Polynomials are expressions whose exponents are non-negative integers and the coefficients are real numbers. The leading term is the term with the highest power. The coefficient of the leading term is the leading coefficient. The power of x in the leading term is called the degree of the polynomial! Here are some examples of polynomials:
Degree Name Example
0 constant 11
1 linear 4x + 7
2 quadratic 3x2 + 4x + 5
3 cubic 4x3 + 3x + 7
4 quartic 3x4 + 2x2 + 4
5 quintic x5 + 3x + 1
Any value of x such that P(x) = 0 is a root of the equation and a zero of the function.
Review of synthetic substitution
To use synthetic substitution, do the following:
1) Write the polynomial in descending order.
2) Make sure any missing terms are replaced with zero!
3) Bring down the leading coefficient.
4) Multiply by the divisor and add to the next term.
5) Repeat the process until the last coefficient is reached.
Example
Use synthetic division to find P(2) for P(x) = 2x3 - 9x2 + 27
2| 2 -9 0 27
4 -10 -20
2 -5 -10 7 The value of P(2) = 7, the last number!!
Sample Problems
1) State whether each is a polynomial function. If yes, find the degree and the zeros.
Problem Polynomial? Degree zeros
a) f(x) = 5 - 4x yes 1 5/4
b) f(x) = 3x2 - 6x yes 2 0, 2
c) f(x) = x - 3/x no
d) f(x) = 18 yes 0 none
e) f(x) = (x-3)/(x+2) no
2) Use synthetic substitution to find P(3) for each function:
a) P(x) = 4x3 - 5x2 + 3
3| 4 -5 0 3
12 21 63
4 7 21 66
Therefore, P(3) = 66
b) P(x) = 3x4 + 2x3 - 5x - 2
3| 3 2 0 -5 -2
9 33 99 282
3 11 33 94 280
Therefore, P(3) = 280
3) If 4 is a zero of f(x) = 3x3 + kx - 2, find the value of k.
Since 4 is a zero, the value of f(4) = 0. Use synthetic substitution.
4| 3 0 k -2
12 48 192 + 4k
3 12 48 + k 190 + 4k
Now 190 + 4k = 0, solve for k
4k = -190
k = -190/4 = -47.5
The answer is b hopefully I helped
The solution to the inequality 
is 
The number line is shown in figure attached.
Step-by-step explanation:
We need to solve the inequality:
Solving the inequality:
Divide by 3 and divide by 12
So, value of x can be less than equal to -4 or value of x is greater than equal to 3.
The number line is shown in figure attached.
The solution to the inequality is
Keywords: Solving inequalities
Learn more about Solving inequalities at:
#learnwithBrainly
Answer: 13%
Step-by-step explanation:
Given : A piece of luggage sells for $225.00 it is on sale this week for $195.00 .
Decrease in price = $225.00-$195.00= $30.00
Formula to find the percent decrease :-
![\dfrac{\text{Decrease in price}}{\text{Previous price}}\times100\\\\=\dfrac{30}{225}\times100=13.3333333333\approx13\%\ \ [\text{Rounded to the nearest whole percent.}]](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7BDecrease%20in%20price%7D%7D%7B%5Ctext%7BPrevious%20price%7D%7D%5Ctimes100%5C%5C%5C%5C%3D%5Cdfrac%7B30%7D%7B225%7D%5Ctimes100%3D13.3333333333%5Capprox13%5C%25%5C%20%5C%20%5B%5Ctext%7BRounded%20to%20the%20nearest%20whole%20percent.%7D%5D)
Hence, the percent decrease = 13%
