(x ^ 2 + 5x)(x ^ 2 + 5x - 3) - 28 factorise
Answers
Answer:
Factoring x2+5x+28
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is +28
Step-1 : Multiply the coefficient of the first term by the constant 1 • 28 = 28
Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is 5 .
-28 + -1 = -29
-14 + -2 = -16
-7 + -4 = -11
-4 + -7 = -11
-2 + -14 = -16
-1 + -28 = -29
1 + 28 = 29
2 + 14 = 16
4 + 7 = 11
7 + 4 = 11
14 + 2 = 16
28 + 1 = 29
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
1
:
x2 + 5x + 28 = 0
STEP
2
:
Parabola, Finding the Vertex:
2.1 Find the Vertex of y = x2+5x+28
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -2.5000
Plugging into the parabola formula -2.5000 for x we can calculate the y -coordinate :
y = 1.0 * -2.50 * -2.50 + 5.0 * -2.50 + 28.0
or y = 21.750
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2+5x+28
Axis of Symmetry (dashed) {x}={-2.50}
Vertex at {x,y} = {-2.50,21.75}
Function has no real roots
Answer:
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is +28
Step-1 : Multiply the coefficient of the first term by the constant 1 • 28 = 28
Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is 5
-28 + -1 = -29
-14 + -2 = -16
-7 + -4 = -11
-4 + -7 = -11
-2 + -14 = -16
-1 + -28 = -29
1 + 28 = 29
2 + 14 = 16
4 + 7 = 11
7 + 4 = 11
14 + 2 = 16
28 + 1 = 29
Observation : No two such factors can be found !!