Quadratic Expression and Equation

Operation in Quadratic Expression

As we discussed on first part about the meaning of quadratic Expression and equation, here we continue in operation:

Factorization:

Some expression may have common number or letter that multiplied by each term in it. For example in this expression 10 + 15, the common number is 5 that multiplied by 2 + 3 and obtained 10 + 5, i.e. 5(2 +3); also in 2x + 6x², here the common number is 2x that multiplied by 1 + 3x i.e. 2x (1 + 3x). so the process of finding and factor out a number is called factorization, and vice versa is expansion.

Lets start with simple factorization:

Example:

(1) Factorize 2c + 4;

Solution:

2c + 4, here we don’t deal with letter c because it is found in only one term, here we deal with 2 and 4. Finding the GCF of 2 and 4, we get 2 so that is the number that should be factored out, 2(      ); by dividing each term by that number "2” we get the answer 2(c + 2).

Therefore = 2(c + 2).

Example:

(1) Factorize 9m + 3mn + 27m²;

Solution:

9m + 3mn + 27m², our common number is 3 and common letter is m. so we get out 3m. after dividing each term by 3m we get 3 + n + 9m.

Therefore = 3m(3 + n + 9m)

TRY YOURSELF:

Factorize the following:

(1) 2x² – 8;       (2) 3r + 5r² – 2r;         (3) 14v – 7v²;

(4) rx² – 8m;    (5) 3x + x² – 2x;        

Expand the following:

(1) 2(x² – 3m);          (2) 4c (3 + c – 2r);        (3) 5y (2y – 7); 

(4) 2fy (1 – y + 4f);    (5) t(2+5t –ft);        

up to here you will have a good idea on how to factorize simple expression;