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

(i) f(x) = x3 + 2x2 - 5x - 6 Putting, x = -1 in f(x) Since, f(-1) = 0, hence (x + 1) is factor of f(x) by factor theorem. Now, dividing f(x) by (x + 1), we get x2 + x - 6 as the quotient and remainder = 0. Hence, x3 + 2x2 - 5x - 6 = (x + 1)(x - 2)(x + 3). (ii) Let f(x) = x3 - 13x - 12 Putting, x = 4 in f(x) Since, f(4) = 0, hence (x - 4) is factor of f(x) by factor theorem. Now, dividing f(x) by (x - 4), we get x2 + 4x + 3 as quotient and remainder = 0. Hence, x3 - 13x - 12 = (x - 4)(x + 1)(x + 3). (iii) Given, f(x) = 6x3 + 17x2 + 4x - 12 Substituting x = -2 in f(x), we get : f(-2) = 6(-2)3 + 17(-2)2 + 4(-2) - 12 = 6 × -8 + 17 × 4 - 8 - 12 = -48 + 68 - 8 - 12 = -68 + 68 = 0. Since, f(-2) = 0, hence (x + 2) is factor of f(x). Dividing f(x) by (x + 2), we get : We get 6x2 + 5x - 6 as the quotient and remainder = 0. ∴ 6x3 + 17x2 + 4x - 12 = (x + 2)(6x2 + 5x - 6) = (x + 2)(6x2 + 9x - 4x - 6) = (x + 2)[3x(2x + 3) - 2(2x + 3)] = (x + 2)(2x + 3)(3x - 2) Hence,6x3 + 17x2 + 4x - 12 = (x + 2)(2x + 3)(3x - 2).

Using factor theorem, show that (x - 2) is a factor of x³ + x² - 4x - 4. Hence, factorise the polynomial completely.

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

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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

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

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Mathematics

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

Factorisation

Related Questions

Using factor theorem, show that (x - 2) is a factor of x³ + x² - 4x - 4. Hence, factorise the polynomial completely.

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

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

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

Mathematics

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

Factorisation

Related Questions

Using factor theorem, show that (x - 2) is a factor of x3 + x2 - 4x - 4. Hence, factorise the polynomial completely.

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

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

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

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

Using factor theorem, show that (x - 2) is a factor of x³ + x² - 4x - 4. Hence, factorise the polynomial completely.

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

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

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