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! :)
+9466 | 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? 
+9466 | 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?
