1. ## 10 Questions, factor

Hey everyone, just need some help on 10 of these questions.

Factor Completely.

1. x^3 -16x +3x^2-48
2. 9x^3 - 9
3. 48a^4b-147b^3
4. Factor the polynomial: X^2 +11xy + 28y^2
5. Factor Completely: x^3 - x^2 - 30x
6. 15y^2 + 22y + 8
7. 512y^3 - 729
8. Solve: x^2 + 3x - 54 = 0
9. Solve: 2x^2-5x-7=0
10. One leg of a right triangle is 21 inches longer than the smaller leg, and the hypotenuse is 24 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

If you could help it would be greatly appreciated, thanks.

2. Hello, tyl4r!

Here are a few of them . . .

$\displaystyle 1)\;x^3 -16x +3x^2-48$

We have: .$\displaystyle x^3 + 3x^2 - 16x - 48$

Factor "by grouping": . $\displaystyle x^2(x + 3) - 16(x + 3)$

Factor out $\displaystyle (x+3)\!:\;\;(x+3)(x^2-16)$

Factor the difference of squares: .$\displaystyle (x + 3)(x - 4)(x + 4)$

$\displaystyle 2)\;9x^3 - 9$

Factor out $\displaystyle 9\!:\;\;9(x^3 - 1)$

Factor the difference of cubes: .$\displaystyle 9(x - 1)(x^2 + x + 1)$

$\displaystyle 3)\; 48a^4b - 147b^3$

Factor out $\displaystyle 3b\!:\;\;3b(16a^4 - 49b^2)$

Factor the difference of squares: .$\displaystyle 3b(4a^2-7b)(4a^2+7b)$

3. Originally Posted by tyl4r
Hey everyone, just need some help on 10 of these questions.

Factor Completely.

1. x^3 -16x +3x^2-48
$\displaystyle (x^3+3x^2)-(16x+48)$
$\displaystyle x^2(x+3)-16(x+3)$
$\displaystyle (x+3)(x^2-16)$
$\displaystyle (x+3)(x+4)(x-4)$
2. 9x^3 - 9
$\displaystyle 9(x^3-1)$
$\displaystyle 9(x-1)(x^2+x+1)$
3. 48a^4b-147b^3
$\displaystyle 3b(16a^4-49b^2)$
$\displaystyle 3b[(4a^2)^2-(7b)^2]$
$\displaystyle 3b(4a^2-7b)(4a^2+7b)$

4. Originally Posted by tyl4r
4. Factor the polynomial: X^2 +11xy + 28y^2
$\displaystyle (x+?y)(x+?y)$
The product must be 28
And sum must be 11.
List factors of 28,
1,28
2,14
Thus,
$\displaystyle (x+4y)(x+7y)$
5. Factor Completely: x^3 - x^2 - 30x
$\displaystyle x(x^2-x-30)$
$\displaystyle x(x-6)(x+5)$
7. 512y^3 - 729
$\displaystyle (8y)^3-9^3$
$\displaystyle (8y-9)(64y^2-72y+81)$

5. Anyone know the answers to #8, 9 and 10?

6. Originally Posted by tyl4r
Anyone know the answers to #8, 9 and 10?
Do you know the quadratic formula?

7. yes, i did it out but it didnt come out right, i got 15, 36 and 39 for the sides. I need more help with 8 and 9 though.

8. Originally Posted by tyl4r
I need more help with 8 and 9 though.
Look at the excel document in the attachments. Put the numbers into the blue boxes that say "# Here" and you will see the solution along with the work