What the r the factors of this expression. 4(5b-3)^2+10(5b-3)-6. plz explain all steps to this answer and thanks :)
let 5b-3 = x, then we have
4x^2 + 10x - 6
= 2(2x^2 + 5x - 3)
= 2(x+3)(2x-1)
replace x with 5b-3 within each bracket , then simplify
So is the final answer 2(5b)(10b-4) then ?
(10b)(10b-7)
To find the factors of the given expression 4(5b-3)^2 + 10(5b-3) - 6, we can follow these steps:
Step 1: Identify the common factor
In the given expression, all the terms have a common factor of (5b-3). Let's factor it out:
Common factor: (5b-3)
Step 2: Divide each term by the common factor
Now, divide each term by the common factor (5b-3):
4(5b-3)^2 / (5b-3) + 10(5b-3) / (5b-3) - 6 / (5b-3)
Simplifying, we get:
4(5b-3) + 10 - 6 / (5b-3)
Step 3: Simplify the expression
Expand the expression 4(5b-3):
20b - 12 + 10 - 6 / (5b-3)
Combine like terms:
20b - 2 / (5b-3)
So, the factored form of the given expression is:
(5b-3)(20b - 2) / (5b-3)
Step 4: Simplify further
Since we have a common factor of (5b-3), we can cancel it out:
(20b - 2)
Therefore, the factors of the expression 4(5b-3)^2 + 10(5b-3) - 6 are (5b-3) and (20b-2).
Note: It is important to be cautious with dividing by common factors, as it may result in "undefined" values if the common factor equals zero. In this case, (5b-3) should not equal zero for the factoring to be valid.