Factorization – ICSE Solutions for Class 10 Mathematics

Formulae

1. Factor Theorem: If f(x) is a polynomial and a is a real number, then (x – a) is a factor of f(x) if f(α) = 0.

2. Remainder Theorem: If a polynomial f(x) is divided by (x – a), then remainder =f(x).

Determine the Following

Question 1. Use remainder theorem and find the remainder when the polynomial g(x) = x3 + x2 – 2x + 1 is divided by x – 3.

Question 2. (i) When x3 + 3x2 – kx + 4 is divided by (x – 2), the remainder is k. Find the value of k.

Question 11. In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:

Question 12. In the following two polynomials, find the value of ‘a’ if x – a is a factor of each of the two:

Question 15. In the following problems use the factor theorem to find if g(x) is a factor of p(x):

Question 16. If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:

Question 17. Find the value of the constant a and b, if (x – 2) and (x + 3) are both factors of

Question 19. If x – 2 is a factor of

Prove the Following

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