Question

what is the remainder when x³-2x²-5x+4divided by( x-2) ​

Answer 1

To check that x−2 is the factor of x3−2x2−5x+4

Then the value of x−2=0, so x=2.

So, put x=2 in expression, we get

f(x)=x3−2x2−5x+4

f(2)=(2)3−2(2)2−5(2)+4

⇒f(2)=8−2×4−5×2+4

⇒f(2)=8−8−10+4

⇒f(2)=−6

Remainder is not zero when x−2 divided polynomial x3−2x2−5x+4. 

Thus x−2 is not a factor of polynomial x3−2x2−5x+4.

Answer 2

Answer:

$\huge \sf \underline{ \ given\: : }$

$\sf {x}^{3} - 2 {x}^{2} - 5x + 4 \: is \: divided$

$\sf \: by \: (x - 2).$

$\huge \sf \underline{to \: find \ \: : }$

$\sf remainder \: obtained \: when \\ \sf \: {x}^{3} - {2x}^{2} - 5x + 4 \: is \: divided \\ \sf \: (x - 2). \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\huge \sf \underline{solution \ \: : }$

$\sf \: p(x) = 0$

$\sf \: p(x) = x - 2$

$\sf \: (x - 2) = 0$

$\sf \: x = 0 + 2$

$\red { \sf{ \to \: x = 2}}$

$\sf \underline{let \: us \: substute \: the \: values \ \: : }$

$\sf \to \: {2}^{3} - 2 ({2})^{2} - 5(2) + 4$

$\to \sf8 - 2(4) - (10) + 4$

$\to \sf(8) -( 8) - (10) + 4$

$\sf \to0 - 6$

$\red \sf \to - 6$

• Therefore the remainder obtained is (-6)

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