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

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