show that P(x)=x³-6x²+11x-6 is divisible by x-1.
Answers
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[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
Show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
[tex] \huge \boxed{\mathfrak{Explanation} \downarrow}[/tex]
To show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1, we must divide the polynomial by x - 1. If we get the remainder as 0, then we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
__________________
So, let's do the division (steps in the attached picture).
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We got the remainder as 0. So, yes p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
__________________
More steps :-x² - 5x + 6
= (x - 3) (x - 2) [use the splitting the middle term method].
So, the zeroes are,
(x - 3)
x - 3 = 0
x = 3 ⇨ 1st zero.
(x - 2)
x - 2 = 0
x = 2 ⇨ 2nd zero.
Now, use the values of x on the equation. If we get 0 as the solution of the equation then we can prove that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
p(x) = x³ - 6x² + 11x - 6
p(3) = 3³ - 6(3)² + 11 (3) - 6
p(3) = 27 - 54 + 33 - 6
p(3) = 0.
p(x) = x³ - 6x² + 11x - 6
p(2) = 2³ - 6(2)² + 11 (2) - 6
p(2) = 8 - 24 + 22 - 6
p(2) = 0
Since we got the solutions as 0 we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
__________________
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Answer:
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Step-by-step explanation:
Hi there!
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Step-by-step explanation:
ekdjnsjs
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
440
Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Show all your work!
Answers
Answer:
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Step-by-step explanation:
Rearrange:
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Equation at the end of step 1:
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Equation of a Straight Line
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Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
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y tells us how far up the line goes
x tells us how far along
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b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line x-3y-6 = 0 and calculate its properties
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Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 2/-1 so this line "cuts" the y axis at y=-2.00000
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Calculate the X-Intercept :
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Calculate the Slope :
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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