Unit 1 Assessment, Part 1 1.(a)Solution

Unit 1 Assessment, Part 1
1.(a)Solution:-f (x) = − 1 /4 x 3 −13 x2 +3x −9
Degree Type of
polynomial
Sign of leading
coefficient
End behaviors Domain
3 Cubic 2 Infinity − 1 /4 x 3 −13 x2
+3x −9
Solution:--
Infinity<x< Infinity
Interval notation :
(-Infinity, Infinity)
1. Degree:- Maximum power of variable x.
2. Types of polynomial:- Depend upon the degree of the polynomial.
If degree= 1 then polynomial is Monomial
If degree= 2 then polynomial is Binomial
If degree= 3 then polynomial is cubic
3. Sign of Level :- No. of sign changes in the equation.
No. of sign changes with different sign from positive to negative.
No. of sign changes = Sign of leading coefficient
4. End Behavior:- That shows the polynomial x- axis goes to end value.
5. Domain:- Range of the polynomial lies is called domain of the polynomial.

1.(b) Solution:-
f (x) = 6x 4 + 7x 2 −8x+9
Degree Type of polynomial Sign of leading
coefficient
End behaviors Domain
4 Quartic 2 Infinity 6x 4 + 7x 2 −8x+9
Solution:-Infinity<x<
Infinity
Interval notation :
(-Infinity, Infinity)
2. Solution :-
f (x) =− ( x−4 ) (x+1) 2 ( x−5 )
x – intercepts and behavior
of graph at each x
intercepts
y − intercept End behaviors
x – intercepts Points:
(4,0),(-1,0),(5,0)
Behavior = Upto Infinity
(0,-20) Infinity

Plotting :-f (x) =−( x−4 ) (x+1) 2 ( x−5 )
3. Solution:-
Equation:-
0 =18 x 4 +87 x 3 +3 x2 −108x
3x(x-1)(3x+4)(2x+9)
3x(x-1)(3x+4)(2x+9)=0
Solve according to zero factor

Case1: X-1 =0
X=1
Case2: 3x+4=0
X= -4/3
Case3: 2x+9=0
X=-9/2
Factors are x=0, 1, -4/3, -9/2
Plotting:-