What must be added in 4x⁴ 2x³ 6x² x - 5 so that the result is exactly divisible by 2x² x - 1

Uh-Oh! That’s all you get for now.

We would love to personalise your learning journey. Sign Up to explore more.

Sign Up or Login

Skip for now

Uh-Oh! That’s all you get for now.

We would love to personalise your learning journey. Sign Up to explore more.

Sign Up or Login

Skip for now

CBSE 10 - Maths

Solve it

Asked by navneetpra499 | 19 Jul, 2022, 05:06: AM

CBSE 10 - Maths

Asked by ravindar.sanka123 | 07 Jul, 2022, 01:30: PM

ANSWERED BY EXPERT

CBSE 10 - Maths

Asked by babadubey9771 | 03 Jul, 2022, 10:53: AM

ANSWERED BY EXPERT

CBSE 10 - Maths

answer this question

Asked by anuragtikekar2006 | 07 May, 2022, 06:33: PM

ANSWERED BY EXPERT

CBSE 10 - Maths

Asked by harshkumar128198k | 29 Mar, 2022, 04:19: PM

ANSWERED BY EXPERT

We know that,

f(x) = g(x) x q(x) + r(x)

f(x) - r(x) = g(x) x q(x)

f(x) + {- r(x)} = g(x) x q(x)

Clearly , Right hand side is divisible by g(x).

Therefore, Left hand side is also divisible by g(x).Thus, if we add - r(x) to f(x), then the resulting polynomial is divisible by g(x).

Let us now find the remainder when f(x) is divided by g(x).

Hence, we should add - r(x) = x - 2 to f(x) so that the resulting polynomial is divisible by g(x).

Page 2

We know that Dividend = Quotient x Divisor + Remainder.

Dividend - Remainder = Quotient x Divisor.

Clearly, Right hand side of the above result is divisible by the divisor.

Therefore, left hand side is also divisible by the divisor.

Thus, if we subtract remainder from the dividend, then it will be exactly divisible by the divisor.

Dividing x4 + 2x3 − 13x2 − 12x + 21 by x2 − 4x + 3

Therefore, quotient = x2 + 6x + 8 and remainder = (2x - 3).

Thus, if we subtract the remainder 2x - 3 from x4 + 2x3 − 13x2 − 12x + 21 it will be divisible by x2 − 4x + 3.