The algebraic expression 5x^2 + 35x can be completely factored into the form 5x(x + c). Wh… — Armed Services Vocational Aptitude Battery (ASVAB)

The algebraic expression $5x^2 + 35x$ can be completely factored into the form $5x(x + c)$ . What is the value of the constant $c$ ?

Answer: 7 / +7 / seven / Seven

By extracting the greatest common factor of

5x

from

5x^2 + 35x

, we divide both terms by

5x

. This leaves

(x + 7)

inside the parentheses. Comparing this to the given structure

5x(x + c)

, it is clear that

c

must be 7.

Identify the greatest common factor (GCF) of the terms

5x^2

and

35x

The GCF is

5x

Both terms are divisible by 5 and share a minimum of one

x

Divide each term of the original expression by the GCF to find the binomial factor.

\frac{5x^2}{5x} = x

and

\frac{35x}{5x} = 7

Factoring out the GCF is the reverse of distributing it.

Write the factored form and compare it to the given form

5x(x + c)

The factored form is

5x(x + 7)

. Therefore, comparing it to

5x(x + c)

c = 7

Matching corresponding terms reveals the value of the unknown constant.

Factoring the Greatest Common Factor (GCF)

Question