I love mathematics

I love Mathematics. I love the challenge in dealing with every question. Lately our class is learning FACTORIZATION which I think I am going to be ‘indulged’ in!

Basically there are 3 fundamental BINOMIAL FORMULAS to bear in mind when solving them.

1 (a-b)(a+b)=a² - b²

2 (a+b)(a+b)=a²+2ab+b²

3 (a-b)(a-b)=a²-2ab+b²

I also found out some complicated formulas in BINOMIAL which I think we won’t be learning this year.

The cube of a binomial.

There are similar formulas to factor some special cubic polynomials:

Sums and differences of two cubes.

Here are two more formulas to handle special cases of cubic polynomials:

(a+b)³ = a³ + 3a²b + 3ab² + b²

(a-b)³ = a³-3a²b + 3ab² – b³

Say, we like to factor x³ + 8. By formula (6), we can write

X³ + 8 =x³ + 2³ = (x + 2) (x² – 2x + 4)

In this case the factorization is complete, since the polynomial x² – 2x + 4 is an irreducible quadratic polynomial.

These are some questions to ponder:

Exercise 1.

Factorize the polynomial x² + 6x + 9 completely.

Exercise 2.

Factorize the polynomial x² + 6x - 9 completely.

Exercise 3.

Factorize the polynomial x⁴ - 2 completely.

Exercise 4.

Factorize the polynomial 125 – 8x³ completely.

Have fun!!!

Algebra Math Quotes

"As long as algebra is taught in school, there will be prayer in school. " -- Cokie Roberts

"It is hard to convince a high-school student that he will encounter a lot of problems more difficult than those of algebra and geometry." -- Edward W. Howe