Solve (2v^2+7v)+(10v+35)=

$$( 2 v ^ { 2 } + 7 v ) + ( 10 v + 35 ) =$$

Factor

$$\left(v+5\right)\left(2v+7\right)$$

Solution Steps

Multiply and combine like terms.

$$2v^{2}+17v+35$$

Factor the expression by grouping. First, the expression needs to be rewritten as 2v^{2}+av+bv+35. To find a and b, set up a system to be solved.

$$a+b=17 ab=2\times 35=70$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 70.

$$1,70 2,35 5,14 7,10$$

Calculate the sum for each pair.

$$1+70=71 2+35=37 5+14=19 7+10=17$$

The solution is the pair that gives sum 17.

$$a=7 b=10$$

Rewrite 2v^{2}+17v+35 as \left(2v^{2}+7v\right)+\left(10v+35\right).

$$\left(2v^{2}+7v\right)+\left(10v+35\right)$$

Factor out v in the first and 5 in the second group.

$$v\left(2v+7\right)+5\left(2v+7\right)$$

Factor out common term 2v+7 by using distributive property.

$$\left(2v+7\right)\left(v+5\right)$$

Evaluate

$$\left(v+5\right)\left(2v+7\right)$$

Solution Steps

Combine 7v and 10v to get 17v.

$$2v^{2}+17v+35$$