How do you factor 40y^2+y-6? Explain the steps please? I am very confused!
5y * 8y
-3 *2
(5y + 2)(8y - 3)
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Factoring a quadratic expression involves finding two binomials whose product is equal to the given expression. In order to factor the expression 40y^2 + y - 6, follow these steps:
Step 1: The general form of a quadratic expression is ax^2 + bx + c. In this case, a = 40, b = 1, and c = -6.
Step 2: Multiply the values of a and c, which is 40 * (-6) = -240.
Step 3: Find two numbers that have a product of -240 and a sum of b, which is 1. In this case, the numbers are -15 and 16. (-15 * 16 = -240 and -15 + 16 = 1)
Step 4: Use these two numbers to rewrite the middle term of the original expression. Split the middle term of the quadratic expression into two terms using the two numbers found in the previous step. Rewrite the expression as follows:
40y^2 - 15y + 16y - 6
Step 5: Factor by grouping. Group the terms together in pairs by common factors and factor out the greatest common factor from each group:
(40y^2 - 15y) + (16y - 6)
Step 6: Factor the greatest common factor from each group. The greatest common factor of the first group is 5y, and for the second group, the greatest common factor is 2:
5y(8y - 3) + 2(8y - 3)
Step 7: Notice that both groups now share a common factor, which is (8y - 3). Factor out this common factor:
(5y + 2)(8y - 3)
Step 8: The factored form of the expression 40y^2 + y - 6 is (5y + 2)(8y - 3).
By following these steps, you can factor the given quadratic expression.