Question

polynomial test
name the polynomial using degree and term:
$6a^7$
$9 + 4m^3$
$-9x + 4x^2 - 2x^3 - 10x^7$
$-n^5$
$-7 + 3n^4$
$-7m^3 - 6m^5 + 7m - 7m^4$
$-2 + 6x - x^2$
$5v + 9v^3 - 3v^3$
$10x^6$
$-2p^4 + 10p^6 + 5p^2$
add and subtract the polynomials (make sure to combine like terms and watch your signs!):
$(5p^2 - 3) + (2p^2 - 3p^2)$
$(a^3 - 2a^2) - (3a^2 - 4a^3)$
$(4 + 2n^3) + (5n^3 + 2)$
$(4n - 3n^3) - (3n^3 + 4n)$
$(3a^2 + 1) - (4 + 2a^2)$
$(4r^3 + 3r^4) - (r^4 - 5r^3)$
$(5a + 4) - (5a + 3)$
$(3x^4 - 3x) - (3x - 3x^4)$
$(-4k^4 + 14 + 3k^2) + (-3k^4 - 14k^2 - 8)$
$(3 - 6n^5 - 8n^4) - (-6n^4 - 3n - 8n^5)$

Explanation:

Part 1: Name the polynomial using degree and term

A polynomial is named by: 1) identifying the highest exponent (degree), 2) counting the number of terms, then combining these (e.g., "quartic monomial" for degree 4, 1 term).

Step1: Remove parentheses, distribute signs

Step2: Combine like terms

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Problem 1: $(5p^2 - 3) + (2p^2 - 3p^3)$

Step1: Remove parentheses

$5p^2 - 3 + 2p^2 - 3p^3$

Step2: Combine like terms

$-3p^3 + (5p^2+2p^2) - 3 = -3p^3 +7p^2 -3$

Answer:

1. $6a^3$: Cubic monomial
2. $9 + 4m^3$: Cubic binomial
3. $-9x + 4x^2 - 2x^3 - 10x^7$: Septic (7th-degree) polynomial
4. $-n^7$: Septic monomial
5. $-7 + 3n^3$: Cubic binomial
6. $-7m^3 - 6m^2 + 7m - 7m^4$: Quartic polynomial
7. $-2 + 6x - x^2$: Quadratic trinomial
8. $5v + 9v^2 - 3v^3$: Cubic trinomial
9. $10x^9$: Nonic monomial
10. $-2p^4 + 10p^6 + 5p^2$: Sixth-degree trinomial

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Part 2: Add and subtract the polynomials