Match the numbers to be subtracted from the respective polynomials so that it is divisible by ( $x - 1$ ).

5 x + 8

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x^{2} - 2 x + 1

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

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Solution

For $p (x)$ to be divisible by $x - 1$ , sum of coefficients should be equal to 0.
Let the number be 'a' that is to be subtracted from the polynomial.
$5 x + 8 - a$ is divisible by $x - 1$ . So, $5 + 8 - a = 0 \to a = 13$ .
$x^{2} - 2 x + 1 - a$ is divisible by $x - 1$ . So, $1 - 2 + 1 - a = 0 \to a = 0$ .
$x^{3} + x^{2} + 1 - a$ is divisible by $x - 1$ . So, $1 + 1 + 1 - a = 0 \to a = 3$ .

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Match the numbers to be subtracted from the respective polynomials so that it is divisible by (x−1).

Match the numbers to be subtracted from the respective polynomials so that it is divisible by ( $x - 1$ ).