x)[/tex]
We can also factor out an x.
[tex]3(x^3 + 3x^2 - 18x)[/tex]
[tex]3x(x^2 + 3x - 18)[/tex]
We need to simply further. We can factor the quadratic into (x+6)(x-3).
[tex]3x(x^2 + 3x - 18)[/tex]
[tex]3x(x+6)(x-3)[/tex]
3rd Question:
Our problem is [tex]x^2 +12x + 20[/tex]
We do not have a coefficient, so we should factor the expression straight away. What two numbers add up to 12 and multiply to 20? the numbers 2 and 10. So:
[tex]x^2 +12x + 20[/tex]
[tex](x+2)(x+10)[/tex]
