ok, I think this is called factoring binomials...

how do you factor
2x^2+3x+1

the example on the page just says: 2x^2+7x+6
the answer given is (2x+3)(x+2)

How do you get that answer?? If there are any websites with additional help that would be great if anyone knows any.

Thanks a bunch!!
Matty

Factoring is a topic that takes up a few lessons in high-school, because there are many different techniques depending on the difficulty of the given expression.

Also it depends on whether you are looking at integer factors, which limits the possible answers.

For a quadratic expression, the sure way (but not the fastest) is to equate it to zero and find the roots of the resulting equation. Convert the roots to factors.

Other techniques include comparison with standard forms, completing the square, examining the possible factors of the constant term and the coefficient of the leading coefficient, etc. You can read about it in many different sites, for example:
http://en.wikipedia.org/wiki/Polynomial_factorization

For the given example, there is a relatively simple way that works only if all the coefficients are positive.
2x^2+3x+1 can be thought of as 231, which has factors of 11 21. So
2x^2+3x+1 = (x+1)(2x+1)

Same for 2x^2+7x+6. Since 276=23*12
we can try:
(2x+3)(x+2)

A check by multiplication is required in both cases.

What is the slope of the line passing through the points (-3, 24) and (10, -41)? Round to the nearest integer if necessary.

To factor the quadratic expression 2x^2 + 3x + 1, you can use a method called "factoring by grouping." Here are the steps to factor this expression:

Step 1: Multiply the leading coefficient (the coefficient of the x^2 term) with the constant term. In this case, the leading coefficient is 2 and the constant term is 1. So, 2 * 1 = 2.

Step 2: Find two numbers that multiply to give you the result from step 1 (2) and also add up to the coefficient of the x term (3). In this example, the numbers are 2 and 1 because 2 * 1 = 2 and 2 + 1 = 3.

Step 3: Rewrite the middle term of the quadratic expression (3x) using the two numbers found in step 2. Therefore, 3x can be written as 2x + 1x.

Now, you have the expression: 2x^2 + 2x + 1x + 1.

Step 4: Group the four terms: (2x^2 + 2x) + (1x + 1).

Step 5: Factor out the greatest common factor from each group. In the first group, you can factor out 2x to get: 2x(x + 1). In the second group, you can factor out 1 to get: 1(x + 1).

Now, you have: 2x(x + 1) + 1(x + 1).

Step 6: Notice that both groups now have a common factor of (x + 1). Factor out this common factor: (x + 1)(2x + 1).

Therefore, the factored form of 2x^2 + 3x + 1 is (x + 1)(2x + 1).

For additional help and practice on factoring binomials, you can check out the following websites:
1. Khan Academy: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-form-quadratic-equations/v/factoring-polynomials-1
2. MathisFun: https://www.mathsisfun.com/algebra/factoring-quadratics.html

These websites provide step-by-step explanations, examples, and practice problems to help you master factoring binomials.