Question

P(x)=2x³-3px²+px+q have x-1 as a factor and have -52 as reminder when divide by x+2..
What value of p and q?

Answer 1

Answer:

p=17/6,q=11/3

Step-by-step explanation:

we can do it using a short cut.

firstly, identify the constants. here they are, 2,-3p,p and q. we know that x-1 is a factor.

let, x-1=0

x=1.

now let'arrange like this,

1 2 -3p p q

0 (we should

put 0 down

the first

constant)

then,

1. add the first constant to zero and write the answer down zero, like this

1 2 -3p p q

0

2

2.multiply the answer with the number we got from the factor(x-1).so here the number is one, which we wrote there in the very right side of our workplace. after multiplying,write the answer below the second constant, like this,

1 2 -3p p q

0 2

2

3.then add the answer with our second constant. here it is -3p.and write below like this,

1 2 -3p p q

0 2

2 -3p+2

4.then multiply the answer with 1 (here). and write the answer below our third constant like this,

1 2 -3p p q

0 2 -3p+2

2 -3p+2

5.repeat the steps and finally we get our workplace like this,

1 2 -3p p q

0 2 -3p+2 p-3p+2

2 -3p+2 p-3p+2 0

:here i wrote zero at last right? because (x-1) is a factor of the polynomial we want to find and so the remainder will be zero. the place where zero stands here is the remainder of the polynomial when we divide it with the factor(X-1).

so we know that adding q with p-3p+2 will be zero. so we get an equation,

q+p-3p+2=0

q-2p=-2----------------------------->eq. no 1

then it is given that the remainder is -52when it is divided by (x+2).

so, x+2=0

x=-2

therefore, we should replace 1 at the very right side of our workplace with -2. and follow the above steps. finally we will get an equation like this

q-14p-16=-52

q-14p=-36------------------------>eq. no 2

solving the above equation 1 and 2,

we will get

p=17/6

q=11/3

hope you understand this.. if you are not satisfied or you cant understand, kindly reply me..