What must be subtracted from the polynomial $x^{3} + 13 x^{2} + 35 x + 25$ so that the resulting polynomials is exactly divisible by $x^{2} + 11 x + 10$ .

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Solution

We divide the polynomial $x^{3} + 13 x^{2} + 35 x + 25$ by $x^{2} + 11 x + 10$ as shown in the above image:

From the above division, we conclude that the quotient is $x + 2$ and the remainder is $3 x + 5$ .

Hence, $3 x + 5$ must be subtracted from the polynomial $x^{3} + 13 x^{2} + 35 x + 25$ so that the resulting polynomial is exactly divisible by $x^{2} + 11 x + 10$ .

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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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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

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Respected Sir,

Please help me in solving my below mentioned doubt:

What must be subtracted from x³- 6x² - 15x + 80 so that the resulting polynomial is exactly divisible by x²+ x + 22?

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What must be subtracted from the polynomial x3+13x2+35x+25 so that the resulting polynomials is exactly divisible by x2+11x+10.

What must be subtracted from the polynomial $x^{3} + 13 x^{2} + 35 x + 25$ so that the resulting polynomials is exactly divisible by $x^{2} + 11 x + 10$ .