TYPES OF POLYNOMIALS LINEAR POLYNOMIALS QUADRATIC POLYNOMIALS CUBIC POLYNOMIALS
LINEAR POLYNOMIALS The general form of a linear polynomial is ax+b Quadraticb polynomials The general form of A quadratic polynomial is ax²+bx+c CUBIC POLYNOMIALS THE GENERAL FORM OF A CUBIC POLYNOMIAL IS ax³+bx²+cx+d
FACTORISATION OF POLYNOMIALS
METHOD -1 FACTORISATION BY TAKING OUT THE COMMON FACTORS: • 9x²-6xy • =3.3.x.x-6.x.y • =3x(3x-2y)
METHOD-2 FACTORISATION BY GROUPING THE TERMS: x²+3x+x+3 =(x²+x)+(3x+3) =x(x+1)+3(x+1) =(x+3)(x+1)
METHOD-3 FACTORISATION BY MAKING A PERFECT SQUARE 4x²+12x+9 =(2x)²+2(2x).3+(3)² =(2x+3)²
METHOD-4 FACTORISE THE DIFFERENCE OF TWO SQUARES a²-b²=(a-b)(a+b) 9a²-4b² =(3a)²-(2b)² =(3a+2b)(3a-2b)
METHOD-5 FACTORISATION BY MAKING A PERFECT CUBE
(a+b)³=a³+b³+3ab(a+b) (a-b)³=a³-b³-3ab(a-b)
8x³+y³+12x²y+6xy² =(2x)³+(y)³+3(2x)(y)(2x+y) =(2x+y)³ =(2x+y)(2x+y)(2x+y)
METHOD 6FACTORISING THE SUM AND DIFFERENCE OF CUBES OF TWO QUANTITIES
a³+b³=(a+b)(a²-ab+b²) a³-b³=(a-b)(a²+ab+b²)
8x³+27y³ =(2x)³+(3y)³ =(2x+3y)[(2x)²-(2x)(3y)+(3y)²] =(2x+3y)(4x²-6xy+9y²)
METHOD 7FACTORISATION OF THE QUADRATIC POLYNOMIAL BY SPLITTING THE MIDDLE TERM:
x²+14x+45 AS,5+9=14 and 5.9=45 x²+14x+45 =x²+5x+9x+45 =(x²+5x)+(9x+45) =x(x+5)+9(x+5) =(x+5)(x+9)
THIS PRESENTATION IS PREPARED BY Mr.Harish Kumar OF GOVT. GIRLS. SEC. SCHOOL, PUTLIGHAR