Question

Use the fuction h(x)=5x-2 and t(x) =4x+6 to complete the fuction operations listed below

Answer 1

Part A
(h + t)(x)
(5x - 2 + 4x + 6)(x)   First plug in the numbers
(9x + 4)(x)   Add h(x) and t(x)
(9x² + 4x)   Then multiply it by x
x(9x + 4)   Lastly, simplify x out (I'm including both answers because I don't know whether your questions will ask for either one)
Unsimplified Answer: 9x² + 4x      Simplified Answer: x(9x + 4)

Part B
(h x t)(x)
(5x - 2)(4x + 6)(x)    First step is to of cource, plug in the numbers
(20x² + 30x -8x -12)(x)   Next we multiply h(x) and t(x)
(20x² + 22x -12)(x)     Simplify it a little
(20x³ + 22x² - 12x)    After that, multiply the whole thing by x
(2x)(10x² + 11x - 6)     Simplify 2x out of the equation
(2x)(5x - 2)(2x + 3)    Lastly, simplify the rest
Unsimplified Answer: (20x³ + 22x² -12x)    Simplified Answer: (2x)(5x - 2)(2x + 3)

Part C
h[t(x)]
(5x - 2) [(4x + 6)(x)]    Plug in the numbers
(5x - 2)(4x² + 6x)       Multiply t(x) and x
(20x³ + 30x² - 8x² -12x)    Multiply that by h(x)
(20x³ + 22x² -12x)     Simplify a little... Wait! That looks like the answer to Part B! Perhaps we did something wrong, let's go back and alter the third step
(5x -2)(2x)(2x + 3)     This time, simplify before multiplying oh wait, that's part B's simplified answer, isn't it.
Well, there's a good explanation for this: Part B and Part C are essentially the same equations, just in slightly different orders!
So, it will have the same answers and Part B! (At least, in theory, I'd recommend checking this for yourself too!)
Unsimplified Answer: (20x³ + 22x² - 12x)   Simplified Answer: (2x)(5x-2)(2x+3)

Well, that's a wrap, Parts A, B, and, C with work and explanations; if you find that I made a mistake or did something wrong let me know. I hope this helped, and good luck!