Hello, I have just started polynomial functions and seem to be going wrong somewhere.
‘The polynomials f(x) and g(x) are 2X² + aX – 3 and 3X² - bX – 2 respectively, where a and b are constants. In the product f(x)g(x), the coefficient of X³ is 6, and the coefficient of X is 1. Find the coefficient of X².’
To tackle the problem, I first attempted to find a and b.
Finding b..
So I first multiplied g(x) by 2X² = 2X² ( 3X² - bX – 2) = 6X^4 – 2bX³ - 4X².
As the coefficient of X² is 6, 2b = 6, so b = 3.
g(x) = 3X² - 3X – 2.
Finding a..
I multiplied g(x) by aX = aX ( 3X² - 3X – 2 ) = 3aX³ - 3aX² - 2aX.
So 3a = 6, meaning a = 2
This is the first section that I am unsure on: a = 2 and b = 3, as I seem to get the wrong answer when finding the coefficient of X².
‘The polynomials f(x) and g(x) are 2X² + aX – 3 and 3X² - bX – 2 respectively, where a and b are constants. In the product f(x)g(x), the coefficient of X³ is 6, and the coefficient of X is 1. Find the coefficient of X².’
To tackle the problem, I first attempted to find a and b.
Finding b..
So I first multiplied g(x) by 2X² = 2X² ( 3X² - bX – 2) = 6X^4 – 2bX³ - 4X².
As the coefficient of X² is 6, 2b = 6, so b = 3.
g(x) = 3X² - 3X – 2.
Finding a..
I multiplied g(x) by aX = aX ( 3X² - 3X – 2 ) = 3aX³ - 3aX² - 2aX.
So 3a = 6, meaning a = 2
This is the first section that I am unsure on: a = 2 and b = 3, as I seem to get the wrong answer when finding the coefficient of X².