MHF 4U Advanced Functions Grade 12
POLYNOMIAL EQUATIONS
TEST 10
Knowledge
1. Divide 6x5 + x + 11 – 9x3 – 11x2 + 2x4 by 2x2 – 3. State any
restrictions. [ /2]
2. Solve the equation: x3(3x + 5)2(x2 – 2x – 4) = 0. [ /3]
3. Solve the inequality: f(x) ≥ g(x) [ /2]
Application
1. Solve the following inequality graphically: 6x2 – 12 > x
[ /3]
2. Solve the inequality: 5(x – 4)3 (2 + x) 4 (x + 1) < 0 [ /3]
3. Factor fully: x4 + x3 + x2 – x – 2
[ /3]
4. Solve the inequality: 2x3 – 8x > 8 – 2x2. [
/4]
5. Find a simplified equation of a family of polynomial functions of 5th
𝟒
degree with roots 1, – 6, ± 𝟑√𝟓 and − , for which y → +∞ as x → −∞.
𝟕
[ /4]
Problem Solving
1. A solid is made of three cubes, each having a side length of x cm,
where x is an integer. Let A cm2 be the surface area and V cm3 be the
volume of the solid. If A = V + 32, find the value of x. [ /4]
2. If –1 is the root of the equation –x2 – c2x = 8c + x – 7, find the value(s)
of c. [ /3]
Communication
1. Chris says that the solution of the equation x3 = 9x is x = 3. Kate tells
him that he is not quite correct. Explain in details why Kate thinks so,
and show all necessary work. [ /2]
2. Fill in the blanks: [ /2]
a) If x2 – x – 6 is a factor of P(x), then P (–2) = ___ and P (3) = ___.
b) If two functions belong to the same family of polynomial functions,
then their graphs are _____________________________________.