Determine the value of the missing coefficient by evaluating the problem below.

Answer:A rectangular solar panel has a length of

(5k - 4)

inches and a width of

(3k + 7)

inches. The area of the panel is represented by the fully expanded polynomial

Ak^2 + Bk + C

square inches. The value of the coefficient

B

is 【23】.

By multiplying the binomials

(5k - 4)

and

(3k + 7)

, the expanded expression is

15k^2 + 35k - 12k - 28

. Combining the middle terms (

35k - 12k

) yields

23k

. Since the polynomial is in the standard form

Ak^2 + Bk + C

, the value of

B

is 23.

Set up the area calculation by multiplying the length and width binomials.

Area =

(5k - 4)(3k + 7)

The area of a rectangle is found by multiplying its length by its width.

Distribute the terms using the FOIL method (First, Outer, Inner, Last).

15k^2 + 35k - 12k - 28

Each term in the first binomial must be multiplied by each term in the second binomial.

Combine the like terms in the middle to find the value of

B

15k^2 + 23k - 28

Adding

35k

and

-12k

simplifies the polynomial to the standard form

Ak^2 + Bk + C

Identify the coefficient

B

corresponding to the

k

term.

B = 23

The polynomial is

15k^2 + 23k - 28

, so the coefficient of the

k

term is 23.

Multiplying binomials and combining like terms to find a specific coefficient.

Question