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 the two remainders is 1.
Factorisation
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Using the Remainder Theorem, find the remainders obtained when x^3 + (kx + 8)x + k is divided by x + 1 and x − 2. Hence find k if the sum of the two remainders is 1

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By remainder theorem, If f(x) is divided by (x - a), then remainder = f(a). Let f(x) = x3 + (kx + 8)x + k = x3 + kx2 + 8x + k Given, Divisor : ⇒ x + 1 = 0 ⇒ x = -1 On dividing x3 + kx2 + 8x + k by x + 1, we get : ⇒ f(-1) = (-1)3 + k(-1)2 + 8(-1) + k = -1 + k - 8 + k = 2k - 9. Divisor : ⇒ x - 2 = 0 ⇒ x = 2. On dividing x3 + kx2 + 8x + k by x - 2, we get : ⇒ f(2) = (2)3 + k(2)2 + 8(2) + k = 8 + 4k + 16 + k = 5k + 24 Given, Sum of two remainders is 1. ⇒ 2k - 9 + 5k + 24 = 1 ⇒ 7k + 15 = 1 ⇒ 7k = 1 - 15 ⇒ k = ⇒ k = -2. Hence, the value of k = -2.

Mathematics

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 the two remainders is 1.

Factorisation

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Mathematics

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 the two remainders is 1.

Factorisation

Related Questions

Find a if the two polynomials ax3 + 3x2 - 9 and 2x3 + 4x + a leave the same remainder when divided by (x + 3).

If (2x3 + ax2 + bx - 2) when divided by (2x - 3) and (x + 3) leaves remainders 7 and -20 respectively, find values of a and b.

Using factor theorem, show that:(x - 3) is a factor of (x3 + x2 - 17x + 15).

Using factor theorem, show that:(x + 1) is a factor of (x3 + 4x2 + 5x + 2).

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 the two remainders is 1.

Find a if the two polynomials ax³ + 3x² - 9 and 2x³ + 4x + a leave the same remainder when divided by (x + 3).

If (2x³ + ax² + bx - 2) when divided by (2x - 3) and (x + 3) leaves remainders 7 and -20 respectively, find values of a and b.

Using factor theorem, show that:
(x - 3) is a factor of (x³ + x² - 17x + 15).

Using factor theorem, show that:
(x + 1) is a factor of (x³ + 4x² + 5x + 2).