Answer
$3a^{2}+10a+7=(3a+7)(a+1)$
Work Step by Step
$3a^{2}+10a+7$
Since the coefficient of $a^{2}$ is not equal to $1$, begin by multiplying the whole expression by $3$, which is the actual coefficient of $a^{2}$. Leave the product between $3$ and the second term expressed:
$3(3a^{2}+10a+7)=...$
$...=9a^{2}+3(10a)+21$
Open two parentheses containing initially the square root of the second term, which is $3a$, followed by the sign of the second term, in the first parentheses, and the product of the signs of the second and third terms, on the second parentheses:
$...=(3a+)(3a+)$
Find two numbers whose product is equal to the third term, $21$ and whose sum is equal to the coefficient of the expression inside parentheses in the second term, $10$.
These two numbers are $7$ and $3$, because $(7)(3)=21$ and $7+3=10$.
$...=(3a+7)(3a+3)$
The expression was affected initially by multiplying it by $3$. Divide it by $3$ to obtain the answer:
$...=(3a+7)\dfrac{(3a+3)}{3}=...$
$...=(3a+7)(a+1)$
