Answer:
a.) f( x ) + g( x ) = 4 x² + 3
b.) f( x ) - g ( x ) = 4x² -6x + 3
c.)f ( x ) . g ( x ) = 12x³ - 5x² + 3x + 2
Step-by-step explanation:
Given :- f ( x) = 4x² - 3x + 2 and g(x)= 3x +1
Substitute the values of f(x) and g(x) and simplify all .
a.) f( x ) + g( x )
( 4x² - 3x + 2 ) + ( 3x + 1 )
4 x² - 3x + 2 + 3 x + 1
collect like terms
4x² - 3 x + 3 x + 2 + 1
4 x² + 3
b.) f ( x ) - g ( x )
( 4x² - 3x + 2 ) - ( 3x + 1 )
4x² - 3x + 2 - 3x - 1
collect like terms
4x² - 3 x - 3x + 2 - 1
4x² -6x + 1
c.) f ( x ) . g ( x )
( 4x² - 3x + 2 ) × ( 3x + 1 )
Use the Distributive property
3 x(4x² - 3x + 2 ) × 1 ( 4x² - 3x + 2 )
Remove the parantheses multiply
12x³ - 9x² + 6x + 4x² - 3x + 2
Collect like terms
12 x³- 9x ² + 4x² + 6x - 3x + 2
12x³ - 5x² + 3x + 2
