Solve (5x^2+25x+20)+(x+4)

$$( 5 x ^ { 2 } + 25 x + 20 ) + ( x + 4 )$$

Evaluate

$$\left(x+4\right)\left(5x+6\right)$$

Solution Steps

Combine 25x and x to get 26x.

$$5x^{2}+26x+20+4$$

Add 20 and 4 to get 24.

$$5x^{2}+26x+24$$

Factor

$$\left(x+4\right)\left(5x+6\right)$$

Solution Steps

Multiply and combine like terms.

$$5x^{2}+26x+24$$

Factor the expression by grouping. First, the expression needs to be rewritten as 5x^{2}+ax+bx+24. To find a and b, set up a system to be solved.

$$a+b=26 ab=5\times 24=120$$

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 120.

$$1,120 2,60 3,40 4,30 5,24 6,20 8,15 10,12$$

Calculate the sum for each pair.

$$1+120=121 2+60=62 3+40=43 4+30=34 5+24=29 6+20=26 8+15=23 10+12=22$$

The solution is the pair that gives sum 26.

$$a=6 b=20$$

Rewrite 5x^{2}+26x+24 as \left(5x^{2}+6x\right)+\left(20x+24\right).

$$\left(5x^{2}+6x\right)+\left(20x+24\right)$$

Factor out x in the first and 4 in the second group.

$$x\left(5x+6\right)+4\left(5x+6\right)$$

Factor out common term 5x+6 by using distributive property.

$$\left(5x+6\right)\left(x+4\right)$$