Answer
$15x+40=5(3x+8)$
For $x=4$
$15x+40=15\cdot4+40=60+40=100$
For $x=4$
$5(3x+8)=5(3\cdot4+8)=5(12+8)=5(20)=100$
Since the values of $15x+40$ and $5(3x+8)$ are equal.
Both the expressions are equivalent. Hence, the results guarantee that the factorization is correct.
Work Step by Step
Firstly make factors of $15$ as follows:
$15=5\cdot3$
Now make factors of $40$ as follows:
$40=5\cdot8$
Now write $15$ and $40$ in factor form in the expression $15x+40$.
We get, $(5\cdot3)x+5\cdot8$
Now use Associative law.
We get, $5(3x)+5\cdot8$
Now use the reverse of the Distributive law.
We get, $5(3x+8)$
Here $5$ and $(3x+8)$ are the factors.
Now substitute $x=4$ in $15x+40$.
We get, $15\cdot4+40=60+40=100$
Now substitute $x=4$ in $5(3x+8)$.
We get, $5(3\cdot4+8)=5(12+8)=5(20)=100$
Since the values of $15x+40$ and $5(3x+8)$ are equal.
Both the expressions are equivalent. Hence, the results guarantee that the factorization is correct.
