I'm so lost on this math Hw it's over factoring variables and I don't get it. Like my teach said that we are supposed to have the number and letter in front of everything.
For example:
-14x^2-7x+21
For factoring I got 7x(-2x-1+3)
Because my teacher told me to to combine both 7 and x. It doesn't come out equally but I'm supposed to have it that way
I did this a few minutes ago
here again
-7 ( 2x + 1 - 3)
-7 (2x+3)(x-1)
But it's supposed to equal to the original equation
It is
(2x +3)(x-1) = 2 x^2 + 1 x - 3
-7 ( 2 x^2 + 1 x - 3)
= -14 x^2 - 7 x + 21
Factoring can be a tricky concept to grasp at first, but I'll help you understand it step by step.
To factor an expression, we want to rewrite it as a product of two or more simpler expressions. In the given example, -14x^2 - 7x + 21, we need to find two expressions that, when multiplied together, yield the original expression.
Here's the process to factor this expression:
Step 1: Find the greatest common factor (GCF) of all terms, if possible. In this case, the GCF is 7.
Common factorizing the GCF, we get:
7(-2x^2 - x + 3)
Step 2: Now we need to factor the quadratic expression (-2x^2 - x + 3). To factor a quadratic expression, we look for two binomials in the form (ax + b)(cx + d) that can multiply together to give the quadratic.
In order to factor the quadratic expression, we need to find two numbers whose product is ac (the coefficient of x^2, which is -2) and whose sum is b (the coefficient of x, which is -1).
We can easily see that -2 and 1 satisfy these conditions, as -2 * 1 = -2 and -2 + 1 = -1.
Therefore, we can rewrite -2x^2 - x + 3 as follows:
7(-2x^2 - x + 3) = 7(-2x + 1)(x - 3)
So, the fully factored form of the expression -14x^2 - 7x + 21 is:
-14x^2 - 7x + 21 = 7(-2x + 1)(x - 3)
It's important to combine like terms and follow certain rules while factorizing, but it seems like you might have made a slight mistake in combining the terms. Remember, when combining terms, we must preserve the correct coefficients and variables in each term.