Question

If (x³ + ax² + bx + 6) has (x – 2) as a factor and leaves a remainder 3 when divided by (x – 3), find the values of a and b.

If x + 2a is a factor of x⁵ – 4a²x³ + 2x + 2a + 3, find a.

One day, the principal of a particular school visited the classroom. Class teacher was teaching the concept of polynomials to students. He was very much impressed by her way of teaching. To check, whether the students also understand the concept taught by her or not, he asked various questions to students. Some of them are given below.

Examine whether x + 2 is a factor of x³ + 3x² + 5x + 6 and of 2x + 4.