Question

If the polynomials f(x) = 3x3 - 5x2 + kx - 2 and g(x)
= - x - x2 + 7x + k leaves the same remainder
when divided by (x + 2), then find the value of k.​

Answer 1

Step-by-step explanation:

Put x=-2 in both p(x) and g(x)

then we get

p(-2) = 9-10+(-2k)-2k

= 9-10-2k-2

p(x) = -3-2k

put x=-2 in g(x)

then we get ..

g(-2)= -(-2)-(-2)2+7(-2)+k

= 2+4-14+k

= 6-14+k

g(x) = -8+k

according to question both remainders are equal then...

p(x)=g(x)

-3-2k = -8+k

-2+8=k+2k

-6=3k

k= -6/3

k= -2

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