When divided by x - 3 the polynomials x 3 - px 2 + x + 6 and 2x 3 - x 2 - (p + 3)x - 6 leave the same remainder . Find the value of 'p'.

By remainder theorem, on dividing f(x) by (x - b), remainder = f(b) ∴ On dividing, f(x) = x 3 - px 2 + x + 6 by (x - 3) Remainder = 3 3 - p(3 2 ) + 3 + 6 = 27 - 9p + 9 = 36 - 9p. ∴ On dividing, f(x) = 2x 3 - x 2 - (p + 3)x - 6 by (x - 3) Remainder = 2(3) 3 - 3 2 - (p + 3)(3) - 6 = 2(27) - 9 - 3p - 9 - 6 = 54 - 9 - 3p - 9 - 6 = 30 - 3p According to question, Hence, the value of p is 1.

What number must be subtracted from 2x² - 5x so that resulting polynomial leaves remainder 2 when divided by 2x + 1 ?

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What number must be added to 2x³ - 3x² - 8x so that resulting polynomial leaves the remainder 10 when divided by 2x + 1?

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Find 'a' if the two polynomials ax³ + 3x² - 9 and 2x³ + 4x + a, leaves the same remainder when divided by x + 3.

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The polynomials ax³ + 3x² - 3 and 2x³ - 5x + a when divided by x - 4 leave the remainder r₁ and r₂ respectively. If 2r₁ = r₂, then find the value of a.

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Mathematics

When divided by x - 3 the polynomials x³ - px² + x + 6 and 2x³ - x² - (p + 3)x - 6 leave the same remainder . Find the value of 'p'.

Factorisation

Related Questions

What number must be subtracted from 2x² - 5x so that resulting polynomial leaves remainder 2 when divided by 2x + 1 ?

What number must be added to 2x³ - 3x² - 8x so that resulting polynomial leaves the remainder 10 when divided by 2x + 1?

Find 'a' if the two polynomials ax³ + 3x² - 9 and 2x³ + 4x + a, leaves the same remainder when divided by x + 3.

The polynomials ax³ + 3x² - 3 and 2x³ - 5x + a when divided by x - 4 leave the remainder r₁ and r₂ respectively. If 2r₁ = r₂, then find the value of a.

Mathematics

When divided by x - 3 the polynomials x3 - px2 + x + 6 and 2x3 - x2 - (p + 3)x - 6 leave the same remainder . Find the value of 'p'.

Factorisation

Related Questions

What number must be subtracted from 2x2 - 5x so that resulting polynomial leaves remainder 2 when divided by 2x + 1 ?

What number must be added to 2x3 - 3x2 - 8x so that resulting polynomial leaves the remainder 10 when divided by 2x + 1?

Find 'a' if the two polynomials ax3 + 3x2 - 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.

The polynomials ax3 + 3x2 - 3 and 2x3 - 5x + a when divided by x - 4 leave the remainder r1 and r2 respectively. If 2r1 = r2, then find the value of a.

When divided by x - 3 the polynomials x³ - px² + x + 6 and 2x³ - x² - (p + 3)x - 6 leave the same remainder . Find the value of 'p'.

What number must be subtracted from 2x² - 5x so that resulting polynomial leaves remainder 2 when divided by 2x + 1 ?

What number must be added to 2x³ - 3x² - 8x so that resulting polynomial leaves the remainder 10 when divided by 2x + 1?

Find 'a' if the two polynomials ax³ + 3x² - 9 and 2x³ + 4x + a, leaves the same remainder when divided by x + 3.

The polynomials ax³ + 3x² - 3 and 2x³ - 5x + a when divided by x - 4 leave the remainder r₁ and r₂ respectively. If 2r₁ = r₂, then find the value of a.