Question

What will be the value of a and b if the polynomial f(x)=30x^4-50x^3+109x^2-23x+25, when divided by 3x^2-5x+10, gives 10x^2+3 as quotient and ax+b as remainder?

(a) a=8, b=5

(b) a=-8, b=5

(c) a=8, b=-5

(d) a=-8, b=-5

The question was posed to me during a job interview.

My query is from Division of Polynomial topic in chapter Polynomials of Mathematics – Class 10

Answer 1

The correct answer is (d) a=-8, b=-5

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.

∴ 30x^4-50x^3+109x^2-23x+25=(10x^2+3)(3x^2-5x+10)+ax+b

30x^4-50x^3+109x^2-23x+25=30x^4-50x^3+109x^2-15x+30+ax+b

30x^4-50x^3+109x^2-23x+25-(30x^4-50x^3+109x^2-15x+30)=ax+b

-23x+25+15x-30=ax+b

-8x-5=ax+b

∴ a=-8, b=-5