Factorize the following expressions
1. 8x^2-18x+9
Answers
Step-by-step explanation:
The first term is, 8x2 its coefficient is 8 .
The middle term is, +18x its coefficient is 18 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 8 • 9 = 72
Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is 18 .
-72 + -1 = -73
-36 + -2 = -38
-24 + -3 = -27
-18 + -4 = -22
-12 + -6 = -18
-9 + -8 = -17
-8 + -9 = -17
-6 + -12 = -18
-4 + -18 = -22
-3 + -24 = -27
-2 + -36 = -38
-1 + -72 = -73
1 + 72 = 73
2 + 36 = 38
3 + 24 = 27
4 + 18 = 22
6 + 12 = 18 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 6 and 12
8x2 + 6x + 12x + 9
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (4x+3)
Add up the last 2 terms, pulling out common factors :
3 • (4x+3)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (4x+3)
Which is the desired factorization
Final result :
(-4x - 3) • (2x + 3)
Step-by-step explanation:
8x² - 18x + 9
18 ± √(18)² - 4*(8)*(9)/16
18 ± √324 - 288/16
18 ± √36/16
18 ± 6/16
Zeroes-
18 + 6/16
24/16 = 3/2
And
18 - 6/16
12/16 = 3/4