Given: f(x)=2x^2+x-3 and g(x)=x-1
Express: f(x)⋅g(x)-[f(x)+g(x)] as a polynomial in standard form
To express f(x)⋅g(x)-[f(x)+g(x)] as a polynomial in standard form, we need to expand and simplify the expression.
First, let's find f(x)⋅g(x):
f(x)⋅g(x) = (2x^2+x-3)⋅(x-1)
To multiply these two polynomials, we can use the distributive property:
f(x)⋅g(x) = 2x^2⋅(x-1) + (x-1)⋅(x-1)
Expanding each term, we have:
f(x)⋅g(x) = 2x^3 - 2x^2 + x^2 - x - x + 1
Combining like terms, we get:
f(x)⋅g(x) = 2x^3 - x^2 - 2x + 1
Now, let's simplify [f(x)+g(x)]:
[f(x)+g(x)] = (2x^2+x-3)+(x-1)
Combining like terms, we have:
[f(x)+g(x)] = 2x^2 + x - 3 + x - 1
Simplifying further, we get:
[f(x)+g(x)] = 2x^2 + 2x - 4
Finally, let's find the result by subtracting [f(x)+g(x)] from f(x)⋅g(x):
f(x)⋅g(x)-[f(x)+g(x)] = (2x^3 - x^2 - 2x + 1) - (2x^2 + 2x - 4)
Expanding the expression, we have:
f(x)⋅g(x)-[f(x)+g(x)] = 2x^3 - x^2 - 2x + 1 - 2x^2 - 2x + 4
Combining like terms, we get:
f(x)⋅g(x)-[f(x)+g(x)] = 2x^3 - 3x^2 - 4
To express f(x)⋅g(x)-[f(x)+g(x)] as a polynomial in standard form, let's start by distributing the negative sign inside the brackets:
f(x)⋅g(x)-[f(x)+g(x)] = f(x)⋅g(x)-f(x)-g(x)
Now let's substitute the given functions:
= (2x^2+x-3)⋅(x-1)-(2x^2+x-3)-(x-1)
Next, we can simplify this expression by multiplying:
= (2x^2+x-3)⋅(x-1) - 2x^2 - x + 3 - x + 1
Using the distributive property, we get:
= 2x^3 - 2x^2 + x^2 - x - 3x + 3 - x + 1
Combining like terms, we have:
= 2x^3 - x^2 - 5x + 4
Therefore, f(x)⋅g(x)-[f(x)+g(x)] expressed as a polynomial in standard form is 2x^3 - x^2 - 5x + 4.
really? Just make the substitutions.
f(x) - g(x) = (2x^2+x-3) - (x-1)
f(x) + g(x) = (2x^2+x-3) + (x-1)
Now just collect like terms as needed