Question

Check weather g(x)=x+1 is a factor of p(x)=2xcube+xsquare-2x-1

Answer 1

Question:

Check whether g(x) = x + 1 is a factor of p(x) = 2x³+ x² - 2x - 1.

Answer:

Yes, g(x) is a factor of p(x)

Explanation:

[ According to the factor theorem, if g(x) = x + 1 is a factor of p(x), then p(-1) should be 0. ( we could use "zero of g(x) if it's not in the form x - a ) ]

Zero of g(x) :

⟹ x + 1 = 0

⟹ x = 0 - 1

⟹ x = -1

-1 is the zero of g(x)

Substituting (-1) in place of x in p(x)

⟹ p(x) = 2x³+ x² - 2x - 1

⟹ p(-1) = 2( -1 )³ + ( -1 )² - 2( -1 ) - 1

⟹ p(-1) = 2( -1 ) + 1 + 2 - 1

⟹ p(-1) = -2 + 1 + 2 - 1

⟹ p(-1) = -3 + 3

⟹ p(-1) = 0

p(-1) is 0, So g(x) is a factor of p(x)