Question

Factor completely. Be sure to factor out the GCF when necessary. Select "Prime" if the polynomial cannot be factored. -y²+12y-27

Answer 1

The quadratic expression -y²+12y-27 can be factored by finding two numbers that multiply to give -45 and add to give 12, which are 15 and -3. Factor by grouping is then used to rewrite and factor the expression to the completely factored form (y-15)(-y-3).

Step-by-step explanation:

The student has asked to factor the quadratic expression -y²+12y-27. First, it is essential to find two numbers that multiply to give the product of the coefficient of the y² term (-1) and the constant term (-27), which is 27, and add up to give the coefficient of the middle term, which is 12. These two numbers are 15 and -3, as 15 * -3 = -45 (note that we need a negative product since the coefficient of y² is negative) and 15 + (-3) = 12.

Next, we can rewrite the middle term (12y) using 15 and -3:

• -y²+15y-3y-27

Now, we will factor by grouping. Group the first two terms together and the last two terms together, and factor out the greatest common factor (GCF) from each group:

• -y(y-15)-3(y-15)

Finally, we see that (y-15) is common to both groups, so we take it out as a factor:

• (y-15)(-y-3)

Thus, the completely factored form of the polynomial is (y-15)(-y-3).