Use Remainder Theorem to factorise the following polynomials completely : (i) 2x 3 + x 2 - 13x + 6 (ii) 3x 3 + 2x 2 - 19x + 6 (iii) 2x 3 + 3x 2 - 9x - 10 (iv) x 3 + 10x 2 - 37x + 26

(i) Let f(x) = 2x 3 + x 2 - 13x + 6 Putting, x = 2 in f(x) Since, f(2) = 0 , (x - 2) is factor of f(x) by factor theorem. Dividing, f(x) by (x - 2), we get, 2x 2 + 5x - 3 as quotient and remainder = 0. Hence, 2x 3 + x 2 - 13x + 6 = (x - 2)(2x - 1)(x + 3). (ii) Let f(x) = 3x 3 + 2x 2 - 19x + 6 Putting, x = 2 in f(x) Since, f(2) = 0, (x - 2) is factor of f(x) by factor theorem. Dividing, f(x) by (x - 2), we get, 3x 2 + 8x - 3 as quotient and remainder = 0. Hence, 3x 3 + 2x 2 - 19x + 6 = (x - 2)(3x - 1)(x + 3). (iii) Let f(x) = 2x 3 + 3x 2 - 9x - 10 Putting, x = 2 in f(x) Since, f(2) = 0, (x - 2) is factor of f(x) by factor theorem. Dividing, f(x) by (x - 2), we get, 2x 2 + 7x + 5 as quotient and remainder = 0. Hence, 2x 3 + 3x 2 - 9x - 10 = (x - 2)(x + 1)(2x + 5). (iv) Let f(x) = x 3 + 10x 2 - 37x + 26 Putting, x = 1 in f(x) Since, f(1) = 0 , (x - 1) is factor of f(x) by factor theorem. Dividing, f(x) by (x - 1), we get, x 2 + 11x - 26 as quotient and remainder = 0. Hence, x 3 + 10x 2 - 37x + 26 = (x - 1)(x - 2)(x + 13).

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Mathematics

Use Remainder Theorem to factorise the following polynomials completely :
(i) 2x³ + x² - 13x + 6
(ii) 3x³ + 2x² - 19x + 6
(iii) 2x³ + 3x² - 9x - 10
(iv) x³ + 10x² - 37x + 26

Factorisation

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Mathematics

Use Remainder Theorem to factorise the following polynomials completely :
(i) 2x³ + x² - 13x + 6
(ii) 3x³ + 2x² - 19x + 6
(iii) 2x³ + 3x² - 9x - 10
(iv) x³ + 10x² - 37x + 26

Factorisation

Related Questions

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Use factor theorem to factorise the following polynomials completely :
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(ii) x³ - 13x - 12
(iii) 6x³ + 17x² + 4x - 12

If (2x + 1) is a factor of 6x³ + 5x² + ax - 2, find the value of a.

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Mathematics

Use Remainder Theorem to factorise the following polynomials completely :(i) 2x3 + x2 - 13x + 6(ii) 3x3 + 2x2 - 19x + 6(iii) 2x3 + 3x2 - 9x - 10(iv) x3 + 10x2 - 37x + 26

Factorisation

Related Questions

Show that 2x + 7 is a factor of 2x3 + 5x2 - 11x - 14. Hence, factorise the given expression completely, using the factor theorem.

Use factor theorem to factorise the following polynomials completely :(i) x3 + 2x2 - 5x - 6(ii) x3 - 13x - 12(iii) 6x3 + 17x2 + 4x - 12

If (2x + 1) is a factor of 6x3 + 5x2 + ax - 2, find the value of a.

If (3x - 2) is a factor of 3x3 - kx2 + 21x - 10, find the value of k.

Use Remainder Theorem to factorise the following polynomials completely :
(i) 2x³ + x² - 13x + 6
(ii) 3x³ + 2x² - 19x + 6
(iii) 2x³ + 3x² - 9x - 10
(iv) x³ + 10x² - 37x + 26

Show that 2x + 7 is a factor of 2x³ + 5x² - 11x - 14. Hence, factorise the given expression completely, using the factor theorem.

Use factor theorem to factorise the following polynomials completely :
(i) x³ + 2x² - 5x - 6
(ii) x³ - 13x - 12
(iii) 6x³ + 17x² + 4x - 12

If (2x + 1) is a factor of 6x³ + 5x² + ax - 2, find the value of a.

If (3x - 2) is a factor of 3x³ - kx² + 21x - 10, find the value of k.