Solve (5x^2-3x+4)+(6x-3x^2-3)

$$( 5 x ^ { 2 } - 3 x + 4 ) + ( 6 x - 3 x ^ { 2 } - 3 )$$

Evaluate

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

Solution Steps

Combine -3x and 6x to get 3x.

$$5x^{2}+3x+4-3x^{2}-3$$

Combine 5x^{2} and -3x^{2} to get 2x^{2}.

$$2x^{2}+3x+4-3$$

Subtract 3 from 4 to get 1.

$$2x^{2}+3x+1$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$2x^{2}+3x+1$$

Factor the expression by grouping. First, the expression needs to be rewritten as 2x^{2}+ax+bx+1. To find a and b, set up a system to be solved.

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

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

$$a=1 b=2$$

Rewrite 2x^{2}+3x+1 as \left(2x^{2}+x\right)+\left(2x+1\right).

$$\left(2x^{2}+x\right)+\left(2x+1\right)$$

Factor out x in 2x^{2}+x.

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

Factor out common term 2x+1 by using distributive property.

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