What is the coefficient of the k term in the expanded product of (3k - 2) and (k + 5)? — Armed Services Vocational Aptitude Battery (ASVAB)

What is the coefficient of the $k$ term in the expanded product of $(3k - 2)$ and $(k + 5)$ ?

Answer: 13

When expanding

(3k - 2)(k + 5)

, the

k

terms are generated by multiplying the outer terms

(3k \times 5 = 15k)

and the inner terms

(-2 \times k = -2k)

. Combining these gives

15k - 2k = 13k

. Therefore, the coefficient of the

k

term is 13.

Identify the terms that will produce a

k

term when multiplied.

The outer terms are

3k

and

5

. The inner terms are

-2

and

k

Only the product of a variable term and a constant term will result in a term with degree 1 (

k

Multiply the outer terms.

(3k)(5) = 15k

This is the 'Outer' multiplication step in expanding two binomials.

Multiply the inner terms.

(-2)(k) = -2k

This is the 'Inner' multiplication step in expanding two binomials.

Combine the resulting like terms.

15k + (-2k) = 13k

Combining like terms gives the final

k

term of the expanded polynomial.

Identify the coefficient.

The coefficient is the numerical factor of the

k

term.

Multiplying polynomials and combining like terms

Question