Use factor theorem to factorise the following polynomials completely : (i) 4x3 + 4x2 - 9x - 9 (ii) x3 - 19x - 30 (iii) 2x3 - x2 - 13x - 6

(i) f(x) = 4x3 + 4x2 - 9x - 9 Let x = -1, substituting the value of x in f(x), Since, f(-1) = 0 hence, (x + 1) is a factor of 4x3 + 4x2 - 9x - 9. On dividing, 4x3 + 4x2 - 9x - 9 by (x + 1), we get (4x2 - 9) as quotient and remainder = 0. Hence, 4x3 + 4x2 - 9x - 9 = (x + 1) (2x - 3)(2x + 3). (ii) f(x) = x3 - 19x - 30 Let x = -2, substituting the value of x in f(x), Since, f(-2) = 0 hence, (x + 2) is a factor of x3 - 19x - 30. On dividing, x3 - 19x - 30 by (x + 2), we get x2 - 2x - 15 as quotient and remainder = 0. Hence, x3 - 19x - 30 = (x + 2) (x + 3)(x - 5). (iii) f(x) = 2x3 - x2 - 13x - 6 Substituting x = -2 in 2x3 - x2 - 13x - 6, we get : ⇒ 2(-2)3 - (-2)2 - 13(-2) - 6 ⇒ 2(-8) - 4 + 26 - 6 ⇒ -16 - 4 + 20 ⇒ -20 + 20 ⇒ 0. ∴ x + 2 is a factor of the polynomial 2x3 - x2 - 13x - 6. Dividing, 2x3 - x2 - 13x - 6 by x + 2, we get : ∴ 2x3 - x2 - 13x - 6 = (x + 2)(2x2 - 5x - 3) = (x + 2)(2x2 - 6x + x - 3) = (x + 2)[2x(x - 3) + 1(x - 3)] = (x + 2)(2x + 1)(x - 3). Hence, 2x3 - x2 - 13x - 6 = (x + 2)(2x + 1)(x - 3).

When 3x² - 5x + p is divided by (x - 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x² - 5x + p - 3.

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Prove that (5x + 4) is a factor of 5x³ + 4x² - 5x - 4. Hence, factorise the given polynomial completely.

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If x³ - 2x² + px + q has a factor (x + 2) and leaves a remainder 9 when divided by (x + 1), find the values of p and q. With these values of p and q, factorise the given polynomial completely.

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If (x + 3) and (x - 4) are factors of x³ + ax² - bx + 24, find the values of a and b. With these values of a and b, factorise the given expression.

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Mathematics

Use factor theorem to factorise the following polynomials completely :
(i) 4x³ + 4x² - 9x - 9
(ii) x³ - 19x - 30
(iii) 2x³ - x² - 13x - 6

Factorisation

Related Questions

When 3x² - 5x + p is divided by (x - 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x² - 5x + p - 3.

Prove that (5x + 4) is a factor of 5x³ + 4x² - 5x - 4. Hence, factorise the given polynomial completely.

If x³ - 2x² + px + q has a factor (x + 2) and leaves a remainder 9 when divided by (x + 1), find the values of p and q. With these values of p and q, factorise the given polynomial completely.

If (x + 3) and (x - 4) are factors of x³ + ax² - bx + 24, find the values of a and b. With these values of a and b, factorise the given expression.

Mathematics

Use factor theorem to factorise the following polynomials completely :(i) 4x3 + 4x2 - 9x - 9(ii) x3 - 19x - 30(iii) 2x3 - x2 - 13x - 6

Factorisation

Related Questions

When 3x2 - 5x + p is divided by (x - 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x2 - 5x + p - 3.

Prove that (5x + 4) is a factor of 5x3 + 4x2 - 5x - 4. Hence, factorise the given polynomial completely.

If x3 - 2x2 + px + q has a factor (x + 2) and leaves a remainder 9 when divided by (x + 1), find the values of p and q. With these values of p and q, factorise the given polynomial completely.

If (x + 3) and (x - 4) are factors of x3 + ax2 - bx + 24, find the values of a and b. With these values of a and b, factorise the given expression.

Use factor theorem to factorise the following polynomials completely :
(i) 4x³ + 4x² - 9x - 9
(ii) x³ - 19x - 30
(iii) 2x³ - x² - 13x - 6

When 3x² - 5x + p is divided by (x - 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x² - 5x + p - 3.

Prove that (5x + 4) is a factor of 5x³ + 4x² - 5x - 4. Hence, factorise the given polynomial completely.

If x³ - 2x² + px + q has a factor (x + 2) and leaves a remainder 9 when divided by (x + 1), find the values of p and q. With these values of p and q, factorise the given polynomial completely.

If (x + 3) and (x - 4) are factors of x³ + ax² - bx + 24, find the values of a and b. With these values of a and b, factorise the given expression.