How do you factor by grouping: #3x^2 + 3 + x^3 + x#?

Answer 1

The factored form of the expression is #(x^2+1)(x+3)#.

First, rearrange the terms. Then, factor #x^2# out from the first two terms and #1# out from the last two terms. Lastly, combine the two factors to get an answer:
#color(white)=3x^2+3+x^3+x#
#=x^3+3x^2+x+3#
#=color(red)(x^2)*x+color(red)(x^2)*3+x+3#
#=color(red)(x^2)(x+3)+x+3#
#=color(red)(x^2)(x+3)+color(blue)1*x+color(blue)1*3#
#=color(red)(x^2)(x+3)+color(blue)1(x+3)#
#=(color(red)(x^2)+color(blue)1)(x+3)#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

This does it: #(x+3)(x^2 + 1)#

I am not sure about the "by grouping" method, but I stumbled on a way to factor that expression.

I noticed that it could be written #3*(x^2 +1) + x*(x^2 +1)#.

From there I put the 3 and the x inside a second set of parentheses and saw that

#3x^2 + 3 + x^3+ x = (3+x)(x^2 + 1)#
So #(3+x)and(x^2 + 1)# are the factors.
A preferable way to write it would probably be #(x+3)(x^2 + 1)#.

I hope this helps, Steve

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To factor by grouping, we first group the terms into pairs:

(3x^2 + x^3) + (3 + x)

Next, we factor out the greatest common factor from each pair:

x^2(3 + x) + 1(3 + x)

Now, we see that both pairs have a common factor of (3 + x). We can factor this out:

(3 + x)(x^2 + 1)

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7