Solve 7h^4+9h^3+2h^2

$$7 h ^ { 4 } + 9 h ^ { 3 } + 2 h ^ { 2 }$$

Factor

$$\left(h+1\right)\left(7h+2\right)h^{2}$$

Solution Steps

Factor out h^{2}.

$$h^{2}\left(7h^{2}+9h+2\right)$$

Consider 7h^{2}+9h+2. Factor the expression by grouping. First, the expression needs to be rewritten as 7h^{2}+ah+bh+2. To find a and b, set up a system to be solved.

$$a+b=9 ab=7\times 2=14$$

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 14.

$$1,14 2,7$$

Calculate the sum for each pair.

$$1+14=15 2+7=9$$

The solution is the pair that gives sum 9.

$$a=2 b=7$$

Rewrite 7h^{2}+9h+2 as \left(7h^{2}+2h\right)+\left(7h+2\right).

$$\left(7h^{2}+2h\right)+\left(7h+2\right)$$

Factor out h in 7h^{2}+2h.

$$h\left(7h+2\right)+7h+2$$

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

$$\left(7h+2\right)\left(h+1\right)$$

Rewrite the complete factored expression.

$$h^{2}\left(7h+2\right)\left(h+1\right)$$

Evaluate

$$\left(h+1\right)\left(7h+2\right)h^{2}$$