Question

Factorize the following expressions.
(a) 4m2 + 44m + 121​

Answer 1

Answer:

4m^2 + 44m^2 + 121

STEP

1

:

Equation at the end of step 1

(22m2 - 44m) + 121

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 4m2-44m+121

The first term is, 4m2 its coefficient is 4 .

The middle term is, -44m its coefficient is -44 .

The last term, "the constant", is +121

Step-1 : Multiply the coefficient of the first term by the constant 4 • 121 = 484

Step-2 : Find two factors of 484 whose sum equals the coefficient of the middle term, which is -44 .

-484 + -1 = -485

-242 + -2 = -244

-121 + -4 = -125

-44 + -11 = -55

-22 + -22 = -44 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -22 and -22

4m2 - 22m - 22m - 121

Step-4 : Add up the first 2 terms, pulling out like factors :

2m • (2m-11)

Add up the last 2 terms, pulling out common factors :

11 • (2m-11)

Step-5 : Add up the four terms of step 4 :

(2m-11) • (2m-11)

Which is the desired factorization

Multiplying Exponential Expressions:

2.2 Multiply (2m-11) by (2m-11)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2m-11) and the exponents are :

1 , as (2m-11) is the same number as (2m-11)1

and 1 , as (2m-11) is the same number as (2m-11)1

The product is therefore, (2m-11)(1+1) = (2m-11)2

Final result :

(2m - 11)2