Question

Help! Algebra! please answer if you only know! and make it undertanding!

Answer 1

1. a)
`-6 x^(4) + 4 x^(2) +2` Just write the terms in descending order from left to right( largest exponents to smallest exponents)

1. b) The polynomial is of degree 4. The degree of a polynomial is determined by the term with the highest exponent.

1. c) The polynomial is a trinomial, meaning it has 3 terms. Terms of an expression are separated by + or - signs not found within ( )'s..

2. a) Since the value of coefficient of the leading term is negative and we have an odd function, the end behavior would be as follows:

x → -∞ f(x) → ∞
x → ∞ f(x) → -∞

2 b) Rewriting the expression in standard form we would see the leading term is
`-3 x^(4)` Note the leading coefficient is negative and the function is even. As such, the end behaviors will be:

x → -∞ f(x) → -∞
x → ∞ f(x) → -∞

3. One example could be: y = (x+2)(x-2)(x-1)
=
`( x^(2) - 4)(x - 1)`
=
`x^(3) - x^(2) - 4x + 4`

4. The zeros of the function are 3,2, and -7 having multiplicities of 1,2, and 3 respectively. Note, the multiplicities are just the exponents of the binomial factors of the function. As a side note, the multiplicities will determine whether you have a bounce or wiggle at the zeros of the function when sketching the graph. Bounce on even multiplicities and Wiggle on odd..

Answer 2

1. a. Pretty much, you just have to rearrange it so that the highest power is in the front. So, here's your answer:

`-6x^4+4x^2+2`
b. It's a 4th-degree polynomial. A degree means that "what's the highest power?"
c. It's a trinomial. It has 3 terms, hence it's a trinomial.

2. a. Since it's an odd power and a negative coefficient, it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→∞
b. The degree is even and the coefficient is negative, so it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→-∞

3. a. This basically means that if you solve for x, you should get -2, 1, and 2. So, to do this, you can just write it in factored form and multiply inwards using any method of your choice (remember that in the parentheses, you should get the above value if you solve for x):

`f(x) = (x-2)(x+2)(x-1)`
If you multiply it out, you get (also your answer):

`x^3-x^2-4x+4`

4. The zeros are at x = 3, 2 and -7. Multiplicity of 3 is 1, for 2 it's 2, and for -7 it's 3.

Hope this helps!