What must be subtracted from polynomial $f (x) = x^{4} + 2 x^{3} - 13 x^{2} - 12 x + 21$ so that the resulting polynomial is exactly divisible by $x^{2} - 4 x + 3$ ?

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Solution

Any division statement can be rewritten in the form of
Dividend = Divisor x Quotient + Remainder.
When the remainder is zero, the dividend is said to be the multiple of the divisor.

When the remainder is not equal to zero, and if it is subtracted from the dividend, then the dividend would become a multiple of the divisor.

Dividend =
Divisor =

Step 1: Divide the dividend by divisor

) (

-_+-_

-__+_-

-+-__

Quotient =
Remainder =

Hence, on subtracting 2x – 3 from the dividend, it will be exactly divisible by the given divisor.

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Similar questions

The expression that should be subtracted from the polynomial f(x) = x⁴ + 2x³ -13x² - 12x + 21 so that the resulting polynomial is exactly divisible by g(x) = x² – 4x + 3 is

Q. What must be subtracted from

x^{4} + 2 x^{3} - 13 x^{2} - 12 x + 21

so that the result is exactly divisible by

x^{2} - 4 x + 3

Q. What must be subtracted from the polynomial

x^{3} + 13 x^{2} + 35 x + 25

so that the resulting polynomials is exactly divisible by

x^{2} + 11 x + 10

Q. What must be added to the polynomial

P (x) = x^{4} + 2 x^{3} - 2 x^{2} + x - 1

. So that the resulting polynomial is exactly divisible by

x^{2} + 2 x - 3

Q. What must be subtracted from

6 x^{4} + 13 x^{3} + 13 x^{2} + 30 x + 20

, so that the resulting polynomial is exactly divisible by

3 x^{2} + 2 x + 5

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What must be subtracted from polynomial f(x)=x4+2x3−13x2−12x+21 so that the resulting polynomial is exactly divisible by x2−4x+3 ?

What must be subtracted from polynomial $f (x) = x^{4} + 2 x^{3} - 13 x^{2} - 12 x + 21$ so that the resulting polynomial is exactly divisible by $x^{2} - 4 x + 3$ ?