Answer:
8 [ (x-3) (2x+1) ]
Step-by-step explanation:
Factoring 2x2 - 5x - 3
The first term is, 2x2 its coefficient is 2 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -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
2x2 - 6x + 1x - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-3)
Add up the last 2 terms, pulling out common factors :
1 • (x-3)
Step-5 : Add up the four terms of step 4 :
(2x+1) • (x-3)
Which is the desired factorization
Answer: (5x2 + 2)(3x – 1)
Step-by-step explanation:
Answer:
Procedure:
1) Form a system of 3 linear equations based on the two zeroes and a point.
2) Solve the resulting system by analytical methods.
3) Substitute all coefficients.
Step-by-step explanation:
A quadratic function is a polynomial of the form:
(1)
Where:
- Independent variable.
- Dependent variable.
, 
, 
- Coefficients.
A value of is a zero of the quadratic function if and only if 
. By Fundamental Theorem of Algebra, quadratic functions with real coefficients may have two real solutions. We know the following three points: 
, 
and 
Based on such information, we form the following system of linear equations:
(2)
(3)
(4)
There are several forms of solving the system of equations. We decide to solve for all coefficients by determinants:
And finally we obtain the equation of the quadratic function given two zeroes and a point.
