I nee help with algebra

Question

How to solve polynomials and simplify them Please show example and everything for subtracting and adding them and multiplying them Please help me

Answer 1

Solving polynomials greater than quadratics is actually quite difficult and not something one will likely have to do aside from special cases where the polynomial can be reduced to a quadratic.

A quadratic is an equation of the form ax²+bx+c=0, and as you may or may not know can be solved by the following formula: x=(-b±√(b²-4ac))/2a.

Adding and subtracting polynomials is quite simple, as it just involves combining like terms. For example, say I have two quadratic polynomial functions, p₁(x)=2x²+3x+1 and p₂(x)=x²+4x-2, then p₁(x)+p₂(x)=(2+1)x²+(3+4)x+(1-2)=3x²+7x-1, the same goes for subtracting polynomials.

Multiplying polynomials is a bit more difficult as it involves using FOIL (Front, Outside, Inside, Last) multiplication. For example lets take two simple polynomials, a(x)=x²+1 and b(x)=x³+2.

a(x)*b(x)=(x²+1)(x³+2)=(x²*x³)+(x²*2)+(1*x³)+(1*2)=x⁵+x³+2x²+2

Answer 2

Hi Eulalie! Let's start with adding polynomials. Below is an example of how that will work. Notice that we are adding like terms. The 3x term is combined with the 4x term, the x² term is combined with the 5x² term and the 7 and 8 are added together.

(x² +3x +7) + (5x² +4x +8) = 6x² + 7x +15

Subtracting works very similarly but it important to remember to distribute negative sign to every term of the polynomial that is being subtracted. Let's use the same polynomials as above but this time subtract the 2nd. The second step shows what I mean by distribute the negative sign.

(x² +3x +7) - (5x² +4x +8) = (x² - 5x²) + (3x - 4x) + (7-8) = -4x² -x -1

Lastly, lets look at multiplying polynomials. Every term in the first polynomial must be multiplied by every term in the second and the products are added as shown below. When multiplying two x terms, you add the superscripts (ex: x³ * x⁶ = x⁹). Like we did in the above examples, add/subtract like terms to simplify.

(4x + 2)(5x + 3) = (4x * 5x) + (4x * 3) + (2 * 5x) + (2 * 3) = 20x² +12x +10x + 6 = 20x² + 22x + 6

I hope this helps! Please reach out if you have any follow up questions.

Answer 3

Hi Eulalie. If you are given 7x squared + 4x + 6 - 4x squared - 8, = ?this is what you do.

First, put the highest exponents in front. Here, it would be the monomials with the “squared”. So you would get 7x squared - 4 x squared = 3x squared.

Then look for the “x with no power shown”. (It is really the first power, though). So here 4x is the only “x by itself”, so use that.

Then we look for “numbers only”. So +6 -8 = -2 (You take the smaller number from the larger number, and keep the sign of the larger number).

So our final answer is 3x squared + 4x - 2.

Please consider hiring me as a tutor. When my schedule is full, I won’t have as much time to give these answers.

Answer 4

That's a very broad question that would require someone to write a textbook. I suggest an excellent source of free tutorials on the subject. The Khan Academy has an extensive offering of video tutorials that are clear and interesting. You can go at your own pace and pick the topics you want. Each comes with a transcription and practice questions and tests. And it is free (I donate, however.).

Go to https://www.khanacademy.org/, set up a free account, and head to the "Courses" at the top. This well provide a menu of a wide range of courses. Pick one of the Algebra classes and get started. Khan provides clear instruction and the site will keep track of what lessons you've done and make suggestions for where you should start the next time you log on.

Enjoy.

Bob