How do you factor the expression 25y^2- 52y + 27?

2 Answers
May 21, 2018

(25y-27)(y-1)

Explanation:

We need to find the factors that when multiplied it gives 675 (25 xx 27) and when added it gives -52.

Multiplying:
675 = 3xx3xx3xx5xx5 = 27 xx 25

Adding:
-52 = -27-25
Hence, -27 xx -25 = 675

So the factors are: -27 and -25

25y^2-52y+27

25y^2-25y-27y+27

25y(y-1)-27(y-1)

(25y-27)(y-1)

Check the answer:
(25y-27)(y-1)
(25yxxy)-25y-27y+27
25y^2-52y+27

May 21, 2018

25y^2-52y+27 = (y-1)(25y-27)

Explanation:

Given:

25y^2-52y+27

Note that 25-52+27 = 0

Hence y=1 is a zero and (y-1) a factor.

The leading term of the other factor must be 25y to get 25y^2 in the product and the trailing term must be -27 in order to get +27 in the product.

So we find:

25y^2-52y+27 = (y-1)(25y-27)