Add the polynomial expressions 3−2p−5p2 and p4−3p+4.(1 point)
The expression 3−2p−5p^2 + p^4−3p+4 can be simplified as p^4 - 5p^2 - 5p + 7.
im confused
I apologize for any confusion. Let me clarify the steps to add the polynomial expressions.
Given the polynomial expressions 3−2p−5p^2 and p^4−3p+4, we need to add them together.
First, we combine the like terms. The terms with the same exponent are considered "like terms."
- In the expression 3−2p−5p^2, we have a constant term 3, a linear term -2p, and a quadratic term -5p^2.
- In the expression p^4−3p+4, we have a quartic term p^4, a linear term -3p, and a constant term 4.
Next, we group the like terms together:
(3 - 2p - 5p^2) + (p^4 - 3p + 4)
This becomes:
p^4 + (-5p^2 - 2p - 3p) + (3 + 4)
Combining the coefficients of like terms:
p^4 - 5p^2 - 5p + 7
So, the sum of the polynomial expressions 3−2p−5p^2 and p^4−3p+4 is p^4 - 5p^2 - 5p + 7.
What is (3x2−2)+(11−5x)?(1 point)
To simplify the expression (3x^2−2)+(11−5x), we first simplify each pair of parentheses separately.
Within the first parentheses, (3x^2−2), there are no like terms to combine, so it remains the same.
Within the second parentheses, (11−5x), there are no like terms to combine, so it also remains the same.
Now, we can rewrite the simplified expression by combining the two simplified terms:
(3x^2−2)+(11−5x)
= 3x^2 - 2 + 11 - 5x
Next, combine the constant terms (-2 + 11) and the x terms (3x^2 - 5x):
= 3x^2 - 5x - 2 + 11
= 3x^2 - 5x + 9
Therefore, the simplified form of (3x^2−2)+(11−5x) is 3x^2 - 5x + 9.
To add the polynomial expressions 3−2p−5p^2 and p^4−3p+4, we need to combine like terms.
The degree of the first polynomial is 2 (because of the term -5p^2) and the degree of the second polynomial is 4 (because of the term p^4).
So, we write the addition in descending order of degree:
p^4 + (-5p^2) + (-2p) + (-3p) + 3 + 4
Now, we combine like terms by adding the coefficients of the terms:
p^4 + (-5p^2) + (-2p - 3p) + 3 + 4
Simplifying further:
p^4 - 5p^2 - 5p + 7
Therefore, the sum of the polynomial expressions 3−2p−5p^2 and p^4−3p+4 is:
p^4 - 5p^2 - 5p + 7.
To add the polynomial expressions 3-2p-5p^2 and p^4-3p+4, we need to combine like terms. Like terms are terms that have the same variable(s) raised to the same powers.
Step 1: First, let's rearrange the terms in each polynomial in descending order of their degree.
For the first polynomial, 3 - 2p - 5p^2, the terms are already in descending order of their degree.
For the second polynomial, p^4 - 3p + 4, we have only one term with a degree of 4, so there's no need to rearrange.
Step 2: Now we can add the like terms.
The like terms in both polynomials are the constant term (3 and 4), the term with p (or p^1) which appears in both polynomials as -2p and -3p, and the term with p^2 which appears as -5p^2 in the first polynomial and 0p^2 in the second polynomial.
Putting all the like terms together, we have:
-5p^2 - 2p - 3p + p^4 + 3 + 4
Step 3: Simplify the expression.
Combining like terms, we get:
p^4 - 5p^2 - 5p + 7