if f(x) = 5x2 – 3x + 4 and g(x) = 2x – 5, what is f(x) • g(x) ?

10x3 + 31x2 – 23x + 20

10x3 + 19x2 – 7x – 20

10x3 – 31x2 + 23x – 20

10x3 – 19x2 – 7x + 20

Question

if f(x) = 5x2 – 3x + 4 and g(x) = 2x – 5, what is f(x) • g(x) ?

 10x3 + 31x2 – 23x + 20

 10x3 + 19x2 – 7x – 20

 10x3 – 31x2 + 23x – 20

 10x3 – 19x2 – 7x + 20

mendicant_bias · Answer

Okay. So this is a function composition kind of problem. Functions are just like numbers in that they can be added, subtracted, multiplied, and divided by for most cases. In this situation, you're multiplying two functions, so you can set them up just like you might set up roots of a quadratic.

$$(5x ^{2}-3x + 4)*(2x-5)$$
From here, just use the distributive property.

mendicant_bias · Answer

$$(5x ^{2}-3x+4)*(2x-5) $$

$$[(5x ^{2})(2x)+(5x ^{2})(-5)] + [(-3x)(2x) + (-3x)(-5)] + [(4)(2x) + (4)(-5)]$$

mendicant_bias · Answer

And from there, simplify. Does this make sense?