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

x - 1

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x - 2

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x + 1

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x + 2

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Solution

The correct option is B $x - 2$
Factors of $x^{2} + 2 x - 3$ are $(x + 3)$ and $(x - 1)$ .

If we use Synthetic Division for $x^{4} + 2 x^{3} - 2 x^{2} + x - 1$ , it should be divided by both $x + 3$ and $x - 1$ .

therefore the term -(-x+2) should be added to $x^{4} + 2 x^{3} - 2 x^{2} + x - 1$

By adding the term $x - 2$ into $x^{4} + 2 x^{3} - 2 x^{2} + x - 1$ , we get the polynomial $x^{4} + 2 x^{3} - 2 x^{2} + 2 x - 3$ which is exactly divisible by $x^{2} + 2 x - 3$ .

Hence, the term $x - 2$ should be added.

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Similar questions

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

x^{2} + x - 2

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

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

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