document.write( "Question 899496: i am working on this question and i need some help on it..\r
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\n" ); document.write( "\n" ); document.write( "Which of the following is the product of (-2x + 5)(3x - 9)?\r
\n" ); document.write( "\n" ); document.write( "a. 6x2 - 3x – 45
\n" ); document.write( "b.-6x2 - 33x + 45
\n" ); document.write( "c.-6x2 - 3x + 45
\n" ); document.write( "d.-6x2 + 33x - 45-i picked\r
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Algebra.Com's Answer #545449 by richwmiller(17219) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

$\"-6%2Ax%5E2%2B33%2Ax-45\"$ Start with the given expression.

$\"-3%282x%5E2-11x%2B15%29\"$ Factor out the GCF $\"-3\"$ .

Now let's try to factor the inner expression $\"2x%5E2-11x%2B15\"$

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Looking at the expression $\"2x%5E2-11x%2B15\"$ , we can see that the first coefficient is $\"2\"$ , the second coefficient is $\"-11\"$ , and the last term is $\"15\"$ .

Now multiply the first coefficient $\"2\"$ by the last term $\"15\"$ to get $\"%282%29%2815%29=30\"$ .

Now the question is: what two whole numbers multiply to $\"30\"$ (the previous product) and add to the second coefficient $\"-11\"$ ?

To find these two numbers, we need to list all of the factors of $\"30\"$ (the previous product).

Factors of $\"30\"$ :

1,2,3,5,6,10,15,30

-1,-2,-3,-5,-6,-10,-15,-30

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to $\"30\"$ .

1*30 = 30
2*15 = 30
3*10 = 30
5*6 = 30
(-1)*(-30) = 30
(-2)*(-15) = 30
(-3)*(-10) = 30
(-5)*(-6) = 30

Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"-11\"$ :

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First Number	Second Number	Sum
1	30	1+30=31
2	15	2+15=17
3	10	3+10=13
5	6	5+6=11
-1	-30	-1+(-30)=-31
-2	-15	-2+(-15)=-17
-3	-10	-3+(-10)=-13
-5	-6	-5+(-6)=-11

From the table, we can see that the two numbers $\"-5\"$ and $\"-6\"$ add to $\"-11\"$ (the middle coefficient).

So the two numbers $\"-5\"$ and $\"-6\"$ both multiply to $\"30\"$ and add to $\"-11\"$

Now replace the middle term $\"-11x\"$ with $\"-5x-6x\"$ . Remember, $\"-5\"$ and $\"-6\"$ add to $\"-11\"$ . So this shows us that $\"-5x-6x=-11x\"$ .

$\"2x%5E2%2Bhighlight%28-5x-6x%29%2B15\"$ Replace the second term $\"-11x\"$ with $\"-5x-6x\"$ .

$\"%282x%5E2-5x%29%2B%28-6x%2B15%29\"$ Group the terms into two pairs.

$\"x%282x-5%29%2B%28-6x%2B15%29\"$ Factor out the GCF $\"x\"$ from the first group.

$\"x%282x-5%29-3%282x-5%29\"$ Factor out $\"3\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

$\"%28x-3%29%282x-5%29\"$ Combine like terms. Or factor out the common term $\"2x-5\"$

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So $\"-3%282x%5E2-11x%2B15%29\"$ then factors further to $\"-3%28x-3%29%282x-5%29\"$

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Answer:

So $\"-6%2Ax%5E2%2B33%2Ax-45\"$ completely factors to $\"-3%28x-3%29%282x-5%29\"$ .

In other words, $\"-6%2Ax%5E2%2B33%2Ax-45=-3%28x-3%29%282x-5%29\"$ .

Note: you can check the answer by expanding $\"-3%28x-3%29%282x-5%29\"$ to get $\"-6%2Ax%5E2%2B33%2Ax-45\"$ or by graphing the original expression and the answer (the two graphs should be identical).

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