"Factor the expression". (....what?)?

Question

x² - 11x + 30

d² + 2d - 15

n² - 64

2x² + 7x - 15

5x² - 45

12x² - 21x + 3

..help? ^^

Answer 1

Okay,here they are:

x² - 11x + 30 = (x-6)(x-5)

d² + 2d - 15 = (d-3)(d+5)

n² - 64 = (n+8) (n-8)

2x² + 7x - 15 =  (x+10) (2x-3)

5x² - 45 = I have no clue

12x² - 21x + 3 = No clue, I forgot.

Answer 2

x² - 11x + 30 = (x-5)(x-6)

d² + 2d - 15 = (d+5)(d-3)

n² - 64 = (n+8)(n-8)

Sorry dude i don't remember my algebra for those last 3 questions that's all i can do

Answer 3

Here are the answers and explanations to each of the factored solutions.

Keep in mind the ax²+bx+c formula.

x² - 11x + 30

Factors: (x - 5) and (x - 6)

I used the product-sum factorization method for this expression. The product of (-5) and (-6) is 30, and the sum of (-5) and (-6) is (-11).

d² + 2d - 15

Factors: (d + 5) and (d - 3)

I used the product-sum factorization method for this expression. The product of (5) and (-3) is (-15), and the sum of (5) and (-3) is (2).

n² - 64

Factors: (n + 8) and (n - 8)

I used the difference of two squares (DOTS) method for this expression. The square root of n² is n, and the square root of 64 is (8) and (8) as well as (-8) and (-8). The product of (8) and (-8) is (-64).

2x² + 7x - 15

Factors: (x + 5) and (2x - 3)

I used the method where in the trinomial the "a" value is NOT equal to one (because it's 2x² ). Therefore, I had to take the (2) in (2x²) and multiply it by (-15) to get (-30). My new trinomial/expression is:

x² + 7x - 30

Now I use the product-sum method to factor this new trinomial. The product of (10) and (-3) is (-30) and the sum of (10) and (-3) is (7). Therefore, the factors of x² + 7x - 30 are (x + 10) and (x - 3). However, we still have another step to do. We have to replace the (2) we originally took out back into the factors.

(2x + 10) and (2x - 3). Then divide out any GCFs (greatest common factors). (2x + 10) can be divided by the GCF of 2. That's how you get your final factors of (x + 5) and (2x - 3).

5x² - 45

Factors: 5(x² - 9)

I used the GCF method in order to factor this expression. The GCF is 5. Therefore, just divide 5x² - 45 by 5. That's how you get your final answer.

12x² - 21x + 3

Factors: 3(4x²  - 7x + 1)

I used the GCF method in order to factor this expression. The GCF is 3. When you divide12x² - 21x + 3 by 3 your final factored answer is 3(4x²  - 7x + 1).

This site might be helpful if you want to learn more:

http://www.scribd.com/doc/3215424/Algebr...

If you do not understand something, please feel free to email me and get it clarified.

Answer 4

x²-11x+30

= (x-6)(x-5)

d²+2d-15

= (d-3)(d+5)

n²-64

= (n-8)(n+8)

2x²+7x-15

= (2x-3)(x+5)

5x²-45

= 5(x-3)(x+3)

12x²-21x+3

= 3(4x²-7x+1)

Answer 5

x² - 11x + 30 = (x-5)(x-6)

d² + 2d - 15 = (d+5)(d-3)

n² - 64 = (n+8)(n-8)

2x² + 7x - 15 = ( x+5)(2x-3)

5x² - 45 = 5(x+3)(x-3)

12x² - 21x + 3 = 3 (4x² - 7x +1)

Answer 6

x² - 11x + 30

first of all how did you get the superscript for the squared.

TIP

Think of two numbers that:

*when multiplied will equal 30; and

*when added will equal 11

-5 and -6

(x -6) (x -5)

Just in case you don't understand how to work it out

(1) multiply the first item within the parenthesis by each item in the other set of parenthesis

     ex.  (x)(x) = x²

     and (x)(-5) = -5x

     giving you x² -5x

(2) multiply the second item within the parenthesis by each item in the other set of parenthesis

     ex. (-6)(x) = -6x

     and (-6)(-5) = 30

     giving you -6x +30

Now combine the two results

x²  -5x-6x +30.  Simplify this to get

x² -11x +30

PERFECT SQUARES

When it comes to n² - 64.

Looking at it, you can see the "n" is obviously squared. You should know the 64 is squared. 8 x 8 = 64

When you have two squared items with a minus sign, it is called a perfect square.

all you have to do is take the root of each to create the factors and place a minus sign in one and an addition sign in the other.

x² => root is x

64 => root is 8

(x-8)(8+8)  = x²-64