Question

Factor the polynomial
r^2-26r+169

Answer 1

(r-13)(r-13)

Answer 2

could you please show some work @genius91

Answer 3

This is a trinomial, so if it's factorable, it will factor into the product of two binomials.
Start by writing two sets of parentheses:
( )( )

Answer 4

On the left side of each parentheses, you need to write what will multiply to r^2. That is r and r, so write it in.
(r )(r )

Answer 5

On the right side of the parentheses, you need to write two numbers that multiply to 169 and add to -26.

Answer 6

Since the numbers must multiply to 169 (a positive number), and they must add to
-26, a negative number, both numbers must be negative. The numbers are -13 and
-13 since (-13)(-13) = 169 and -13 + (-13) = -26. Just fill in the parentheses.
(r - 13)(r - 13)
That's the factorization.
To check, multiply it out using FOIL to be sure you get back to r^2 - 26r + 169.

Answer 7

Thank you so much @mathstudent55 !