Question

2x cube -5x square +px+3 leaves the remainder-4 when divided by x-1. find p and hence factorize polynomial completely​

Answer 1

Answer:

p=-4

Factors are (x-1)( 2x²-3x-7)

Step-by-step explanation:

p(x) = 2x³- 5x²+ px + 3

Here remainder r=-4

x-1=0,x=1

So p(1)=-4

2*1³-5*1²+p*1+3=-4

2-5+p+3= -4

p=-4

Remainder is -4

So p(x)=q(x) ( x-1) -4

So p(x) +4 = q(x) (x-1)

Thus p(x)+4 =2x³-5x²-4x+7

=2x³-2x²-3x²+3x-7x+7

=2x²( x-1) -3x(x-1) -7(x-1)

=(x-1)( 2x²-3x-7)

Answer 2

Answer:

p = -4

( X-1) (2x²- 3x -7)

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