Solve (3x^2+x-30)+(x-3)

$$( 3 x ^ { 2 } + x - 30 ) + ( x - 3 )$$

Evaluate

$$\left(x-3\right)\left(3x+11\right)$$

Solution Steps

Combine x and x to get 2x.

$$3x^{2}+2x-30-3$$

Subtract 3 from -30 to get -33.

$$3x^{2}+2x-33$$

Factor

$$\left(x-3\right)\left(3x+11\right)$$

Solution Steps

Multiply and combine like terms.

$$3x^{2}+2x-33$$

Factor the expression by grouping. First, the expression needs to be rewritten as 3x^{2}+ax+bx-33. To find a and b, set up a system to be solved.

$$a+b=2 ab=3\left(-33\right)=-99$$

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 -99.

$$-1,99 -3,33 -9,11$$

Calculate the sum for each pair.

$$-1+99=98 -3+33=30 -9+11=2$$

The solution is the pair that gives sum 2.

$$a=-9 b=11$$

Rewrite 3x^{2}+2x-33 as \left(3x^{2}-9x\right)+\left(11x-33\right).

$$\left(3x^{2}-9x\right)+\left(11x-33\right)$$

Factor out 3x in the first and 11 in the second group.

$$3x\left(x-3\right)+11\left(x-3\right)$$

Factor out common term x-3 by using distributive property.

$$\left(x-3\right)\left(3x+11\right)$$