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Question

# If (x+k) is a factor of the polynomial x2−2x−15 and x2+a. Find k and a.

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Solution

## x(k+2)(x+k))¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯x2−2x−15x2+kx________________________(−k−2)x−15−(k+2)x−k(k+2)___________________________k(k+2)−15(x+k) is a factor of x2−2x−15 and x2+a⇒k(k+2)−15=0⇒k2+2k−15=0⇒k2+5k−3k−15=0⇒k(k+5)−3(k+5)=0⇒k=3or−5if k=3x−3(x+3))¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯x2+a x2+3x_______________−3x+a−3x−9________________9+a9+a=0a=−9if k=−5x+5(x−5))¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯x2+a x2−5x_______________5x+a5x−25________________25+a25+a=0⇒ a=−25∴ The solution are (k,a)=(3,−9) and (−5,−25)

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