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.

Question

CASE_STUDIESTypes of Polynomials Based on DegreeFactor Theorem for Polynomials4 sub-questions

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

Classify the following as linear, quadratic and cubic polynomials:

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

TextFactor Theorem for Polynomials

Find the value of k, if x – 1 is a factor of 4x³ + 3x² – 4x + k.

Factorise 6x² + 17x + 5 by splitting the middle term, and by using the Factor Theorem.

Determine which of the following polynomials has (x + 1) a factor: