Solve 2a^2-6a-a+3

$$2 a ^ { 2 } - 6 a - a + 3$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$2a^{2}-7a+3$$

Factor the expression by grouping. First, the expression needs to be rewritten as 2a^{2}+pa+qa+3. To find p and q, set up a system to be solved.

$$p+q=-7 pq=2\times 3=6$$

Since pq is positive, p and q have the same sign. Since p+q is negative, p and q are both negative. List all such integer pairs that give product 6.

$$-1,-6 -2,-3$$

Calculate the sum for each pair.

$$-1-6=-7 -2-3=-5$$

The solution is the pair that gives sum -7.

$$p=-6 q=-1$$

Rewrite 2a^{2}-7a+3 as \left(2a^{2}-6a\right)+\left(-a+3\right).

$$\left(2a^{2}-6a\right)+\left(-a+3\right)$$

Factor out 2a in the first and -1 in the second group.

$$2a\left(a-3\right)-\left(a-3\right)$$

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

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

Evaluate

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

Solution Steps

Combine -6a and -a to get -7a.

$$2a^{2}-7a+3$$