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

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