# Thread: Pre-Calc Questions including division, critical numbers, and Inequalities

1. ## Pre-Calc Questions including division, critical numbers, and Inequalities

Any help is greatly appreciated.

Thanks!

1. Solve the inequality and graph the solution on the real number line.
x3 + 3x2 – 9x27 ≤ 0

2. Find the critical numbers of the expression. (Enter your answers as a comma-separated list.)
3x3 – 32x2

3. Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero f(x) = x3 + x2 + 4x + 4 2i

4. Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) 4, 4i, –4i

5. Use long division to divide. (8x3 + 4x2 + 2x + 5) ÷ (2x2 + 1)

2. Originally Posted by 305boy
Any help is greatly appreciated.

Thanks!

1. Solve the inequality and graph the solution on the real number line.
x3 + 3x2 – 9x27 ≤ 0

start by factoring the left side of the inequality using the grouping method

2. Find the critical numbers of the expression. (Enter your answers as a comma-separated list.)
3x3 – 32x2

set the expression equal to 0 and solve for x

3. Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero f(x) = x3 + x2 + 4x + 4 2i

if 2i is a root, then so is -2i ... the last root will be real. also note that f(x) will factor.

4. Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) 4, 4i, –4i

$\displaystyle \textcolor{blue}{f(x) = (x-r_1)(x-r_2)(x-r_3)}$ where each "r" is a zero

5. Use long division to divide. (8x3 + 4x2 + 2x + 5) ÷ (2x2 + 1)

it's kind of difficult to show long division in this venue

Polynomial Long Division
in future, note that exponents can be designated by the caret symbol, i.e. x "squared" can be written x^2

3. Originally Posted by 305boy
Any help is greatly appreciated.

Thanks!

1. Solve the inequality and graph the solution on the real number line.
x3 + 3x2 – 9x27 ≤ 0

2. Find the critical numbers of the expression. (Enter your answers as a comma-separated list.)
3x3 – 32x2

3. Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero f(x) = x3 + x2 + 4x + 4 2i

4. Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) 4, 4i, –4i

5. Use long division to divide. (8x3 + 4x2 + 2x + 5) ÷ (2x2 + 1)
What is the significance of the red numbers? In any case, what have you tried and what has you stumped?

4. The red are the "important numbers".

I'm assuming he is copying and pasting from an online homework website such as WebAssign or something similar. :P