Addition & Subtraction of Polynomials

Polynomial

Meaning: A polynomial is an expression with one or more algebraic terms.

Definition: A polynomial is made from constants, variables, and whol$e-n$umber powers of variables using addition or subtraction.

3$x^{2} + 2$$x - 7$ is a polynomial.

• At this level, focus on terms and like terms.

Like Terms

Meaning: Like terms have the same variable part.

Definition: Terms are like terms if their variables and powers are exactly the same.

5xy an$d -2$xy are like terms. 5x and 5$x^{2}$ are not like terms.

• Check the variable.
• Check the power.
• Combine only the coefficients.

Adding Polynomials

Meaning: Addition combines like terms.

Definition: To add polynomials, group like terms and add their coefficients.

$(3x + 4) + (2x + 5) = 5$$x + 9$.

• Remove brackets with plus sign.
• Group like terms.
• Add coefficients.

Subtracting Polynomials

Meaning: Subtraction means taking away every term of the second polynomial.

Definition: To subtract a polynomial, change the sign of each term being subtracted, then combine like terms.

$(5x + 3) - (2x - 4) = 5$$x + 3 - 2$$x + 4 = 3$$x + 7$.

• Change every sign inside the second bracket.

Easy

Question: Add 4$x + 7$x.

1. Both terms are like terms.
2. Add coefficients: $4 + 7 = 11$.
3. Answer: 11x.

Medium

Question: Add (3$x^{2} + 5$$x - 2$) and (4$x^{2} - 2$$x + 9$).

1. Group like terms.
2. $x^{2}$ terms: 3$x^{2} + 4$$x^{2} = 7$$x^{2}$.
3. x terms: 5$x - 2$$x = 3$x.
4. Constants: -$2 + 9 = 7$.
5. Answer: 7$x^{2} + 3$$x + 7$.

Exam-level

Question: Subtract 2$x^{2} - 3$$x + 4$ from 6$x^{2} + x - 5$.

1. Write $(6x^{2} + x - 5) - (2x^{2} - 3x + 4)$.
2. Change signs in the second bracket: 6$x^{2} + x - 5 - 2$$x^{2} + 3$$x - 4$.
3. Combine like terms.
4. Answer: 4$x^{2} + 4$$x - 9$.