Solve 3a^2+8a^+5

$$3 { a }^{ 2 } +8 { a }^{ } +5$$

Factor

$$\left(a+1\right)\left(3a+5\right)$$

Solution Steps

Multiply and combine like terms.

$$3a^{2}+8a+5$$

Factor the expression by grouping. First, the expression needs to be rewritten as 3a^{2}+pa+qa+5. To find p and q, set up a system to be solved.

$$p+q=8 pq=3\times 5=15$$

Since pq is positive, p and q have the same sign. Since p+q is positive, p and q are both positive. List all such integer pairs that give product 15.

$$1,15 3,5$$

Calculate the sum for each pair.

$$1+15=16 3+5=8$$

The solution is the pair that gives sum 8.

$$p=3 q=5$$

Rewrite 3a^{2}+8a+5 as \left(3a^{2}+3a\right)+\left(5a+5\right).

$$\left(3a^{2}+3a\right)+\left(5a+5\right)$$

Factor out 3a in the first and 5 in the second group.

$$3a\left(a+1\right)+5\left(a+1\right)$$

Factor out common term a+1 by using distributive property.

$$\left(a+1\right)\left(3a+5\right)$$

Evaluate

$$\left(a+1\right)\left(3a+5\right)$$

Solution Steps

Calculate a to the power of 1 and get a.

$$3a^{2}+8a+5$$