Question

p(x)=2x³+5x²+6x+8by 2x+3 find the remainder








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Answer 1

Answer:

If p(x)=2x³+5x²+6x+8by 2x+3 then the remainder is 7/2.

Step-by-step explanation:

If 2x + 3 = 0

then x = -3/2

Put x =-3/2 in p(x)=2x³+5x²+6x+8

$p(-\frac{3}{2} )= 2(-\frac{3}{2} )^3 + 5(-\frac{3}{2})^2 + 6(-\frac{3}{2})+ 8\\= 2(\frac{-27}{8} ) + 5(\frac{9}{4}) + 6(\frac{-3}{2})+ 8\\= \frac{-27}{4}+ \frac{45}{4}- 9 + 8\\= (\frac{-27 + 45}{4} )-1\\= (\frac{ 18}{4} )- 1\\= (\frac{ 9}{2} ) - 1 \\= (\frac{ 9 - 2}{2} )\\ = (\frac{ 7}{2} )$