Solve 4x+3*1-2xdiv2x+2

$$4x+3 \times 1-2x \div 2x+2$$

Evaluate

$$-\left(x-5\right)\left(x+1\right)$$

Solution Steps

Multiply 3 and 1 to get 3.

$$4x+3-\frac{2x}{2}x+2$$

Cancel out 2 and 2.

$$4x+3-xx+2$$

Multiply x and x to get x^{2}.

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

Add 3 and 2 to get 5.

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

Factor

$$-\left(x-5\right)\left(x+1\right)$$

Solution Steps

Multiply and combine like terms.

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

Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx+5. To find a and b, set up a system to be solved.

$$a+b=4 ab=-5=-5$$

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. The only such pair is the system solution.

$$a=5 b=-1$$

Rewrite -x^{2}+4x+5 as \left(-x^{2}+5x\right)+\left(-x+5\right).

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

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

$$-x\left(x-5\right)-\left(x-5\right)$$

Factor out common term x-5 by using distributive property.

$$\left(x-5\right)\left(-x-1\right)$$