Question

find the value of such that x minus 4 is a factor of x cube + 3 x square - 2 X + b

Answer 1

Step-by-step explanation:

Let p(x) be the given cubic polynomial.

p(x)= x³+3x²-2x+b

Given that x-4 is a factor of given polynomial.

•Note:If (x-@) is a factor of a polynomial,then @ would be a zero of the polynomial.

Thus,

p(x)=p(4)=0

Substituting the value,

p(4)=(4)³+3(4)²-2(4)+b

→64+48-8+b=0

→b+64+40=0

→b= -104

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The polynomial would be:

p(x)=x³+3x²-2x-104

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