It is given that (x − 2) is a factor of polynomial 2x3 − 7x2 + kx − 2. Find: (a) the value of ‘k’. (b) hence, factorise the resulting polynomial completely.

(a) Since (x − 2) is a factor of 2x3 − 7x2 + kx − 2. Thus, on substituting x = 2, in 2x3 − 7x2 + kx − 2, the remainder will be equal to zero. ⇒ 2(2)3 − 7(2)2 + k(2) − 2 = 0 ⇒ 16 − 28 + 2k − 2 = 0 ⇒ −14 + 2k = 0 ⇒ 2k = 14 ⇒ k = ⇒ k = 7. Hence, k = 7. (b) Substituting k = 7 in 2x3 − 7x2 + kx − 2, we get : Polynomial : 2x3 − 7x2 + 7x − 2. Dividing 2x3 − 7x2 + 7x − 2 by x - 2, we get : ⇒ 2x3 − 7x2 + 7x − 2 = (x - 2)(2x2 - 3x + 1) ⇒ 2x3 − 7x2 + 7x − 2 = (x - 2)[2x2 - 2x - x + 1] ⇒ 2x3 − 7x2 + 7x − 2 = (x - 2)[2x(x - 1) - 1(x - 1)] ⇒ 2x3 − 7x2 + 7x − 2 = (x - 2)(2x - 1)(x - 1). Hence, 2x3 − 7x2 + 7x − 2 = (x - 2)(2x - 1)(x - 1).

Mathematics

It is given that (x − 2) is a factor of polynomial 2x³ − 7x² + kx − 2.
Find:
(a) the value of ‘k’.
(b) hence, factorise the resulting polynomial completely.

Factorisation

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Mathematics

It is given that (x − 2) is a factor of polynomial 2x3 − 7x2 + kx − 2.Find:(a) the value of ‘k’.(b) hence, factorise the resulting polynomial completely.

Factorisation

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It is given that (x − 2) is a factor of polynomial 2x³ − 7x² + kx − 2.
Find:
(a) the value of ‘k’.
(b) hence, factorise the resulting polynomial completely.