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Mathematics
Layton
14 October, 15:58
Show all work to solve
3x^2 - 5x - 2 = 0
+4
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1
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Skylar Drake
14 October, 18:50
0
Factor and set each factor equal to zero.
x = 2, - 1/3
Explanation:
The first term is, 3x2 its coefficient is 3.
The middle term is, - 5x its coefficient is - 5.
The last term, "the constant", is - 2
Step-1 : Multiply the coefficient of the first term by the constant 3 • - 2 = - 6
Step-2 : Find two factors of - 6 whose sum equals the coefficient of the middle term, which is - 5.
-6 + 1 = - 5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 6 and 1
3x2 - 6x + 1x - 2
Step-4 : Add up the first 2 terms, pulling out like factors:
3x • (x-2)
Add up the last 2 terms, pulling out common factors:
1 • (x-2)
Step-5 : Add up the four terms of step 4:
(3x+1) • (x-2)
Which is the desired factorization
Equation at the end of step 2:
(x - 2) • (3x + 1) = 0
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