Use the Remainder theorem to find which of the following is a factor of 2x 3 + 3x 2 - 5x - 6. (i) x + 1 (ii) 2x - 1 (iii) x + 2

(i) x + 1 = 0 ⇒ x = -1 Required remainder = Value of given polynomial 2x 3 + 3x 2 - 5x - 6 at x = -1. ∴ Remainder = 2(-1) 3 + 3(-1) 2 - 5(-1) - 6 = 2(-1) + 3(1) + 5 - 6 = -2 + 3 + 5 - 6 = 8 - 8 Since, remainder = 0 ∴ x + 1 is a factor of 2x 3 + 3x 2 - 5x - 6 (ii) 2x - 1 = 0 ⇒ x = Required remainder = Value of given polynomial 2x 3 + 3x 2 - 5x - 6 at x = . Since, remainder ≠ 0 ∴ 2x - 1 is not a factor of 2x 3 + 3x 2 - 5x - 6. (iii) x + 2 = 0 ⇒ x = -2 Required remainder = Value of given polynomial 2x 3 + 3x 2 - 5x - 6 at x = -2. ∴ Remainder = 2(-2) 3 + 3(-2) 2 - 5(-2) - 6 = 2(-8) + 3(4) + 10 - 6 = -16 + 12 + 10 - 6 = 22 - 22 = 0. Since, remainder = 0 ∴ x + 2 is a factor of 2x 3 + 3x 2 - 5x - 6.

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x⁴ + 1 is divisible by x + 1.

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Mathematics

Use the Remainder theorem to find which of the following is a factor of 2x³ + 3x² - 5x - 6.
(i) x + 1
(ii) 2x - 1
(iii) x + 2

Factorisation

Related Questions

Find in each case, the remainder when :
x⁴ + 1 is divisible by x + 1.

Show that 3x + 2 is a factor of 3x² - x - 2.

If 2x + 1 is a factor of 2x² + ax - 3, find the value of a.

Find the value of k, if 3x - 4 is a factor of the expression 3x² + 2x - k.

Mathematics

Use the Remainder theorem to find which of the following is a factor of 2x3 + 3x2 - 5x - 6.(i) x + 1(ii) 2x - 1(iii) x + 2

Factorisation

Related Questions

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Show that 3x + 2 is a factor of 3x2 - x - 2.

If 2x + 1 is a factor of 2x2 + ax - 3, find the value of a.

Find the value of k, if 3x - 4 is a factor of the expression 3x2 + 2x - k.

Use the Remainder theorem to find which of the following is a factor of 2x³ + 3x² - 5x - 6.
(i) x + 1
(ii) 2x - 1
(iii) x + 2

Find in each case, the remainder when :
x⁴ + 1 is divisible by x + 1.

Show that 3x + 2 is a factor of 3x² - x - 2.

If 2x + 1 is a factor of 2x² + ax - 3, find the value of a.

Find the value of k, if 3x - 4 is a factor of the expression 3x² + 2x - k.