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Standard X

Mathematics

Remainder Theorem

What is the r...

Question

What is the remainder obtained when the polynomial, $p (x) = x^{7} + 9 x^{5} + 5 x^{3} + x - 1$ is divided by $x - 1$ ? Also, what is the value of $p (1)$ ?

15, 15

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15, 0

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0, 15

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Solution

The correct option is A 15, 15
$By remainder theorem, we know that if a polynomial f(x) is divided by (x - a), the remainder obtained is f(a).$

So, remainder is equal to $p (1)$ .

$p (1) = 1^{7} + 9 \times 1^{5} + 5 \times 1^{3} + 1 - 1$
$p (1) = 1 + 9 + 5 + 1 - 1 = 15$

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What is the remainder obtained when the polynomial P(x) = $x^{7} + 9 x^{5} + 5 x^{3} + x - 1$ is divided by $x - 1$ ?

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What is the remainder obtained when the polynomial, p(x)=x7+9x5+5x3+x−1 is divided by x–1? Also, what is the value of p(1)?

The correct option is A 15, 15By remainder theorem, we know thatif a polynomial f(x) is divided by (x - a), the remainder obtained is f(a). So, remainder is equal to p(1). p(1)=17+9×15+5×13+1−1 p(1)=1+9+5+1−1=15

What is the remainder obtained when the polynomial, $p (x) = x^{7} + 9 x^{5} + 5 x^{3} + x - 1$ is divided by $x - 1$ ? Also, what is the value of $p (1)$ ?

The correct option is A 15, 15
$By remainder theorem, we know that if a polynomial f(x) is divided by (x - a), the remainder obtained is f(a).$

So, remainder is equal to $p (1)$ .

$p (1) = 1^{7} + 9 \times 1^{5} + 5 \times 1^{3} + 1 - 1$
$p (1) = 1 + 9 + 5 + 1 - 1 = 15$