Question

Find the values of a and b so that the polynomial x^4 + ax^3 − 3x^2 − 2x +b is exactly divisible by (x-1) as well as (x+2)​

Answer 1

Answer:

Let f(x) = x4 + ax3 − 3x2 + 2x + b be the given polynomial. By factor theorem, (x+1)and (x-1)are the factors of f(x) if f(−1) and f(1) both are equal to zero. Hence, the value of a and b are – 2 and 2 respectively. Concept: Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0.

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