•I am having trouble figuring out this question. Why is (3x + 5) (x - 2) + (2x - 3) (x - 2) not in factored form? Show specifically how to find the correct final factored form. What is this factoring method called?
Please help. Thank you.
(x-2) is common in both terms so you can take that out as a factor.
(3x + 5) (x - 2) + (2x - 3) (x - 2) is partially factored
to finish ...
= (x-2)(3x+5 + 2x-3)
= (x-2)(5x+2)
What I got waas (x-2)(5x+2). Is this right? What would I call this method? Is it distribution?
To determine if (3x + 5)(x - 2) + (2x - 3)(x - 2) is in factored form, we need to check if any common factors can be extracted from the expression.
Let's start by factoring out the common factor (x - 2) from both terms:
(3x + 5)(x - 2) + (2x - 3)(x - 2)
= (x - 2)(3x + 5 + 2x - 3)
Now, let's combine like terms inside the parentheses:
= (x - 2)(5x + 2)
The expression (3x + 5)(x - 2) + (2x - 3)(x - 2) is not in factored form because there is a common factor, (x - 2), that can be extracted.
The factoring method used in this process is called factoring by grouping. This method involves grouping terms with common factors and factoring out these common factors from each group. This helps simplify the expression and rewrite it in factored form.