when the polynomial px is divided by x 1 x 2 and x 3 the respective remainders are 9 10 and 23 f

Name: when the polynomial px is divided by x 1 x 2 and x 3 the respective remainders are 9 10 and 23 find the remainder when px is divided by x3 6x2 11x 6 83592
Uploaded: 2022-06-17T08:42:32-08:00
Duration: 5 min 23 s
Channel: Ankit Singh
Description: when the polynomial px is divided by x 1 x 2 and x 3 the respective remainders are 9 10 and 23 find the remainder when px is divided by x3 6x2 11x 6 83592

Step 1: We are given that when P(x) is divided by (x-1), the remainder is 9. This means that P(1

When the polynomial px is divided by x 1 x 2 and x 3 the...

Transcript

00:01 So in this question, the polynomial px, polynomial px, and that is simply x to the power 4, x to the power 4, minus 2x cube, plus 3x square, plus 3x square minus ax, minus ax, plus 3a, minus 7 is divided by x plus 1.

00:31 So if this polynomial is divided by x plus 1, so in this case remainder would be 19.

00:39 Reminder would be 19.

00:41 If the same is divided by x plus 2, then we need to tell what is the remainder in this case.

00:53 We need to tell what is the remainder in this case.

00:55 Also we need to tell what is the value of a.

00:57 So basically there are two parts here.

01:00 Now we are aware of the fact that by the fact that by remindor theorem we can say that by rememinder theorem by remedter theorem we can say that by remedter theorem we know that we know that if x minus a divided divides p of x then p of a is the value of remainder value of remainder so if x plus 1 is divided is divides is divide or we can say that px is divided by x plus 1 so in this case this would be the remainder so basically we can say that p of minus 1 is equal to 19 and this is given so minus 1 to the power 4 i'm calculating the value of p of minus 1 that is minus 1 to the power 4 minus 2 times of minus minus 1 cube plus 3 times of minus 1 square minus a times of minus 1 plus 3a minus 7 and that is equal to 19 so in this case if we further simplify this value we will get 1 then plus 2 plus 3 plus a plus 3a minus 7 is equal to 19 and from here we have 4a minus 1 equals to 19 and from here we can say that value of 4a would be 19 plus 1 and that is 20 and from here value of a would be simply 20 upon 4 and that is nothing but simply 5...

Question

When the polynomial P(x) is divided by (x-1), (x-2), and (x-3), the respective remainders are 9, 10, and 23. Find the remainder when P(x) is divided by x^3 - 6x^2 + 11x - 6.

Question

When the polynomial P(x) is divided by (x-1), (x-2), and (x-3), the respective remainders are 9, 10, and 23. Find the remainder when P(x) is divided by x^3 - 6x^2 + 11x - 6.

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