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On dividing 3x ^3 -2x^2 +5x …

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On dividing 3x ^3 -2x^2 +5x +5 by the polynomial p (x), the quotient and reminder are x^2-x+2 and -7 respectively find p (x)?

Posted by Arun Tiwari 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

It is given that
f(x) = 3x³- 2x²+ 5x - 5
q(x) = (x² - x + 2)
r(x) = (-7)
According to division algorithm,
f(x) = p(x).q(x) + r(x)
{tex}\Rightarrow{/tex}3x³ - 2x² + 5x - 5 = p(x).(x² - x + 2) + (-7)
{tex}\Rightarrow{/tex}3x³ - 2x² + 5x - 5 + 7 = p(x)(x² - x + 2)
{tex}\Rightarrow{/tex} p(x) = {tex}\frac { 3 x ^ { 3 } - 2 x ^ { 2 } + 5 x + 2 } { x ^ { 2 } - x + 2 }{/tex}

{tex}\therefore{/tex} p(x) = 3x + 1

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