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if X + 2 factor of x power 4 the square minus 4 then what will the value of what will the value of a |
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Answer» Consider the given polynomial isP(X)=4x^4+2x^3-3x^2+8x+5aP(x)=4x 4 +2x 3 −3x 2 +8x+5aWe NEED to find the value of a when (x+2) is a factor of P(x).If (x-c) is a factor of P(x), the P(c)=0.Since (x+2) is a factor of P(x), it means P(-2)=0.Substitute x=-2 in the given polynomial.P(-2)=4(-2)^4+2(-2)^3-3(-2)^2+8(-2)+5aP(−2)=4(−2) 4 +2(−2) 3 −3(−2) 2 +8(−2)+5aP(-2)=4(16)+2(-8)-3(4)-16+5aP(−2)=4(16)+2(−8)−3(4)−16+5aP(-2)=20+5aP(−2)=20+5aEquate P(-2)=0.20+5a=020+5a=05a=-205a=−20Divide both SIDES by 5.a=-4a=−4 |
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