10 Questions, factor

• Dec 13th 2006, 09:09 AM
tyl4r
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.
• Dec 13th 2006, 09:34 AM
Soroban
Hello, tyl4r!

Here are a few of them . . .

Quote:

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

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

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

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

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

Quote:

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

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

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

Quote:

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

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

Factor the difference of squares: . $3b(4a^2-7b)(4a^2+7b)$
• Dec 13th 2006, 09:36 AM
ThePerfectHacker
Quote:

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

Factor Completely.

1. x^3 -16x +3x^2-48

$(x^3+3x^2)-(16x+48)$
$x^2(x+3)-16(x+3)$
$(x+3)(x^2-16)$
$(x+3)(x+4)(x-4)$
Quote:

2. 9x^3 - 9
$9(x^3-1)$
$9(x-1)(x^2+x+1)$
Quote:

3. 48a^4b-147b^3
$3b(16a^4-49b^2)$
$3b[(4a^2)^2-(7b)^2]$
$3b(4a^2-7b)(4a^2+7b)$
• Dec 13th 2006, 09:40 AM
ThePerfectHacker
Quote:

Originally Posted by tyl4r
4. Factor the polynomial: X^2 +11xy + 28y^2

$(x+?y)(x+?y)$
The product must be 28
And sum must be 11.
List factors of 28,
1,28
2,14
Thus,
$(x+4y)(x+7y)$
Quote:

5. Factor Completely: x^3 - x^2 - 30x
$x(x^2-x-30)$
$x(x-6)(x+5)$
Quote:

7. 512y^3 - 729
$(8y)^3-9^3$
$(8y-9)(64y^2-72y+81)$
• Dec 13th 2006, 01:05 PM
tyl4r
Anyone know the answers to #8, 9 and 10?
• Dec 13th 2006, 01:53 PM
Quick
Quote:

Originally Posted by tyl4r
Anyone know the answers to #8, 9 and 10?

Do you know the quadratic formula?
• Dec 13th 2006, 02:40 PM
tyl4r
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.
• Dec 13th 2006, 03:08 PM
Quick
Quote:

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 :)