Consider the expansion of (x^2+px-3)(3x-5),where p is a constant.If the coefficient of x of the expansion is -44,find the value

Question

1 year ago

15

of p

1 answer:

V125BC [204] · Answer 1 · 2023-09-09T01:14:17+03:00

Answer:

p = 7

Step-by-step explanation:

(x² + px - 3)(3x - 5)

each term in the second factor is multiplied by each term in the first factor, that is

x²(3x - 5) + px(3x - 5) - 3(3x - 5) ← distribute parenthesis

= 3x³ - 5x² + 3px² - 5px - 9x + 15 ← collect like terms

= 3x³ +x²(3p - 5) - x(5p + 9) + 15

given the coefficient of the x- term is - 44 , then

-(5p + 9) = - 44 ← - (5p + 9) is th coefficient of x in the expansion

- 5p - 9 = - 44 ( add 9 to both sides )

- 5p = - 35 ( divide both sides by - 5 )

p = 7