We at **ask-math **believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

**We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.**

**Affiliations with Schools & Educational institutions are also welcome.**

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

a) Find the roots of constant term name them as P.

b) Find the roots of leading coefficient ( term with highest degree) name them as ‘q’.

c) Possible roots are $\pm$ P/q

1) Find the factors of 3x

Factors of 6 =P = 1,2,3,6

Leading coefficient = 3

Factors of 3 = q =1 , 3

Possible factors are p/q = $\pm$ 1,2,3,6,1/3,2/3

Now, use synthetic division with 1

As remainder is 0.

As in synthetic division numbers below are 3, 5 and -2 (three numbers)

So next polynomial will be 3x

Polynomial | 3x^{2} + 5x -2 |

Multiply coefficient of first term and last term | (3) x ( -2) = -6 |

Find the factors of -6 to get the middle term 5 | Factors ---> +6 and -1 |

Write polynomial using these factors | 3x^{2}+ 6x - 1x -2 |

Find the common factors from 1st two terms and last two terms | 3x(x +2)-1(x+2) |

Take common parenthesis as a common factor | Factors are ( 3x-1)(x+2) |

So the total factors of the given polynomial are

_______________________________________________________________

2) Find all possible rational x-intercepts of x

Constant term = 12 ⇒ Factors of 12 = p = 1,2,3,4,6,12

Leading coefficient = q = 1

Possible factors are p/q = $\pm$ 1,2,3,4,6,12

= –12, –6, –4, –3, –2, –1, 1, 2, 3, 4, 6, 12

• Degree of the Polynomial

• Zeros of Polynomial

• Remainder Theorem

• Find remainder by Synthetic Division

• Rational root test in Polynomial

• Solved Examples on Polynomial

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers