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The polynomial ax power 3 minus 3x power x power 2 plus 4 and 2x power 3 |
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Answer» pls MARK brainliest Step-by-step explanation:It is GIVEN that a polynomial ax 3 −3x 2 +4 when divided by (x−2) leaves the remainder p. Let us substitute x=2 in ax 3 −3x 2 +4 and equate it to p as follows:a(2) 3 −3(2) 2 +4=p⇒(a×8)−(3×4)+4=p⇒8a−12+4=p⇒8a−8=p....(1)SIMILARLY, given a polynomial 2x 3 −5x+a when divided by (x−2) leaves the remainder q. Let us substitute x=2 in 2x 3 −5x+a and equate it to q as follows:2(2) 3 −(5×2)+a=q⇒(2×8)−10+a=q⇒16−10+a=q⇒6+a=q....(2)It is also given that p−2q=4, we, now substitute the values of p and q from equations 1 and 2 as SHOWN below:p−2q=4⇒8a−8−2(6+a)=4⇒8a−8−12−2a=4⇒6a−20=4⇒6a=4+20⇒6a=24⇒a= 624 ⇒a=4Hence, a=4. |
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