POLYNOMIALS

POLYNOMIALS

1. A POLYNOMIAL OF ONE TERM IS CALLED MONOMIAL.

2. A POLYNOMIAL OF TWO TERMS IS CALLED BINOMIAL.

3. A POLYNOMIAL OF THREE TERMS IS CALLED TRINOMIAL.

4. 0 - CONSTANT

   • 1 - LINEAR
     • 2 - QUADRATIC
       • 3 - CUBIC
       • 6 - DEGREE OF 6....
     • 5 - QUINTIC
   • 4 - QUARTIC

5. A REAL NUMBER "a" IS SAID TO BE A ZERO OF THE POLYNOMIAL P(x) IF P(a) = 0

6. DIVISION ALGORITHM :- DIVIDENT = DIVISOR * QUOTIENT + REMAINDER

7. REMAINDER THEOREM :- IF F(x) IS A POLYNOMIAL, WHICH IS DIVIDED BY A LINEAR POLYNOMIAL (x - a), THEN THE REMAINDER IS F(a).

8. FACTOR THEOREM :- IF A POLYNOMIAL F(x) IS DIVIDED BY A LINEAR POLYNOMIAL (x - a), THEN IF F(x) = 0, THEN WE SAY (x- a ) IS A FACTOR OF F(x), OTHERWISE NOT.

9. IDENTITY 1 : (x + a) (x + b) = x² + (a + b)x + ab IDENTITY 2 : (a + b)² = a² + 2( a + b) + b² IDENTITY 3 : (a – b)² = a² - 2( a + b) + b² IDENTITY 4 : (x – y) (x + y) = x² - y²

10. IDENTITY 5 : ( x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx IDENTITY 6 : (x + y)³ = x³ + y³ + 3xy(x + y) IDENTITY 7 : (x – y)³ = x³ - y³ - 3xy(x – y) IDENTITY 8 : x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy – yz – zx) IDENTITY 9 : x³ + y³ = (x + y)(x² - xy + y²) IDENTITY 10 : x³ - y³ = (x – y)(x² + xy + y²)