Factor the polynomial below.
x2 - 10x + 9
(x-9)(x-1)
To factor the polynomial x^2 - 10x + 9, you need to find two binomials that, when multiplied together, result in the given polynomial.
Step 1: Look at the coefficient of the squared term (x^2) which is 1.
Step 2: Identify two numbers that multiply to give the constant term (9) and add up to the coefficient of the linear term (-10).
In this case, the numbers are -1 and -9 since -1 * -9 = 9 and -1 + (-9) = -10.
Step 3: Rewrite the middle term (-10x) using these two numbers.
x^2 - 1x - 9x + 9
Step 4: Group the terms and factor out the greatest common factor (if it exists).
(x^2 - 1x) - (9x - 9)
Step 5: Factor out the common terms from each group.
x(x - 1) - 9(x - 1)
Step 6: Notice that (x - 1) is a common factor, so factor it out.
(x - 1)(x - 9)
Therefore, the factored form of the polynomial x^2 - 10x + 9 is (x - 1)(x - 9).