Question

use the factor theoram p(x) =x^3+3x^2+3x+1, g(x) =x+2​

Answer 1

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I am Devanshu for you..

Here's we have p(x) = x³ + 3x² + 3x + 1

p(x) = x³ + 3x² + 3x + 1and g(x) = x + 2

Therefore, by using Factor Theorem..

Now we put the value of x in above given polynomial. We get..

p(–2) = (–2)³ + 3(–2)² + 3(–2) + 1

p(–2) = (–2)³ + 3(–2)² + 3(–2) + 1p(–2) = –8 + 3( 4 ) – 6 + 1

p(–2) = (–2)³ + 3(–2)² + 3(–2) + 1p(–2) = –8 + 3( 4 ) – 6 + 1p(–2) = –8 + 12 – 5

p(–2) = (–2)³ + 3(–2)² + 3(–2) + 1p(–2) = –8 + 3( 4 ) – 6 + 1p(–2) = –8 + 12 – 5 p(–2) = 4 – 5

p(–2) = (–2)³ + 3(–2)² + 3(–2) + 1p(–2) = –8 + 3( 4 ) – 6 + 1p(–2) = –8 + 12 – 5 p(–2) = 4 – 5 p(–2) = –1

=> p(–2) ≠ 0...

=> p(–2) ≠ 0...So g(x) is not a factor of p(x)...

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