Question

If the polynomial 6x6 – 4x5 + 9x – 6 is to be factored by grouping, which step should be taken?

Answer 1

To factor the given polynomial by grouping, students need to follow a step-by-step process.

Step-by-step explanation:

To factor the polynomial 6x6 - 4x5 + 9x - 6 by grouping, the following step should be taken:

1. Step 1: Group the terms in pairs.
2. Step 2: Find the greatest common factor (GCF) for each pair of terms.
3. Step 3: Factor out the GCF from each pair of terms.
4. Step 4: Factor out the remaining common factor from the factored pairs.
5. Step 5: Combine the factored pairs.

Answer 2

I think you're trying to say 6x^6-4x^5+9x-6. ^ Is a symbol that means the number after it is an exponent.
First step, find the gcf (greatest common factor) between the first two parts. The gcf of 6x^6-4x^5 is 2x^5.
Now take it out. You get
2x^5(3x-2)
If you expand that equation, you will get 6x^6-4x^5 which is why you know it's correct.
Now do the same for the second half.
The gcf for the second two parts is 3.
3(3x-2)
Notice anything? Yep, in both of them, after you take out the gcf, you get (3x-2)
Now, you combine them into one equation
2x^5(3x-2)+3(3x-2)
Then you do this
(2x^5+3)(3x-2)
That's your factored form.