Factoring Polynomials:
2x to the second power -3x-2
could you please explain to me how to do this.
(-2+x) (1+2x)
can you please explain to me how you got the answer because i have no idea how to do this..
To factor a polynomial, such as 2x^2 - 3x - 2, you can use a method called factoring by grouping. Here's how you do it:
Step 1: Split the middle term
Take the coefficient of the x term, which is -3 in this case, and find two numbers that multiply to give you the product of the coefficient of the x^2 term (2) times the constant term (-2). In this case, the product of 2 and -2 is -4. The two numbers that satisfy this condition are -4 and 1.
Step 2: Rewrite the polynomial
Rewrite the polynomial by splitting the middle term using the two numbers obtained in step 1. This will be:
2x^2 - 4x + x - 2
Step 3: Grouping
Group the terms so you have pairs:
(2x^2 - 4x) + (x - 2)
Step 4: Factor by grouping
Now, factor each pair separately:
2x(x - 2) + 1(x - 2)
Step 5: Common factor
Notice that the terms in parentheses are the same. Factor out the common factor:
(x - 2)(2x + 1)
So, the factored form of the polynomial 2x^2 - 3x - 2 is (x - 2)(2x + 1).