Practice30 Create account

The polynomial $x^{3} + a x^{2} + b x - 6$ is divisible by both $(x - 1)$ and $(x - 2)$ . Find $a + b$ .

Competition practiceAlgebra

A5
B−1
C11
D6

Step-by-Step Solution

f(1) = 1 + a + b − 6 = 0 gives a + b = 5 straight away. (f(2) = 0 then gives a = −6, b = 11.)

Answer: A) 5

Master this topic in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Algebra practice questions

More Algebra practice

If 2^a = 3^b = 6^c, which expression equals c?Find the sum of all solutions of 4^x − 3 · 2^(x + 1) + 8 = 0.Solve [√(x + 5) + √(x − 5)] ÷ [√(x + 5) − √(x − 5)] = 3.How many real numbers x satisfy x² − 5|x| + 6 = 0?The squares of three consecutive positive integers add up to 245. What is the sum of the…