Show that P(x)=x³-6x²+11x-6 is divisible by x-1.

Mathematics

2 answers:

creativ13 [48]2 years ago

8 0

Hello haohaoxNienie!

$\huge \boxed{\mathfrak{Question} \downarrow}$

Show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

$\huge \boxed{\mathfrak{Explanation} \downarrow}$

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.

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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.

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<h3>More steps :-</h3>

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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Hope it'll help you!

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