When px-x3-a x2-a is divided by x-a- the remainder isa 0b ac 2 ad 3 a

(b) a x a=0 #8658;x=a By the remainder theorem, we know that when nbsp;p(x) is divided by (x nbsp; a), the remainder is nbsp;p(a). Thus, we have: pa=a ...

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Standard IX

Mathematics

Remainder Theorem

When px=x3-a ...

Question

When p(x) = x³ − ax² + a is divided by (x − a), the remainder is
(a) 0
(b) a
(c) 2a
(d) 3a

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Solution

(b) a

$x - a = 0 \Rightarrow x = a$
By the remainder theorem, we know that when p(x) is divided by (x $-$ a), the remainder is p(a).
Thus, we have:
$p (a) = a^{3} - a \times a^{2} + a = a^{3} - a^{3} + a = a$

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When p(x) = x3 − ax2 + a is divided by (x − a), the remainder is (a) 0 (b) a (c) 2a (d) 3a

(b) a x-a=0⇒x=a By the remainder theorem, we know that when p(x) is divided by (x - a), the remainder is p(a). Thus, we have: pa=a3-a×a2+a =a3-a3+a =a

When p(x) = x³ − ax² + a is divided by (x − a), the remainder is
(a) 0
(b) a
(c) 2a
(d) 3a

(b) a

$x - a = 0 \Rightarrow x = a$
By the remainder theorem, we know that when p(x) is divided by (x $-$ a), the remainder is p(a).
Thus, we have:
$p (a) = a^{3} - a \times a^{2} + a = a^{3} - a^{3} + a = a$