Factorize *
y² – 14 y +49
x2 + 3x - 40

The first term is, y2 its coefficient is 1 .

The middle term is, -14y its coefficient is -14 .

The last term, "the constant", is +49

Step-1 : Multiply the coefficient of the first term by the constant 1 • 49 = 49

Step-2 : Find two factors of 49 whose sum equals the coefficient of the middle term, which is -14 .

-49 + -1 = -50

-7 + -7 = -14 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -7

y2 - 7y - 7y - 49

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

y • (y-7)

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

7 • (y-7)

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

(y-7) • (y-7)

Which is the desired factorization

Multiplying Exponential Expressions:

1.2 Multiply (y-7) by (y-7)

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

In our case, the common base is (y-7) and the exponents are :

1 , as (y-7) is the same number as (y-7)1

and 1 , as (y-7) is the same number as (y-7)1

The product is therefore, (y-7)(1+1) = (y-7)2

Final result :

(y - 7)2

The first term is, x2 its coefficient is 1 .

The middle term is, +3x its coefficient is 3 .

The last term, "the constant", is -40

Step-1 : Multiply the coefficient of the first term by the constant 1 • -40 = -40

Step-2 : Find two factors of -40 whose sum equals the coefficient of the middle term, which is 3 .

-40 + 1 = -39

-20 + 2 = -18

-10 + 4 = -6

-8 + 5 = -3

-5 + 8 = 3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 8

x2 - 5x + 8x - 40

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

x • (x-5)

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

8 • (x-5)

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

(x+8) • (x-5)

Which is the desired factorization

Final result :

(x + 8) • (x - 5)

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