factor (x-3)^2 +10(x-30)+24

To factor the given expression, we need to look for common factors and then apply appropriate factoring techniques.

Given expression: (x-3)^2 + 10(x-30) + 24

Step 1: We can expand the first term, (x-3)^2, using the formula for a binomial squared.

(x-3)^2 = (x-3)(x-3) = x^2 - 3x - 3x + 9 = x^2 - 6x + 9

Now, the expression becomes: x^2 - 6x + 9 +10(x-30) + 24

Step 2: Distribute the 10 into the second term, (x-30).

10(x-30) = 10x - 300

The expression is now: x^2 - 6x + 9 + 10x - 300 + 24

Step 3: Combine like terms.

x^2 - 6x + 9 + 10x - 300 + 24 = x^2 + 4x - 267

Therefore, the factored form of the given expression is: x^2 + 4x - 267