Simplify the expression.
5(x − 1) − 3(x2 + 4x + 5) − 8(x + 7)
Classify the answer by number of terms and degree.
1st-degree monomial
1st-degree binomial
1st-degree trinomial
2nd-degree binomial
2nd-degree trinomial
well, the x^2 term will not go away, so it will be a 2nd-degree expression.
Simplify it and note that there are 3 terms, so it's a trinomial.
To simplify the expression 5(x − 1) − 3(x^2 + 4x + 5) − 8(x + 7), we will apply the distributive property and combine like terms.
First, distribute the 5 to (x - 1):
5(x - 1) = 5x - 5
Next, distribute the 3 to (x^2 + 4x + 5):
3(x^2 + 4x + 5) = 3x^2 + 12x + 15
Lastly, distribute the 8 to (x + 7):
8(x + 7) = 8x + 56
Now, substitute these simplified terms back into the original expression:
5x - 5 - 3x^2 - 12x - 15 - 8x - 56
Next, combine like terms:
(5x - 12x - 8x) + (-3x^2) + (-5 - 15 - 56)
Simplifying further:
-15x + (-3x^2) - 76
So, the simplified expression is -3x^2 - 15x - 76.
Now, let's classify the answer based on the number of terms and degree:
The simplified expression -3x^2 - 15x - 76 is a 1st-degree trinomial because it consists of three terms and the highest power of x (degree) is 1.