factorize : 49n²–42n+9.
Answers
Step-by-step explanation:
Answer
The first term is, 49n2 its coefficient is 49 .
The middle term is, -42n its coefficient is -42 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 49 • 9 = 441
Step-2 : Find two factors of 441 whose sum equals the coefficient of the middle term, which is -42 .
-441 + -1 = -442
-147 + -3 = -150
-63 + -7 = -70
-49 + -9 = -58
-21 + -21 = -42 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and -21
49n² - 21n - 21n - 9
Step-4 : Add up the first 2 terms, pulling out like factors :
7n • (7n-3)
Add up the last 2 terms, pulling out common factors :
3 • (7n-3)
Step-5 : Add up the four terms of step 4 :
(7n-3) • (7n-3)
Which is the desired factorization