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
Answer:
Brainliest?
'''For an obtuse-angled triangle, the altitude is outside the triangle. For such triangles, the base is extended and then a perpendicular is drawn from the opposite vertex to the base. For an obtuse triangle, the altitude is shown in the triangle below.'''
5integer 0/1 is the mixed fraction of 5 units
Answer:
C.
yes; y = 1.8x
Step-by-step explanation:
Answer for the question :
Yes, Y varies directly with X, and the equation is :
Y = 1.8X
NOTE : For every value of X, when you multiply them with 1.8, you will get the corresponding Y.
Y = 1.8 x X
5.4 = 1.8 x 3
12.6 = 1.8 x 7
21.6 = 1.8 x 12 (Q.E.D.)
That’s the answer, good luck in solving the question!
:-)
ideal all you ought to do is to divide the y via potential of x and u get the equation working occasion #a million y=32 / x=4 then u have y/x=32/4 ----> y=8x and do the comparable indoors something so #2 y=-20 & x=-20 so y/x=-20/-20 y=x etc
Answer:
John must scan at least 863 images before he pays less on his own rather than in the store
Please vote for Brainliest and I hope this helps!
