Solve 3c^2-1+c-1

$$3 c ^ { 2 } - 1 + c - 1$$

Factor

$$\left(3c-2\right)\left(c+1\right)$$

Solution Steps

Multiply and combine like terms.

$$3c^{2}+c-2$$

Factor the expression by grouping. First, the expression needs to be rewritten as 3c^{2}+ac+bc-2. To find a and b, set up a system to be solved.

$$a+b=1 ab=3\left(-2\right)=-6$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -6.

$$-1,6 -2,3$$

Calculate the sum for each pair.

$$-1+6=5 -2+3=1$$

The solution is the pair that gives sum 1.

$$a=-2 b=3$$

Rewrite 3c^{2}+c-2 as \left(3c^{2}-2c\right)+\left(3c-2\right).

$$\left(3c^{2}-2c\right)+\left(3c-2\right)$$

Factor out c in 3c^{2}-2c.

$$c\left(3c-2\right)+3c-2$$

Factor out common term 3c-2 by using distributive property.

$$\left(3c-2\right)\left(c+1\right)$$

Evaluate

$$\left(3c-2\right)\left(c+1\right)$$

Solution Steps

Subtract 1 from -1 to get -2.

$$3c^{2}-2+c$$