Question

Please help me out!!!!!!! 54 points!

1) Factor the expression.

x^2+4x-5



2) Find the zeros of the quadratic equation by factoring.

x^2+4x-5=0


3) Factor the expression.

x^2+2x-48



4) Find the zeros of the quadratic equation by factoring.

x^2+2x-48=0


5) Factor the expression.

3x^2-14x-24



6) Find the zeros of the quadratic equation by factoring.

3x^2-14x-24=0


7) Factor the expression.

x^2+6x+9

8) Find the zeros of the quadratic equation by factoring.

x^2+6x+9=0


9) Factor the expression.

x^2-25


10) Find the zeros of the quadratic equation by factoring.

x^2-25=0

Answer 1

1. (x+5)(x-1)

6. (3x+4)(x-6)

9. (x+5)(x-5)

Explanation:

To factor an equation, break the polynomial into two binomials which multiply to make it. There are three main ways to factor:

Regular: Find two numbers that multiply to C and add to B from
`ax^2 + bx + c`.

`x^2+4x-5 = (x+5)(x-1)`

Grouping: Find two numbers that multiply to A*C and add to B. Then split B into the two factors and factor by GCF.

`3x^2-14x-24\\3x^2 - 18x + 4x - 24\\(3x^2-18x)+(4x-24)\\3x(x-6)+4(x-6)\\(3x+4)(x-6)`

Difference of Squares: Factor by taking the square root of each term.
`a^2-b^2 = (a-b)(a+b)`

`x^2 - 25 = (x+5)(x-5)`