Question

If p(x) = 2x4- 5x3 + 8a + 1 leaves the remainder 2 when divided by x-1. Find the value of a.
Pls answer this Q​

Answer 1

Answer:

Ok

Step-by-step explanation:

The division algorithm states that Dividend=Divisor×Quotient+Remainder that is f(x)=g(x)⋅q(x)+r(x)

Here, it is given that the dividend is f(x)=2x

4 −5x 3 +x 2 +3x−2, the divisor is 2x 2

−5x+3 and the remainder is −2x+1, therefore, by applying division algorithm we have:

2x 4 −5x 3 +x 2 +3x−2=(2x 2 −5x+3)g(x)+(−2x+1)

⇒2x

4 −5x 3 +x 2 +3x−2−(−2x+1)=(2x 2 −5x+3)g(x)

⇒2x

4 −5x 3 +x 2 +3x−2+2x−1=(2x 2 −5x+3)g(x)

⇒2x

4 −5x 3 +x 2 +5x−3=(2x 2 −5x+3)g(x)

⇒g(x)= 2x 2 −5x+32x

4 −5x 3 +x 2 +5x−3

Let us now divide 2x

4 −5x 3 +x 2 +5x−3 by 2x 2 −5x+3 as shown in the above image:

From the division, we observe that the quotient is x 2 −1 and the remainder is 0.

Hence, the quotient q(x)=x

2 −1.

Answer 2

Step-by-step explanation:

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