Chapter 8.4, Problem 5MRE

To determine

Factor: the given expression.

Answer to Problem 5MRE

The factorization of $3s^2+7s+4$ is $\left(3s+4\right)\left(s+1\right)$ .

Explanation of Solution

Given information:

The expression $3s^2+7s+4$ .

Formula used: -

Splitting the middle term: To factorize the quadratic equation using this method, the middle term of the equation is splitted in such a way that the product of coefficients of its parts are equal to product of constant and coefficient of quadratic term.

  $3s^2+7s+4$

Now we need to split $7s$ in such a way that product of coefficient of its part is equal to product of 3 and 4 that is 12.

  $\begin{array}{l}=3s^2+3s+4s+4\\ =3s\left(s+1\right)+4\left(s+1\right)\\ =\left(3s+4\right)\left(s+1\right)\end{array}$

The factorization of $3s^2+7s+4$ is $\left(3s+4\right)\left(s+1\right)$ .