What must be subtracted from x4-2 x3-2 x2-4 x-6 so that the result is exactly divisible by x2-2 x-3 -

Dividing nbsp;(x4 nbsp;+ 2x3 nbsp;– 2x2 nbsp;+ 4x nbsp;+ 6) by nbsp;(x2 nbsp;+ 2x nbsp;– 3) using long division method, we have Here, the n ...

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Standard VIII

Mathematics

Factors of Natural Numbers

What must be ...

Question

What must be subtracted from (x⁴+ 2x³– 2x² + 4x + 6) so that the result is exactly divisible by (x²+ 2x – 3)?

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Solution

Dividing (x⁴+ 2x³– 2x² + 4x + 6) by (x²+ 2x – 3) using long division method, we have

Here, the remainder obtained is (2x + 9).

Thus, the remainder (2x + 9) must be subtracted from (x⁴+ 2x³– 2x² + 4x + 6) so that the result is exactly divisible by (x²+ 2x – 3).

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

Q. What must be subtracted from

4 x^{4} - 2 x^{3} - 6 x^{2} + x - 5

so that result is exactly divisible by

2 x^{2} + x - 1

Q. What must be added to x⁴ + 2x³ − 2x² + x − 1 , so that the resulting polynomial is exactly divisible by x²+ 2x − 3?

Q. What must be added to

x^{4} + 2 x^{3} - 2 x^{2} + x - 1

. So that result is exactly divisible by

x^{2} + x - 2

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

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What must be subtracted from (x4 + 2x3 – 2x2 + 4x + 6) so that the result is exactly divisible by (x2 + 2x – 3)?

Dividing (x4 + 2x3 – 2x2 + 4x + 6) by (x2 + 2x – 3) using long division method, we have Here, the remainder obtained is (2x + 9). Thus, the remainder (2x + 9) must be subtracted from (x4 + 2x3 – 2x2 + 4x + 6) so that the result is exactly divisible by (x2 + 2x – 3).

What must be subtracted from (x⁴+ 2x³– 2x² + 4x + 6) so that the result is exactly divisible by (x²+ 2x – 3)?

Dividing (x⁴+ 2x³– 2x² + 4x + 6) by (x²+ 2x – 3) using long division method, we have

Here, the remainder obtained is (2x + 9).

Thus, the remainder (2x + 9) must be subtracted from (x⁴+ 2x³– 2x² + 4x + 6) so that the result is exactly divisible by (x²+ 2x – 3).