how do you factor 2x^2-3x+1
(-2x+1)(-x+1)
Thank you!
how did you do that?
If you reverse 2x^2-3x+1 to get 1-3x+2x^2, it becomes easier to factor:
F irst terms must multiply to yield 1
O utside and
I nside terms must add to yield -3x
L ast terms must multiply to yield 2x^2
Therefore, the factors must be:
(1-2x)(1-x)
To factor the quadratic expression 2x^2 - 3x + 1, you can use various factoring techniques such as factoring by grouping, using the quadratic formula, or using the trial and error method. In this case, we will use the trial and error method to find the factors of the quadratic expression.
Step 1: Write down the equation in the standard form: 2x^2 - 3x + 1 = 0.
Step 2: Look at the coefficient of x^2, which is 2. We need to find two numbers that multiply to give 2 (coefficient of x^2) and add up to -3 (coefficient of x).
Step 3: Think of pairs of integers that multiply to give 2. The possible pairs are (2,1) and (-2,-1).
Step 4: Test each pair by adding the numbers.
- Pair (2,1): 2 + 1 = 3.
- Pair (-2,-1): -2 + (-1) = -3.
Step 5: Since the pair (-2, -1) adds up to -3, these numbers will be our factors.
Step 6: Express the middle term (-3x) using the factors found in step 5. We can rewrite -3x as (-2x - 1x).
2x^2 - 3x + 1 can be now written as 2x^2 - 2x - 1x + 1.
Step 7: Group the terms in pairs and factor out the greatest common factor from each pair.
2x(x - 1) - 1(x - 1).
Step 8: Notice that (x - 1) is common in both terms. Factor it out.
(x - 1)(2x - 1).
Therefore, the factored form of 2x^2 - 3x + 1 is (x - 1)(2x - 1).