Factor the given polynomial: 3y2+5y-8
the 2 is an exponent...
To factor the given polynomial 3y^2 + 5y - 8, we can follow these steps:
Step 1: Check for common factors (if any).
In this case, there are no common factors among the coefficients (3, 5, and -8).
Step 2: Check for any potential grouping.
Since there is no obvious grouping pattern, we move to the next step.
Step 3: Identify the two numbers whose product is the product of the coefficient of the quadratic term (3) and the constant term (-8), which is -24. Additionally, the sum of these two numbers should be equal to the coefficient of the linear term (5).
After some trial and error or by using the quadratic formula, we find that the numbers are 8 and -3. Therefore, 8 * -3 = -24, and 8 + (-3) = 5.
Step 4: Rewrite the middle term (5y) using the two numbers found in Step 3.
By replacing the coefficient of the linear term (5y) with the sum obtained in Step 3 (8 - 3), the expression becomes:
3y^2 + 8y - 3y - 8
Step 5: Group the terms and factor them by grouping.
Rearranging the expression by grouping the terms, we get:
(3y^2 + 8y) - (3y + 8)
Step 6: Factor out the greatest common factor (GCF) from each group.
Factoring out the GCF from each group yields:
y(3y + 8) - 1(3y + 8)
Step 7: Factor out the common binomial factor.
Since we have a common binomial factor (3y + 8) in both terms, we can factor it out:
(3y + 8)(y - 1)
Therefore, the factored form of the given polynomial 3y^2 + 5y - 8 is (3y + 8)(y - 1).