Solve 3x^2-10x+7+x-1

$$3 { x }^{ 2 } -10x+7+x-1$$

Evaluate

$$3\left(x-2\right)\left(x-1\right)$$

Solution Steps

Combine -10x and x to get -9x.

$$3x^{2}-9x+7-1$$

Subtract 1 from 7 to get 6.

$$3x^{2}-9x+6$$

Factor

$$3\left(x-2\right)\left(x-1\right)$$

Solution Steps

Multiply and combine like terms.

$$3x^{2}-9x+6$$

Factor out 3.

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

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

$$a+b=-3 ab=1\times 2=2$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.

$$a=-2 b=-1$$

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

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

Factor out x in the first and -1 in the second group.

$$x\left(x-2\right)-\left(x-2\right)$$

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

$$\left(x-2\right)\left(x-1\right)$$

Rewrite the complete factored expression.

$$3\left(x-2\right)\left(x-1\right)$$