Hello.

Can you explain to me how to factor the following.

30x^2 - 48x

x2 + 6x + 7

on the first, factor out 6x

On the second, are you certain bout the signs? If the 7 is negative, then factors are 7,-1 If the six and seven are both positive, there are no real roots.

Of course! Let's start with factoring the expression 30x^2 - 48x.

To factor the given expression, we need to find the greatest common factor (GCF) of the terms 30x^2 and -48x. In this case, the GCF is 6x because it is the highest common factor that divides both terms evenly.

Now, let's factor out the GCF 6x from each term:
30x^2 - 48x = 6x(5x - 8)

So, the factored form of 30x^2 - 48x is 6x(5x - 8).

Moving on to the second expression x^2 + 6x + 7.

To factor a quadratic trinomial like this, we need to determine two binomials that, when multiplied, give us the original expression.

The first term of each binomial will be x because x multiplied by x gives us x^2.

Now, we need to find two numbers that add up to 6 (the coefficient of the middle term) and multiply to give us 7 (the constant term). In this case, the numbers are +1 and +7.

So, we can rewrite the expression as:
x^2 + x + 7x + 7

Next, we group the terms and factor them by taking out the greatest common factor:
(x^2 + x) + (7x + 7) = x(x + 1) + 7(x + 1)

Notice that we now have a common binomial term, (x + 1), which we can factor out:
= (x + 1)(x + 7)

Therefore, the factored form of x^2 + 6x + 7 is (x + 1)(x + 7).

I hope this explanation helps you understand the process of factoring these expressions! Let me know if there's anything else I can assist you with.