Chapter 5, Problem 1RE

To determine

To calculate: Thefactored form of the binomial $7t+14$.

Answer to Problem 1RE

Solution:

The factored form of the binomial $7t+14$ is $7\left(t+2\right)$.

Explanation of Solution

Given Information:

The binomial $7t+14$.

Formula used:

There are following steps for factoring out the greatest common factor:

Step1: Obtain the prime factors of all the terms.

Step 2: Select the variable or prime number that is common to all the terms.

Step 3: Select the least exponents from the common prime.

Step 4: Multiply the common primes.

Distributive property:

$a\left(b+c\right)=ab+ac$

Where, a, b and c are the real numbers.

Calculation:

Consider the binomial.

$7t+14$

Obtain the factors of the terms,

$\begin{array}{c}7t=7\cdot t\\ 14=2\cdot 7\end{array}$

Here, the greatest common factor is 7.

So, the binomial becomes,

$7t+14=7\cdot t+2\cdot 7$

Apply the Distributive property,

$7t+14=7\left(t+2\right)$

Therefore, the factored form of $7t+14$ is $7\left(t+2\right)$.