Algebra and Applications Test 1

Question : 20 of 40

Marks: +1, -0

When

q^3 + 2q^2 + 4q + k

is divided by

q + 1,

the quotient is

q^2 + jq + 3

and the remainder is

-3 + 2k.

What are the values of j and k respectively?

Solution:

∵ q^3 + 2q^2 + 4q + k = (q + 1) (q^2 + jq + 3) - 3 + 2k

⇒ q^3 + 2q^2 + 4q + k = q^3 + (j + 1)q^2 + (3 + j) q + 2k

Comparing the coefficient of like terms on both sides, we get
j + 1 = 2 and 2k = k
⇒ j = 1 and k(2 - 1) = 0
⇒ j = 1 and k = 0

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