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Chapter 6: Q. 232 (page 604)

Maribel factored y2-30y+81as (y-9)2. Was she right or wrong? How do you know?

Short Answer

Expert verified

The factors maribel found are wrong and the correct factors arey-27y-3

Step by step solution

01

Step 1. Given Information

The given expression isy2-30y+81

02

Step 2. Explanation

We will use perfect square trinomial pattern that is using the pattern (a-b)2

The first and last terms of trinomial y2-30y+81are perfect squares that is,

y2=y2=a81=92=b

Now, we will check the middle term,

2ab=2y脳9=18y

Here middle term is not equal to the given middle term. Thus, the binomial square pattern does not fits the trinomial.

03

Step 3. Calculation

The given trinomial is of the form ax2+bx+c. By comparing it with the given expression, we get, a=1,b=-30,c=81

Now, we will use the middle term splitting method to find the correct factors.

y2-30y+81=y2-27y-3y+81=y(y-27)-3(y-27)=(y-3)(y-27)

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