Answer:
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
2
:
3x2 - 13x - 40 = 0
STEP
3
:
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = 3x2-13x-40
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 3 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.1667
Plugging into the parabola formula 2.1667 for x we can calculate the y -coordinate :
y = 3.0 * 2.17 * 2.17 - 13.0 * 2.17 - 40.0
or y = -54.083
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = 3x2-13x-40
Axis of Symmetry (dashed) {x}={ 2.17}
Vertex at {x,y} = { 2.17,-54.08}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.08, 0.00}
Root 2 at {x,y} = { 6.41, 0.00}
Step by step solution :
STEP
1
:
Equation at the end of step 1
(3x2 - 13x) - 40 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 3x2-13x-40
The first term is, 3x2 its coefficient is 3 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is -40
Step-1 : Multiply the coefficient of the first term by the constant 3 • -40 = -120
Step-2 : Find two factors of -120 whose sum equals the coefficient of the middle term, which is -13 .
-120 + 1 = -119
-60 + 2 = -58
-40 + 3 = -37
-30 + 4 = -26
-24 + 5 = -19
-20 + 6 = -14
-15 + 8 = -7
-12 + 10 = -2
-10 + 12 = 2
-8 + 15 = 7
-6 + 20 = 14
-5 + 24 = 19
-4 + 30 = 26
-3 + 40 = 37
-2 + 60 = 58
-1 + 120 = 119
