Factor: 2x^2 - 5x + 2
am confused with this problem?
What method has been taught to you?
This one is really easy
look at the front, you know it has to be
(x ....)(2x....)
look at the end, you know it has to be
(.... -2)(.... -1) or (.... +2)( ..... +1)
but the middle is - , so they must both end with a negative
how about
(2x - 1)((x-2) , yup, that works.
multiply the term on the left with the term on the right.
In this problem,
2*2
That will give you 4.
Now you need to find two numbers that will multiply to 4, and also add to equal the middle number.
In this problem the middle number is 5.
So, we need two numbers that multiply to equal 4 and also add to equal 5.
The two numbers that come to mind are 4 and 1.
Now we break the problem into two parts while substituting the 4 and 1 into the problem for the middle term (5x).
doing this, we obtain:
(2x^2+4x) and (1x+2)
Notice that we can factor something out of each of these two expressions.
(2x^2+4x)
Here, we can pull out a 2x
(1x+2)
Here, we can pull out a 1
Notice how when we factor out these two numbers, our two expressions are equal.
(2x^2+4x) turns into 2x(1x+2)
(1x+2) turns into 1(1x+2)
For these problems you will always have two factors. The first will be the numbers left in the parenthesis, (1x+2), the second will be the sum of the numbers we pulled out (2x+1).
The answer is
(1x+2) and (2x+1)
Correction*
The middle number is -5 and so the factors will have - signs rather than + signs
If you need extra help, I would suggest going to Dogpile search engine and typing in your equation. A ton of good math sites popped up. :-)
To factor the quadratic expression 2x^2 - 5x + 2, we can use the factoring method.
Step 1: Look at the coefficients in the expression: 2, -5, and 2.
Step 2: Multiply the leading coefficient (2) by the constant term (2): 2 * 2 = 4.
Step 3: Find two numbers that add up to the middle term (-5) and multiply to give the product of the leading coefficient and the constant term (4). In this case, the two numbers are -4 and -1, since -4 + (-1) = -5 and (-4) * (-1) = 4.
Step 4: Rewrite the middle term (-5x) using the two numbers found in the previous step (-4 and -1).
2x^2 - 4x - x + 2
Step 5: Group the terms into two pairs and factor out the greatest common factor (GCF) from each pair.
(2x^2 - 4x) + (-x + 2)
2x(x - 2) - 1(x - 2)
Step 6: Notice that the terms inside the parentheses are the same, which means that we can factor out the common factor (x - 2).
(2x - 1)(x - 2)
Therefore, the factored form of 2x^2 - 5x + 2 is (2x - 1)(x - 2).