DIVIDING POLYNOMIALS WITH UNKNOWN COEFFICIENS WORKSHEET

Problem 1 :

If y = 1 is a zero of the polynomial

q(y) = 4y³ + ky² - y - 1

then find the value of k.

Solution

Problem 2 :

For what value of m is x³ - 2mx² + 16 is divisible by x + 2.

Solution

Problem 3 :

The polynomials x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6 when divided by x + 1 and x - 2 respectively, leave remainders R₁ and R₂ respectively. Find the value of a in each of the following cases :

i) R₁ = R₂

ii) R₁ + R₂ = 0

iii) 2R₁ + R₂ = 0

Solution

Problem 4 :

When a polynomial

p(x) = x⁴ - 2x³ + 3x² - ax + b

is divisible by x - 1 and x + 1, the remainders are 5 and 19 respectively. Find the remainder when p(x) is divided by x - 2.

Solution

Problem 5 :

If x - 3 and x - 1/3 are both factors of ax² + 5x + b, show that a = b.

Solution