Question

3. Find q(a + 1) --29(a) if g(x) = x2 + 3x + 4.​

Answer 1

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+3

2x

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.