factor the expression 2x^2+5x-22
To factor the expression 2x^2 + 5x - 22, we can use the factoring method.
Step 1: Multiply the coefficient of the quadratic term (2) by the constant term (-22).
2 * -22 = -44
Step 2: Find two numbers whose product is -44 and whose sum is the coefficient of the linear term (5).
The two numbers are -11 and 4, because -11 * 4 = -44 and -11 + 4 = -7.
Step 3: Rewrite the expression using the two numbers found in step 2.
2x^2 - 11x + 4x - 22
Step 4: Group the terms in pairs and factor out the greatest common factor from each pair.
(x is the greatest common factor in the first pair and 2 is the greatest common factor in the second pair)
(x(2x - 11) + 2(2x - 11))
Step 5: Notice that the (2x - 11) term is common to both groups. Factor out (2x - 11) from both pairs.
(2x - 11)(x + 2)
Therefore, the factored form of the expression 2x^2 + 5x - 22 is (2x - 11)(x + 2).
To factor the expression 2x^2 + 5x - 22, we need to find two binomials that, when multiplied together, result in this expression.
Step 1: Multiply the coefficient of the quadratic term (2) with the constant term (-22). In this case, 2 * -22 = -44.
Step 2: We need to find two numbers that add up to the coefficient of the linear term (5) and multiply to give us -44. Let's break it down:
-1 * 44 = -44
-2 * 22 = -44
-4 * 11 = -44
Step 3: Among these options, we need to choose the pair that adds up to 5, the coefficient of the linear term. In this case, -4 + 11 = 7.
So, we can rewrite the expression as (2x - 4)(x + 11).