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

x² + 4

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x² - 3

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x - 4

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2x - 3

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Solution

The correct option is D
2x - 3

Divide f(x) by g(x) and find the remainder r(x) = 2x - 3. Hence, (2x – 3) should be subtracted.

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Similar questions

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 $x^{2} - 4 x + 3$ ?

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

The expression that should be added to the polynomial f(x) = x⁴ + 2x³ – 2x² + x + 1, so that it should be exactly divisible by (x² + 2x – 3) is

Q. What must be added to

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

so that the resulting polynomial is divisible by

g (x) = x^{2} + 2 x - 3

Q. What must be added to x⁴ + 2x³ − 2x² + x − 1 , so that the resulting polynomial is exactly divisible by x²+ 2x − 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

The correct option is D 2x - 3Divide f(x) by g(x) and find the remainder r(x) = 2x - 3. Hence, (2x – 3) should be subtracted.

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

The correct option is D
2x - 3

Divide f(x) by g(x) and find the remainder r(x) = 2x - 3. Hence, (2x – 3) should be subtracted.