Question

What is the product of the polynomials. (5x^2-2x+4) (2x^2+3x+1)

Answer 1

I got 10x^4-6x^2-4. Is this correct?

Answer 2

No.
The x^3 term and x term are missing, and some therms are incorrect.

Answer 3

How do I get this term?

Answer 4

Multiply every term of the first polynomial by every term of the second polynomial.
After that step, you should have 9 terms.
Then collect like terms.

Answer 5

10x^4+15x^3+5x^2

Answer 6

This is confusing -_-

Answer 7

\( (5x^2-2x+4)(2x^2+3x+1) \)
\(= ~~5x^2 \times 2x^2 + 5x^2 \times 3x + 5x^2 \times 1 \)
\(~~ - 2x \times 2x^2 - 2x \times 3x - 2x \times 1 \)
\(~~ + 4 \times 2x^2 + 4 \times 3x + 4 \times 1\)

Answer 8

Now you do all those multiplications, then you collect like terms.

Answer 9

30^6-12^2+24^2

Answer 10

Is that correct @mathstudent55

Answer 11

No.
Here is the next step after all the multiplications are done.
10x^4 + 15x^3 + 5x^2 - 4x^3 - 6x^2 - 2x + 8x^2 + 12x + 4

Answer 12

Now you need to collect like terms.

Answer 13

22^4+11^3+7x^2.

Answer 14

I only see one term with x^4; it's 10x^4. How do you get 22x^4?

Answer 15

I added all the x^4 up.

Answer 16

Like terms are terms that have the same variable part. That means the same variable and the same exponent.

Answer 17

How can you add all the x^4 terms up if there is only one?

Answer 18

About 12x^4?

Answer 19

10x^4 + 15x^3 + 5x^2 - 4x^3 - 6x^2 - 2x + 8x^2 + 12x + 4
^^^^
only x^4 term is this one, 10x^4

Answer 20

Oh!

Answer 21

That means you start collecting like terms by writing the x^4 term:
10x^4
Now move on to the next lower term, x^3

Answer 22

10x^4+11^3+7x^2+4?

Answer 23

Im confused on the 12x+4.

Answer 24

10x^4 + 15x^3 + 5x^2 - 4x^3 - 6x^2 - 2x + 8x^2 + 12x + 4
^^^^^ ^^^^
x^3 terms are + 15x^3 and - 4x^3.
Collect them together and get: 11x^3, so you write that next:
10x^4 + 11x^3

Answer 25

We'll get there.

Answer 26

10x^4+11x^3+7x^2.

Answer 27

Now we move on to the next lower power of x, x^2. Let's look for all x^2 terms:
10x^4 + 15x^3 + 5x^2 - 4x^3 - 6x^2 - 2x + 8x^2 + 12x + 4
^^^^ ^^^^^ ^^^^^
We collect together 5x^2 - 6x^2 + 8x^2 and we get +7x^2, so we write it next:
10x^4 + 11x^3 + 7x^2

Answer 28

Now that the x^2 terms are done, we move on to the next lower power of x, x to the 1 power, or just plain x.
10x^4 + 15x^3 + 5x^2 - 4x^3 - 6x^2 - 2x + 8x^2 + 12x + 4
^^^ ^^^^
The x terms are -2x + 12x. We add them together and get: 10x.
We write that next:
10x^4 + 11x^3 + 7x^2 + 10x

Answer 29

About the 4?

Answer 30

The last step is the term with no x, called the constant term.
There is only one of them, it's + 4, so we write that last:
10x^4 + 11x^3 + 7x^2 + 10x + 4

Answer 31

That is the final answer.

Answer 32

Thank you so much.

Answer 33

This is what you need to do for all these problems of multiplying polynomials together.