Given f(x)=4x^2+6x and g(x)=2x^2+13x+15, find (f/g)(x). Show your work.

1 answer:

3 0

(f/g)(x)= (4x^2+6x)/(2x^2+13x+15)

first simplify expression and write 13x as a sum to make easier factorization

(4x^2+6x)/(2x^2+10x+3x+15)

then factorize numerator and denominator

(2x(2x+3))/(2x(x+5) + 3(x+5))

rewrite and factor out denominator
(2x(2x+3))/((2x+3)(x+5))

reduce fraction
2x/(x+5)
hope that help you out

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Which of the following is a solution of x2 + 2x + 8?

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A solution of a quadratic equation (ax^2+bx+c) is the point at which the parabola crosses the x-axis. We can find this by using the Quadratic formula, which is $\frac{-b+- \sqrt{b^2-4ac} }{2a}$ . We can solve the equation as follows:

$\frac{-b+- \sqrt{b^2-4ac} }{2a} \\ \frac{-2+- \sqrt{2^2-4(1)(8)} }{2(1)} \\ \frac{-2+- \sqrt{4-32} }{2} \\ \frac{-2+- \sqrt{-28} }{2}$
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