Revision Polynomials
Math Core 1 Revision Chapter 9. Polynomials Brief Info: A polynomial is an expression consisting of a sum of multiples of non-negative integer powers of x. You can add, subtract and multiply polynomials. It is named on the highest power of the polynomial.
Constant-when the degree is zero (0) - (3x0). Linear- when the degree is one (1) - (2x1). Quadratic- when the degree is two (2) - (5x2-2). Cubic- when the degree is three (3) - (4x3+3x2-6x -3). Quartic- when the degree is four (4) - (6x4-3x3+4x2+6x-5) (There are names for some polynomials of higher degree, but it is not worth learning them).
Adding Polynomials m(x) = x3-7x+4
l(x) = 2x2+3x-7
m(x) + l(x) = x3-7x+4 + (2x2+3x-7) m(x) + l(x) = x3+2x2-4x-3
Subtracting Polynomials m(x) = x3-7x+4
l(x) = 2x2+3x-7
m(x) – l(x) = x3-7x+4 – (2x2+3x-7) m(x) + l(x) = x3-2x2-10x+11
Multiplying Polynomials m(x) = x3-7x+4
l(x) = 2x2+3x-7
m(x) * l(x) = (x3-7x+4)(2x2+3x-7) m(x) * l(x) = (2x5+3x4-7x3) - (14x3-21x2-49x) + (8x2+12x-28) m(x) * l(x) = 2x5+3x4-21x3-13x2-37x-28
Polynomials
What is a polynomial? • A polynomial is an expression consisting of a sum of multiples of non-negative integer powers.
Types of polynomial • • • • •
Degree 0 is called a constant polynomial Degree 1 is called a linear polynomial Degree 2 is called a quadratic polynomial Degree 3 is called a cubic polynomial Degree 4 is called a quartic polynomial
Addition and subtraction of polynomial • Add or subtract the coefficients of the corresponding powers
Multiplying polynomials • You times each term in 1 bracket by each term in the other bracket. • (a+b)(c+d)=ac+ad+ba+bd • When you mutiply two polynomials, the degree of the product is the sum of the degrees of the two polynomials.
Constant-when the degree is zero (0) - (3x0). Linear- when the degree is one (1) - (2x1). Quadratic- when the degree is two (2) - (5x2-2). Cubic- when the degree is three (3) - (4x3+3x2-6x -3). Quartic- when the degree is four (4) - (6x4-3x3+4x2+6x-5) (There are names for some polynomials of higher degree, but it is not worth learning them).
Adding Polynomials m(x) = x3-7x+4
l(x) = 2x2+3x-7
m(x) + l(x) = x3-7x+4 + (2x2+3x-7) m(x) + l(x) = x3+2x2-4x-3
Subtracting Polynomials m(x) = x3-7x+4
l(x) = 2x2+3x-7
m(x) – l(x) = x3-7x+4 – (2x2+3x-7) m(x) + l(x) = x3-2x2-10x+11
Multiplying Polynomials m(x) = x3-7x+4
l(x) = 2x2+3x-7
m(x) * l(x) = (x3-7x+4)(2x2+3x-7) m(x) * l(x) = (2x5+3x4-7x3) - (14x3-21x2-49x) + (8x2+12x-28) m(x) * l(x) = 2x5+3x4-21x3-13x2-37x-28
Polynomials
What is a polynomial? • A polynomial is an expression consisting of a sum of multiples of non-negative integer powers.
Types of polynomial • • • • •
Degree 0 is called a constant polynomial Degree 1 is called a linear polynomial Degree 2 is called a quadratic polynomial Degree 3 is called a cubic polynomial Degree 4 is called a quartic polynomial
Addition and subtraction of polynomial • Add or subtract the coefficients of the corresponding powers
Multiplying polynomials • You times each term in 1 bracket by each term in the other bracket. • (a+b)(c+d)=ac+ad+ba+bd • When you mutiply two polynomials, the degree of the product is the sum of the degrees of the two polynomials.
