Question

check whether x+1 is a factor x3+3x2+3x+1 using factor theorem,​

Answer 1

Answer:

Given: x³+3x²+3x+1 and (x+1)

To find: Cheak whether (x+1) is a factor of x³+3x²+3x+1 Or not

Step-by-step explanation:

Solution,

If (x+1) is a factor of x³+3x²+3x+1 then x= -1 must satisfy the equation.

= (-1)³+3(-1)²+3(-1) +1

= -1+ 3-3+1

= 0 Answer.

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Answer 2

$let \: p(x) = {x}^{3} + 3 \times 2 + 3x + 1$

$if \: x + 1 \: is \: a \: factor \: of \: p(x), then \: p( - 1)=0$

$∴ p(- 1) = ({ - 1}^{3}) + 3(- 1) {}^{2} + 3(- 1) + 1$

$= - 1 + 3 - 3 + 1 = 0$

$∵ p(- 1) = 0$

$∴ \: x + 1 \: is \: a \: factor \: of \: p(x)$