Question

if x-3 is a factir of x2-kx+12 then find tha value of k also find the other factors of the polynomial for this value of k

Answer 1

$Let \:the \: polynomial \: p(x) = x^{2}-kx+12$

$If \:(x-3) \:is \:a \: factor \:of \:p(x) \:then \:p(3) = 0$

$\implies 3^{2} - k\times 3 + 12 = 0$

$\implies 9 - 3k + 12 =0$

$\implies - 3k + 21 =0$

$\implies - 3k = -21$

$\implies k = \frac{-21}{-3}$

$\implies k = 7$

$Now , p(x) = x^{2} - 7x + 12$

x-3) x² - 7x + 12 ( x - 4

***** x² - 3x

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********* -4x + 12

********* -4x + 12

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Remainder (0)

$p(x) = (x-3)(x-4)$

Therefore.,

$\red { Value \:of \:k } \green {= 7 }$

$\red { Another \:factor } \green {= x-4 }$

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