Can someone please tell me Why is (4x + 5) (2x - 1) + (x - 9) (2x - 1) not in factored form? What is the correct final factored form? What is this factoring method called?
If it is in factored form, it should have a common factor for the whole expression.
(4x+5) is not a factor for the whole expression, just the first term (before the + sign).
To factor "completely", we need to expand the expression, collect similar terms and factor from there.
(4x + 5) (2x - 1) + (x - 9) (2x - 1)
=8x²+6x-5 + 2x²-19x+9
=10x²-13x+4
=(5x-4)(2x-1)
Or, note that (2x-1) is a common factor, so if you factor it out, you get
(2x-1)(4x+5 + x-9) = (2x-1)(5x-4)
Thanks, Steve!
To determine why (4x + 5)(2x - 1) + (x - 9)(2x - 1) is not in factored form, let's simplify it first.
(4x + 5)(2x - 1) + (x - 9)(2x - 1)
To simplify this expression, we can use the distributive property.
First, distribute (4x + 5) to both terms inside the second parentheses:
(4x + 5)(2x - 1) + (x - 9)(2x - 1)
= (8x^2 - 4x + 10x - 5) + (2x^2 - x - 18x + 9)
Simplifying further:
= 8x^2 + 6x - 5 - 16x^2 -19x + 9
= -8x^2 - 13x + 4
Now that we have simplified the expression, we can see that it is not in factored form. In factored form, the expression would be written as a product of two or more factors, usually using parentheses.
To find the correct final factored form of -8x^2 - 13x + 4, we need to factor it. The factoring method used here is called factoring by grouping.
Let's first look for pairs of terms that we can factor out.
The first two terms, -8x^2 and -13x, have a common factor of -x.
-8x^2 - 13x = -x(8x + 13)
The last two terms, - 13x and 4, don't have a common factor.
So, the final factored form of -8x^2 - 13x + 4 is -x(8x + 13) + 4.
And this factoring method, factoring by grouping, is used to factor expressions by grouping them into pairs and finding common factors.