If x 3 - 2x 2 + 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.

By factor theorem (x - b) is a factor of f(x), if f(b) = 0. f(x) = x 3 - 2x 2 + px + q Given, (x + 2) or (x - (-2)) is a factor of f(x). ∴ f(-2) = 0 By remainder theorem, on dividing f(x) by (x - a), the remainder left is f(a). ∴ On dividing f(x) by (x + 1) or (x - (-1)), Remainder = f(-1) Given, Remainder = 9 ∴ f(-1) = 9 Putting value of q = 2p + 16 from equation 1, Now putting p = -4 and q = 8 in f(x), f(x) = x 3 - 2x 2 - 4x + 8 Since, (x + 2) is a factor of f(x), on dividing f(x) by (x + 2), we get x 2 - 4x + 4 as quotient and remainder = 0. Hence, value of p = -4 and q = 8; x 3 - 2x 2 - 4x + 8 = (x + 2) (x - 2) 2 .

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

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

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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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If (2x + 1) is a factor of both the expressions 2x² - 5x + p and 2x² + 5x + q, find the values of p and q. Hence, find the other factors of both the polynomials.

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Mathematics

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.

Factorisation

Related Questions

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

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

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.

If (2x + 1) is a factor of both the expressions 2x² - 5x + p and 2x² + 5x + q, find the values of p and q. Hence, find the other factors of both the polynomials.

Mathematics

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.

Factorisation

Related Questions

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

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

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.

If (2x + 1) is a factor of both the expressions 2x2 - 5x + p and 2x2 + 5x + q, find the values of p and q. Hence, find the other factors of both the polynomials.

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.

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

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

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.

If (2x + 1) is a factor of both the expressions 2x² - 5x + p and 2x² + 5x + q, find the values of p and q. Hence, find the other factors of both the polynomials.