Question

The quotient if the polynomial f(x)=50x^2-90x-25 leaves a remainder of -5, when divided by 5x-10, will be __________

(a) 10x+2

(b) 10x-2

(c) -10x+2

(d) -10x-2

I have been asked this question in an interview.

The question is from Division of Polynomial in division Polynomials of Mathematics – Class 10

Answer 1

Right choice is (a) 10x+2

Explanation: We know that,

f(x)=q(x)×g(x)+r(x)

Where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.

∴ 50x^2-90x-25=q(x)×5x-10-5

50x^2-90x-25+5=q(x)×5x-10

\(\frac {50x^2-90x-20}{5x-10}\)=q(x)

We get, q(x)=10x+2