4n2 +5n-636 solve by division method
Answers
Answer:
The first term is, 4n2 its coefficient is 4 .
The middle term is, +5n its coefficient is 5 .
The last term, "the constant", is -636
Step-1 : Multiply the coefficient of the first term by the constant 4 • -636 = -2544
Step-2 : Find two factors of -2544 whose sum equals the coefficient of the middle term, which is 5 .
-2544 + 1 = -2543
-1272 + 2 = -1270
-848 + 3 = -845
-636 + 4 = -632
-424 + 6 = -418
-318 + 8 = -310
-212 + 12 = -200
-159 + 16 = -143
-106 + 24 = -82
-53 + 48 = -5
-48 + 53 = 5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -48 and 53
4n2 - 48n + 53n - 636
Step-4 : Add up the first 2 terms, pulling out like factors :
4n • (n-12)
Add up the last 2 terms, pulling out common factors :
53 • (n-12)
Step-5 : Add up the four terms of step 4 :
(4n+53) • (n-12)
Which is the desired factorization
Equation at the end of step
2
:
(n - 12) • (4n + 53) = 0
STEP
3
:
Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.