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

By remainder theorem, on dividing f(x) by (x - b), remainder = f(b) ∴ On dividing, f(x) = ax 3 + 3x 2 - 9 by (x + 3) or (x - (-3)) Remainder = f(-3) = a(-3) 3 + 3(-3) 2 - 9 = -27a + 27 - 9 = 18 - 27a ∴ On dividing, f(x) = f(-3) = 2x 3 + 4x + a by (x + 3) or (x - (-3)) Remainder = 2(-3) 3 + 4(-3) + a = -54 - 12 + a = a - 66 According to question, Hence, the value of p is 3.

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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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'.

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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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Using the remainder theorem, find the remainders obtained when x³ + (kx + 8)x + k is divided by x + 1 and x - 2. Hence, find k if the sum of two remainders is 1.

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Mathematics

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

Factorisation

Related Questions

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

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'.

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.

Using the remainder theorem, find the remainders obtained when x³ + (kx + 8)x + k is divided by x + 1 and x - 2. Hence, find k if the sum of two remainders is 1.

Mathematics

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

Factorisation

Related Questions

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

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'.

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.

Using the remainder theorem, find the remainders obtained when x3 + (kx + 8)x + k is divided by x + 1 and x - 2. Hence, find k if the sum of two remainders is 1.

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

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

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'.

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.

Using the remainder theorem, find the remainders obtained when x³ + (kx + 8)x + k is divided by x + 1 and x - 2. Hence, find k if the sum of two remainders is 1.