MATHS PROJECT WORK:- It's all about polynomials and its related terms and terminology, different types of polynomials, relationship between zeroes of polynomials to its coefficients, a short recap of remainder and factor theorem and algebraic expressions. We will be talking about the quadratic equation in detail.
49. FACTOR THEOREM
• If p(x) is a polynomial of degree greater than or
equal to one where a is a real number then:
x – a is a factor of p(x), if p(x) = 0
OR
p(x) = 0 ,if x – a is a factor of p(x)
50. REMAINDER THEOREM
• Let p(x) be a polynomial of degree greater than or
equal to one and a be any real number. If p(x) is
divided by the linear polynomial (x – a), the quotient
is q(x) and remainder is r(x),i.e.,
p(x) = (x – a) q(x) + r(x)
As degree of (x – a) is less than 1
So the degree of r(x) = 0, thus r(x) is a constant.
So, degree of r(x) = 0
r(x) = r
p(x) p(x) = (x – a) q(x) + r(x)
If x = a ; p(a) = (a – a) q(x) + r(x)
p(a) = r
51. ALGEBRAIC IDENTITIES
• (x + y)2
= x2
+ 2xy + y2
• (x - y)2
= x2
- 2xy + y2
• x2
- y2
= (x + y) (x – y)
• (x + a) (x + b) = x2
+ (a + b )x + ab
• (x + y)3
= x3
+ y3
+ 3x2
y + 3xy2
• (x – y)3
= x3
– y3
– 3x2
y + 3xy2
• x + y + z – 3xyz=(x + y + z) (x + y + z – xy – yz – xz)
52. SPECIAL THANKS TO :-
• The readers for whom we put our time,
hard work and dedication for a noble
cause. Our work will be more valuable if
students of our age group is able to graps
some idea about the chapter – polynomial
and come across some of the important
aspects and question regarding this
chapter. Thank you for watching this
presentation.
!! THANK YOU !!
