Solution of Cubic Polynomial Using Factor Theorem MHF4U

Test Remainder Theorem:
Q1. f(x)=2x^3-7x^2-17x+10
Use factor theorem and division to factorise f(x) completely.

Q2. g(x)=4x^3-8x^2-35x+75
Use factor theorem to show that (x + 3) is a factor of g(x)
Hence show that g(x) can be written in the form of
g(x) = (x + 3)(ax + b)2, where a and b are the constants to be found

 
Q3. f(x)=x^3+6x^2+px+q
Given that f(4) = 0 and f(-5) = 36
Find value of p and q
Factorise f(x) completely.

 
Q4. f(x)=〖2x〗^3-x^2-13x+14
Use factor theorem to show that (x – 2) is a factor of f(x)
Solve f(x) = 0 giving answer to two decimal places.


 
Q5. f(x)=x^3+kx-2
Given that (x – 2) is a factor of f(x) find the value of k
Solve the equation f(x) = 0

 
Q6. f(x)=x^3+6x^2+4x-15
Use factor theorem to show x = -3 is the solution to f(x)=0
Find other solutions, giving answer to two decimal places.

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