POLYNOMIALS : Factors and Zeroes of Polynomials

Example 1

A polynomial P  is  given as  P(x) = x^3- 2x^2 -5x + 6.  

(a) Show that  x = 1, x=-2 and x=3 are zeroes of P(x). 

(b) Express P(x) as the product of linear factors;

Happy trying

Hafsah

POLYNOMIAL

Answer  the following.

1.  A polynomial P is defined as P(x) = 9x^3 + 18x^2-x-2. Show that  x+2 is a factor of P(x). Hence, factorise P(x) and find the solution set for P(x)>0.                                                                           (8 m)

Happy trying dear.... 

Pn Hafsah

Polynomial

           

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hafsah_hbo@yahoo.com

Polynomials

Answer the following:


Given that P(x)=2x^3-7x^2-2x+7. Show that x+1 is a factor of P(x).

Hence,

(a) find all factors of P(x)

(b) solve P(x)=0

(c) find the set solution for P(x)>0.


Happy Trying !

Hafsah

POLYNOMIAL

nswer all of the following

1. Given that a polynomial P(x) =4x^3-8x^2-x+2.

(a) Show that x-2 is a factor of P(x)

(b) Factorise P(x)

(c) Find the zeroes of P(x)

(d) Find the solution set for P(x) > 0


2. Express (8x+4)/(x^2+2x-3) as partial fractions.


Happy trying! Email me your answer!

POLYNOMIAL

Answer all of the following

1. Given that a polynomial P(x) = x^3-6x^2+11x-6.

(a) Show that x-1 is a factor of the polynomial.

(b) Hence, factorise P(x) and solve P(x)=0


2. Given that f(x) = (x-2)/(x+1)(2x-1).
Find the set of values for f(x)<0.


3. Express 1/((x+2)(x-3)) in partial fractions.

4. Express (x^2-x+5)/((x^2+x-2) in the form A + B/(x+2)+c/(x-1).

Email me your answer at huffy64@gmail.com

Modulus

Modulus of x is written as |x|. It is defined as x if x > 0 or -x if x < 0.
If |x| = b then x = b or x=-b for any real number.
If |x| < b then -b < x < b
If |x| > b then x <-b or x >b

Try the following question.

1. Find the value of x for the following modulus equation.

(a) |x| =3

(b) |3x| = 12

2. Solve the following inequalities and express your answer in an interval notation.

(a) |x| < 5

(b) |x| > 2

(c) |x-1| > 6

(d) |2x+3| > 2

(e) |2-x| > 7

Polynomials

Answer all of the following.

1. A polynomial P(x)= 2x³ +3x²-2x-3

(a) Find P(2), P(-1)

(b) Determine if x-1 is a factor.


2. Given that a polynomial P(x) = x³ +2x² -7x+4.

(a) If x+4 is a factor of P(x), find the other two factors,

(b) Find the set of values of x for which P(x)>0


Happy trying email to huffy64@gmail.com