How do you factor 2w^2+11w-30 ???
(2w-15)(w+2)
If you rewrite the expression as:
2w(w-2)+15(w-2)
You can factor out (w-2) as a common factor and get the final answer.
To factor the quadratic expression 2w^2 + 11w - 30, we need to find two binomials whose product is equal to this expression.
Step 1: Multiply the coefficient of the quadratic term (2) by the constant term (-30). In this case, it will be (2)(-30) = -60.
Step 2: Find two numbers whose product is -60 and whose sum is equal to the coefficient of the linear term (11). In this case, the numbers are 15 and -4, because 15 × -4 = -60 and 15 + (-4) = 11.
Step 3: Rewrite the quadratic expression by splitting the linear term using the numbers found in Step 2. We have: 2w^2 + 15w - 4w - 30.
Step 4: Group the terms and factor out the greatest common factor (GCF) from each group. We have: (2w^2 + 15w) - (4w + 30).
Step 5: Factor out the GCF from each group. We have: w(2w + 15) - 2(2w + 15).
Step 6: Notice that the terms inside the parentheses are the same. Factor out the common binomial: (w - 2)(2w + 15).
Therefore, the factored form of the expression 2w^2 + 11w - 30 is (w - 2)(2w + 15).