Solve g-1g^2+3g-4

$$g - 1 g ^ { 2 } + 3 g - 4$$

Factor

$$-\left(g-2\right)^{2}$$

Solution Steps

Multiply and combine like terms.

$$-g^{2}+4g-4$$

Factor the expression by grouping. First, the expression needs to be rewritten as -g^{2}+ag+bg-4. To find a and b, set up a system to be solved.

$$a+b=4 ab=-\left(-4\right)=4$$

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 4.

$$1,4 2,2$$

Calculate the sum for each pair.

$$1+4=5 2+2=4$$

The solution is the pair that gives sum 4.

$$a=2 b=2$$

Rewrite -g^{2}+4g-4 as \left(-g^{2}+2g\right)+\left(2g-4\right).

$$\left(-g^{2}+2g\right)+\left(2g-4\right)$$

Factor out -g in the first and 2 in the second group.

$$-g\left(g-2\right)+2\left(g-2\right)$$

Factor out common term g-2 by using distributive property.

$$\left(g-2\right)\left(-g+2\right)$$

Evaluate

$$-\left(g-2\right)^{2}$$

Solution Steps

Combine g and 3g to get 4g.

$$4g-g^{2}-4$$