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zmey [24]
2 years ago
8

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.

__________________

So, let's do the division (steps in the attached picture).

__________________

We got the remainder as 0. So, yes p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

__________________

<h3><u>More steps :-</u></h3>

x² - 5x + 6

= <u>(x - 3) (x - 2)</u> [use the splitting the middle term method].

So, the zeroes are,

(x - 3)

x - 3 = 0

<u>x = 3 ⇨ 1</u><u>s</u><u>t</u><u> </u><u>zero.</u>

(x - 2)

x - 2 = 0

<u>x = 2 ⇨ 2nd zero.</u>

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

<u>p(3) = 0.</u>

p(x) = x³ - 6x² + 11x - 6

p(2) = 2³ - 6(2)² + 11 (2) - 6

p(2) = 8 - 24 + 22 - 6

<u>p(2) = 0</u>

Since we got the solutions as 0 we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

__________________

Hope it'll help you!

ℓu¢αzz ッ

Montano1993 [528]2 years ago
7 0

HERE IS YOUR ANSWER MATE

HOPE ITS HELPFUL

HAVE A GREAT FUTURE

LOVE FROM INDIA

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