MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Factor Theorem

Find the valu...

Question

Find the values of p and q so that x⁴ + px³ + 2x³ − 3x + q is divisible by (x² − 1).

Open in App

Solution

Let and be the given polynomials.

We have,

Here, are the factor of g(x).

If f(x) is divisible by and , then and are factor of f(x).

Therefore, f(1) and f(−1) both must be equal to zero.

Therefore,

and

Adding both the equations, we get,

Putting this value in (i)

Hence, the value of p and q are 3, −3 respectively.

Suggest Corrections

thumbs-up

94

Similar questions

Q. Find the values of p and q, if the polynomial

x^{4} + p x^{3} + 2 x^{2} - 3 x + q

is divisible by the polynomial

x^{2} - 1.

Q. Find the values of p and q so that by

x^{4} + x^{3} + 8 x^{2} + p x + q

is divisible by

x^{2} + 1

. [Hint: Perform long division and then put remainder = 0]

Q. If the expression

(p x^{3} + x^{2} - 2 x - q)

is divisible by

(x - 1)

(x + 1)

, what are the values of

p

q

Q. The polynomial

p x^{3} + 4 x^{2} - 3 x + q

is completely divisible by

x^{2} - 1

; find the value of p and q .Also for these values of p and q completely factories the given polynomial.

Q. Find the value of

p

q

(x + 1)

(x + 2)

are the factors of

x^{4} + p x^{3} + 2 x^{2} - 3 x + q

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Remainder Theorem

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon