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)
