Factorisation Test - 1

If x² - 7x + 11 is divided by 3x - 2, what is the remainder?

When the polynomial x³ + 3x² – 6ax – 5 is divided by (x – 1), the remainder is P and when the polynomial x³ + ax² – 15x + 20 is divided by (x + 2), the remainder is Q. Find the value of 'a' if 2P + Q = 0.

If x² - (a + 1) x + 56 is divisible by x - 7, what is the value of a?

Find the remainder when polynomial 7x³ + 2x² - 2x + 5 is divided by (x - 1).

What is the remainder obtained when y³ + 4y² - 3y + 10 is divided by y + 4?

If polynomial P(x) = x² + (3a + 2) x + 60 is perfectly divisible by (x + a), find the value of 'a'.

Which of the following is divisible by x - 3?

If the coefficients of a cubic polynomial are rational, which of the following is true?
(A) All zeroes are rational.                     
(B) Two zeroes are irrational that are conjugate of each other.
(C) All zeroes are irrational.                   
(D) One zero is rational and two are irrational.

Using the remainder theorem factorize completely the following polynomial.
5x³ + 3x² - 25x - 2

If 3x - 5 is a factor of quadratic polynomial 3x² + 5x - a, find the value of a.

Find p(x), if it is obtained by the product of (x - 2) and (x² + 8x + 12).

If k x + 1 is a factor of 2x³ - x² - 5x - 2, find the value of k.

If the remainder of a cubic polynomial on dividing by (2x - 3) is 18 and quotient is x2 - 16x + 48, find the polynomial.

Using factor theorem, factorise x³ + 4x² + 3x - 2 completely.