when the expression: 4x^4 + 24x^3 + 12x^3 + 8x is factored completely, what is the largest factor that can be factored out?

Mathematics

2 answers:

Juliette [100K]3 years ago

6 0

D. 4x

they all have at least one x, and 4 goes into all of the numbers at least once

Fofino [41]3 years ago

5 0

Let's start by grouping like terms so we can factor out the most
(4x^4+24x^3)+(12x^2+8x)
now let's factor out as much as possible. we see all coefficients are multiples of 4, we will also factor out as high a degree of x as we can
4x^3(x+6)+4x(3x+2)
now we see that we still have a common multiple of 4x that we can remove
4x(x^2(x+6)+(3x+2))
so we find 4x is the largest value we can factor out

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The points (6, -3) and (7, -10) fall on a particular line. What is its equation in point-slope form? Use one of the specified po

kumpel [21]

Answer:

Step-by-step explanation:

Given the coordinate points (6, -3) and (7, -10), we are to find the equation of a line passing through this two points;

The standard equation of a line is y = mx+c

m is the slope

c is the intercept

Get the slope;

m = Δy/Δx = y2-y1/x2-x1

m = -10-(-3)/7-6

m = -10+3/1

m = -7

Get the intercept;

Substitute the point (6, -3) and m = -7 into the expression y = mx+c

-3 = -7(6)+c

-3 = -42 + c

c = -3 + 42

c = 39

Get the required equation by substituting m = -7 and c= 39 into the equation y = mx+c

y = -7x + 39

Hence the required equation is y = -7x + 39

6 0

3 years ago

Find an equation in standard form of the parabola passing through these points: (0,-6),(-1,-12),(3,0)

Elan Coil [88]

One form of the equation of a parabola is
y = ax² + bx + c

The curve passes through (0,-6), (-1,-12) and (3,0). Therefore
c = - 6 (1)
a - b + c = -12 (2)
9a + 3b + c = 0 (3)

Substitute (1) into (2) and into (3).
a - b -6 = -12
a - b = -6 (4)
9a + 3b - 6 = 0
9a + 3b = 6 (5)

Substitute a = b - 6 from (4) into (5).
9(b - 6) + 3b = 6
12b - 54 = 6
12b = 60
b = 5
a = b - 6 = -1

The equation is
y = -x² + 5x - 6

Let us use completing the square to write the equation in standard form for a parabola.
y = -[x² - 5x] - 6
= -[ (x - 2.5)² - 2.5²] - 6
= -(x - 2.5)² + 6.25 - 6

y = -(x - 2.5)² + 0.25
This is the standdard form of the equation for the parabola.
The vertex us at (2.5, 0.25).
The axis of symmetry is x = 2.5
Because the leading coefficient is -1 (negative), the curve opens downward.
The graph is shown below.

Answer: y = -(x - 2.5)² + 0.25