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If h(x) = f(x)g(x) and f(x) = 2x +5, determine g(x).

 

I'm given h(x) = 10x\({^2}\) + 13x -30.

 

I did \({10x^2 + 13x - 30 \over 2x + 5}\) to isolate for g(x), but I tried factoring the numerator and it doesn't seem factorable?

 

How should I get the textbook answer of g(x) = 5x - 6?

 

Thank you! :)

 Jun 12, 2019

Best Answer 

 #1
avatar+8848 
+2
To factor   10x2 + 13x - 30 , 
let's split  13x  into two terms such that the product of their coefficients  =  (10)(-30)  =  -300

 

 

What two numbers add to  13  and multiply to  -300  ?     +25  and  -12 
So we can split the middle term like this:

 

 

10x2 + 13x - 30

 

=  10x2 + 25x - 12x  - 30

                                             Factor  5x  out of the first two terms.

=  5x(2x + 5) - 12x - 30

                                             Factor  -6  out of the last two terms.

=  5x(2x + 5) - 6(2x + 5)

                                             Factor  (2x + 5)  out of both remaining terms.

=  (2x + 5)(5x - 6)

 

Does that help answer your question? smiley

 Jun 12, 2019
 #1
avatar+8848 
+2
Best Answer
To factor   10x2 + 13x - 30 , 
let's split  13x  into two terms such that the product of their coefficients  =  (10)(-30)  =  -300

 

 

What two numbers add to  13  and multiply to  -300  ?     +25  and  -12 
So we can split the middle term like this:

 

 

10x2 + 13x - 30

 

=  10x2 + 25x - 12x  - 30

                                             Factor  5x  out of the first two terms.

=  5x(2x + 5) - 12x - 30

                                             Factor  -6  out of the last two terms.

=  5x(2x + 5) - 6(2x + 5)

                                             Factor  (2x + 5)  out of both remaining terms.

=  (2x + 5)(5x - 6)

 

Does that help answer your question? smiley

hectictar Jun 12, 2019
 #2
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+1

Ah yes! Thank you!

Guest Jun 12, 2019

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