Question

please explain step by step.
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Answer 1

Step-by-step explanation:

given p(X)=x³+3x²+3x+1

1)X+1=0

x=-1

p(-1) =(-1)³+3(-1)²+3(-1)+1

=-1+3-3+1

= 0

therefore , remainder in this case is 0

2)x-1/2=0

x=1/2

p(1/2) =(1/2)³+3(1/2)²+3(1/2)+1

=1/8+3*1/4+3*1/2+1

=1/8+3/4+3/2+1

=1/8+6/8+12/8+8/8

=27/8

therefore , remainder in this case will be 27/8

3)X+π=0

x=-π

p(-π)=(-π)³+3(-π)²+3(-π)+1

= -π³+3π²-3π+1

Answer 2

ans no 2

$p(x) = {x}^{3} - a {x}^{2} + 6x - a \\ take = x - a = 0 \\ x = 0 + a \\ x = a \\ p(a) = ({a}^{3} ) - ( {a}^{2} ) + 6(a) - a \\ {a}^{3} - {a}^{3} + 6a - a \\ 6a - a \\ 5a$

ans 3

$take \: 7 + 3x = 0 \\ 3x = - 7 \\ x = \binom{ - 7}{3} \\ p \binom{ - 7}{3} = 3 \binom{ - 7}{3}^{3} + 7 \binom{ - 7}{3} \\ = 3 \binom{ - 343}{27} - \binom{ - 49}{3} \\ = - \frac{1029}{27} + \frac{49}{3} \\ = \binom{ - 1029} {27} + 441 = \frac{1470}{27}$

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