Question

Check whether p(x) is multiple of g(x) or not:
i) p(x) = 2√2x³- 5√2x²+ 7√2,g(x) =x+1​

Answer 1

→p(x)=2√2x³-5√2x²+7√2

→g(x)=x+1.

Let g(x)=0.

=> x+1=0

.°. x =-1.

Putting this value in p(x)

=>p(-1)=2√2(-1)³-5√2(-1)²+7√2.

=>p(-1)=-2√2-5√2+7√2

=>p(-1)=7√2-7√2.

.°. p(-1)=0.

Hence p(x) is a multiple of p(x).

Answer 2

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ANSWER ::

The zero of the polynomial x + 1 is given by

x + 1 = 0

= 0

So x = - 1

P(x) = 2√2x³- 5√2x²+ 7√2

Now by the Remainder Theorem the required Remainder is

P(-1) = 2√2 (-1)³- 5√2(-1)²+ 7√2 = - 2√2- 5√2+ 7√2 = 0

So g(x) is a multiple of P(x)