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# Finding g(x)

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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

#1
+8207
+1
 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)

Jun 12, 2019

#1
+8207
+1
 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)