Question

Find the sum of coefficients of x⁴ and x in the polynomial f(x) = −4x5 + x4 + 2x2 − 7x 8 + 6​

Answer 1

Answer:

First expand the term (1+2x)

4

by binomial expansion.

(1+2x)

4

=

4

C

0

(1)

4

(2x)

0

+

4

C

1

(1)

3

(2x)

1

+

4

C

2

(1)

2

(2x)

2

+

4

C

3

(1)

1

(2x)

3

+

4

C

4

(1)

0

(2x)

4

=1+8x+24x

2

+32x

3

+16x

4

(1)

Now expand the term (2−x)

5

by binomial expansion,

(2−x)

5

=

5

C

0

(2)

5

(x)

0

−

5

C

1

(2)

4

(x)

1

+

5

C

2

(2)

3

(x)

2

−

5

C

3

(2)

2

(x)

3

+

5

C

4

(2)

1

(x)

4

−

5

C

5

(2)

0

(x)

5

=32−80x+80x

2

−40x

3

+10x

4

−x

5

(2)

Multiply the coefficients of those powers which can give the term x

4

and then add from equation (1) and (2).

=1×10+8(−40)+24(80)+32(−80)+16(32)

=−438

Therefore, the coefficient of x

4

is −438.

Step-by-step explanation:

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