Find the values of p and q given that x⁴ + x³ - 7x² + px + q is divisible by (x - 1) and (x + 2)

p = - 5, q = 10

Step-by-step explanation:

If f(x) is divisible by (x - h) then f(h) = 0

Here

f(x) = + x³ - 7x² + px + q

dividing by (x - 1) with h = 1 , then

+ 1³ - 7(1)² + p + q = 0, that is

1 + 1 - 7 + p + q = 0

- 5 + p + q = 0 ( add 5 to both sides )

p + q = 5 → (1)

Dividing by (x + 2) with h = - 2 , then

+ (- 2)³ - 7(- 2)² - 2p + q = 0 , that is

16 - 8 --- 28 - 2p + q = 0

- 20 - 2p + q = 0 ( add 20 to both sides )

- 2p + q = 20 → (2)

Subtract (1) from (2) term by term, thus eliminating q

- 3p = 15 ( divide both sides by - 3 )

p = - 5

Substitute p = - 5 into (1) and solve for q

- 5 + q = 5 ( add 5 to both sides )

q = 10

answer: add the !

step-by-step explanation: then we will answer