Question

5.
Classify the following polynomials as linear.
quadratic and cubic polynomials. 7x^3+5x ^2+8
root 7x ^2+9
​

Answer 1

Answer:

Step-by-step explanation:

3x4-4x3-5x2-1)+(7x4-6x3-7x2-8)  

Final result :

 10x4 - 10x3 - 12x2 - 9

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((((3•(x4))-(4•(x3)))-(5•(x2)))-1)+((((7•(x4))-(6•(x3)))-7x2)-8)

Step  2  :

Equation at the end of step  2  :

 ((((3•(x4))-(4•(x3)))-(5•(x2)))-1)+((((7•(x4))-(2•3x3))-7x2)-8)

Step  3  :

Equation at the end of step  3  :

 ((((3•(x4))-(4•(x3)))-(5•(x2)))-1)+(((7x4-(2•3x3))-7x2)-8)

Step  4  :

Equation at the end of step  4  :

 ((((3•(x4))-(4•(x3)))-5x2)-1)+(7x4-6x3-7x2-8)

Step  5  :

Equation at the end of step  5  :

 ((((3•(x4))-22x3)-5x2)-1)+(7x4-6x3-7x2-8)

Step  6  :

Equation at the end of step  6  :

 (((3x4 -  22x3) -  5x2) -  1) +  (7x4 - 6x3 - 7x2 - 8)

Step  7  :

Checking for a perfect cube :

7.1    10x4-10x3-12x2-9  is not a perfect cube

Trying to factor by pulling out :

7.2      Factoring:  10x4-10x3-12x2-9  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -12x2-9  

Group 2:  10x4-10x3  

Pull out from each group separately :

Group 1:   (4x2+3) • (-3)

Group 2:   (x-1) • (10x3)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

7.3    Find roots (zeroes) of :       F(x) = 10x4-10x3-12x2-9

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  10  and the Trailing Constant is  -9.

The factor(s) are:

of the Leading Coefficient :  1,2 ,5 ,10

of the Trailing Constant :  1 ,3 ,9

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -1.00      

     -1       2        -0.50        -10.13      

     -1       5        -0.20        -9.38      

     -1       10        -0.10        -9.11      

     -3       1        -3.00        963.00      

Note - For tidiness, printing of 19 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result :

 10x4 - 10x3 - 12x2 - 9

Processing ends successfully

Answer 2

Answer:

7x^3 + 5x^2 + 8 => Cubic polynimial

√7x^2+9 => Quadratic polynomial