➕ Algebra 1 · Exponents and Polynomials
Adding and Subtracting Polynomials flashcards
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All 16 flashcards at a glance
Card 1
What is a polynomial?
A monomial or a sum of monomials: each term is a number times a variable (or several variables) raised to whole-number exponents 0, 1, 2 and so on. For example, 3x2 − 5x + 1.
Card 2
What do monomial, binomial and trinomial mean?
A polynomial with 1, 2 and 3 terms. Examples: −8x, x2 + 3 and 2x2 − x + 6.
Card 3
What is the degree of 7x2 − 4x6 + 1?
6. With one variable, the degree is the highest exponent, even though 7x2 is written first.
Card 4
Write 3x − 7x2 + 10 in standard form.
−7x2 + 3x + 10. Highest power first, and each sign moves with its term.
Card 5
What is the leading coefficient of 2x − 8x2 + 5?
−8. In standard form, −8x2 + 2x + 5, the leading term is −8x2.
Card 6
Is 5/x + 2 a polynomial?
No. 5/x = 5x−1 has a negative exponent. Polynomial exponents are whole numbers: 0, 1, 2 and so on.
Card 7
Is √x + 4 a polynomial?
No. √x = x1/2, and 1/2 is not a whole-number exponent.
Card 8
Add (5x + 1) + (3x − 6).
8x − 5. The x terms: 5 + 3 = 8. The constants: 1 + (−6) = −5.
Card 9
Subtract (6x − 1) − (4x − 9).
2x + 8. Since −(4x − 9) = −4x + 9, the expression is 6x − 1 − 4x + 9.
Card 10
What does the minus sign in front of a parenthesized polynomial do?
It multiplies every term inside by −1, so every sign flips: −(x2 − 3x + 5) = −x2 + 3x − 5.
Card 11
Why check with x = 3 instead of 0, 1 or 2?
At 0 only the constants get tested. At 1 every power of x equals 1. At 2, 2x2 and 4x are both 8. These can make a wrong answer look right. A value like 3 reveals more mistakes, but no single value catches everything (at 3, x2 and 3x are both 9), so test a second value too.
Card 12
Is the sum of two polynomials always a polynomial? Is its degree always the larger of the two degrees?
Yes to the first. No to the second: leading terms can cancel. (x2 + x) + (−x2 + 3) = x + 3 has degree 1.
Card 13
In vertical form, what do you write for a missing power?
A 0 placeholder, so like terms stay in the same column. For example, 2x4 − 7 becomes 2x4 + 0x3 + 0x2 + 0x − 7.
Card 14
In this lesson’s SIGN trick for subtracting polynomials, what do the letters stand for?
Spot the polynomial after the minus sign. Invert the sign of every one of its terms. Group like terms. Number-check with x = 3.
Card 15
What does “subtracting is adding the opposite” mean?
A − B = A + (−B). The opposite of B has every sign changed. Change every sign in B, then add.
Card 16
Are 4x2y and 4xy2 like terms?
No. Like terms need the same letters with the same exponents. x2y and xy2 both have degree 3, but their variable parts differ, so they do not combine.