Solve {l}{(5x^2-3x+2)+(7x^2+2x+10)}{-2x^2-5x+12}

$$\left. \begin{array} { l } { ( 5 x ^ { 2 } - 3 x + 2 ) + ( 7 x ^ { 2 } + 2 x + 10 ) } \\ { - 2 x ^ { 2 } - 5 x + 12 } \end{array} \right.$$

Evaluate

$$10x^{2}-6x+24$$

Solution Steps

Combine 5x^{2} and 7x^{2} to get 12x^{2}.

$$12x^{2}-3x+2+2x+10-2x^{2}-5x+12$$

Combine -3x and 2x to get -x.

$$12x^{2}-x+2+10-2x^{2}-5x+12$$

Add 2 and 10 to get 12.

$$12x^{2}-x+12-2x^{2}-5x+12$$

Combine 12x^{2} and -2x^{2} to get 10x^{2}.

$$10x^{2}-x+12-5x+12$$

Combine -x and -5x to get -6x.

$$10x^{2}-6x+12+12$$

Add 12 and 12 to get 24.

$$10x^{2}-6x+24$$

Factor

$$2\left(5x^{2}-3x+12\right)$$

Solution Steps

Multiply and combine like terms.

$$10x^{2}-6x+24$$

Factor out 2. Polynomial 5x^{2}-3x+12 is not factored since it does not have any rational roots.

$$2\left(5x^{2}-3x+12\right)$$