Question

2. Write an assignment on Polynomials.It must include Introduction, related mathematicians,
standard form, identities, expanded forms, factorization.
Write 4 examples from daily life ,where we use Polynomials.​

Answer 1

$\mathbb{\purple {MATHEMATICS :}}$

We are surrounded by extremely wonderful things. But we ignore them throughout life. Things have been doing wonders in our lives and here we are just enjoying benefits. Mathematics is one of those wonders. From preparing food to the construction of a dream house tell me where math is not used?

Today I will light you. how? You may ask. Well I'm going to light you with one of the most wonderful things we have got to date in form of knowledge which we sometimes give a tag of "headache "

$\mathfrak{\red {HISTORY :}}$

Mathematics was classified into five major branches. They are :

• Algebra
• Geometry
• Trigonometry
• Calculus
• Statistics and probability

I don't know if you know this greatest mathematician called Carl Gauss. Carl Gaus has contributed mathematics with wonders. The earliest people who played with mathematics were most probably Sumerians. If you don't know they were the earliest people to make civilization in Mesopotamia.

Today, We will pick up one of the most interesting forms of maths and toy with that. called Polynomial.

$\mathcal{POLYNOMIALS}$

Polynomials are one of the most fascinating ways to experience maths.

Rene Descartes. He is rewarded like the one who introduced the idea of graphs in polynomials. Now we must bless this branch more with making out realities about these polynomials.

While we are playing with polynomials some identities makes the game more interesting. So, without wasting much time I will proceed towards all identities.

${(a + b)}^{2} = {a}^{2} + 2.a.b + {b}^{2}$

${(a - b)}^{2} = {a}^{2} - 2.a.b + {b}^{2}$

$(x + a)(x + b) = {x}^{2} + (a + b)x + ab$

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2.a.b + 2.b.c + 2.c.a$

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3.a.b(a + b)$

${(a - b)}^{3} = {a}^{3} - {b}^{3 } - 3.a.b (a - b)$

${a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$

${a}^{3} + {b}^{3} + {c}^{3} = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)$

So there were identities .