Question

Find the condition when x^3 + (p +q)x + a is exactly divisible by x + p + q.​

Answer 1

Answer:

Condition for a

${(p + q)}^{2} (p + q + 1) = a$

then only the polynomial is completely divisible by x+p+q.

Step-by-step explanation:

If

${x}^{3} + (p + q)x + a$

is completely divisible by

$x + p + q$

then according to remainder theorem on putting the value of x,in the given polynomial we will get remainder zero.

So

$x = - p - q$

put in the polynomial

${( - p - q)}^{3} + (p + q)( - p - q) + a = 0\\ \\ - ( {p + q)}^{3} - ( {p + q)}^{2} + a = 0 \\ \\ - ( {p + q)}^{3} - ( {p + q)}^{2} = - a \\ \\ ( {p + q)}^{3} + ( {p + q)}^{2} = a \\ \\ {(p + q)}^{2} (p + q + 1) = a$

If the value of a will be equal to

${(p + q)}^{2} (p + q + 1) = a$

then only the polynomial is completely divisible by x+p+q.

Hope it helps you.

Answer 2

Step-by-step explanation:

Refer Attachment.

answer p+q whole square p+q+1