Math 9
1.
Ch 5.1 Polynomial Bellwork.
Identify the polynomials in the following expressions.
1
a) 2m2 + 1
Non - polynomial
1
d) x2+ x
Polynomial
Name the coefficients, variable, degree, and constant term of each polynomial.
a) –8y
a)
b)
c)
d)
b) 12
c) –2b2 – b + 10
d) –4 – b
coefficient –8; variable y; degree 1; no constant term
no coefficient; no variable; degree 0; constant term 12
coefficients –2, –1; variable b; degree 2; constant term 10
coefficient –1; variable b; degree 1; constant term –4
Identify each polynomial as a monomial, binomial, or trinomial.
a) 19t
monomial
4.
Polynomial
e) 0.25y2
Non - polynomial
3.
c) –4x
b) 3x 2
Polynomial
2.
Name:_____Key______
b) g – 4g2 + 5
c) –1 + xy + y2
d) 4 – 11w
trinomial
trinomial
binomial
Identify the equivalent polynomials.
a) –h2 – 3 + 4h
b)
–h2 + 4h – 3
c) 5m – 3
–h2 + 4h – 3
d)
5m – 3
e) y2 + 5xy – 2
y2 + 5xy – 2
a and b; e and d; c and f
–3 + 4h – h2
–2 + y2 + 5xy
y2 + 5xy – 2
f)
–3 + 5m
5m – 3
5.
6.
Use algebra tiles to model each polynomial. Sketch the tiles.
a) –5 + y2
b) 2x – 1
c) –3a2 – 2a + 1
d) 3z
Write a polynomial to match the following conditions.
a) 2 terms, degree 1, with a constant term of 4
Answers will vary.
3m + 4
b) 3 terms, degree 2, with the coefficient on the 2nd degree term –2
–2y2 + 5y – 1
Math 9
Ch 5.2 Polynomial Bellwork.
Name:_______Key______
Like Terms and Unlike Terms
1. From the list, identify terms that are like 2w2. Explain how you know they are like
terms.
–5w, –6w2, –2, 4w, 3w2, –w2, 11w, 2
–6w2, 3w2, –w2; like terms have the same variable raised to the same exponent.
2. Combine like terms, then sketch the tiles for the simplified polynomial.
a) 4 + x + 1 + 5x + 1
6x + 6
c) 2x2 + 8 – 11 – 4x2 + 5x2
3x2 – 3
3. Simplify each polynomial.
a) 7d – 2d + 1 – 6
5d – 5
c) –4 + 2a + 7 – 4a
–2a + 3
b) –3y2 + 3y – 2
–3y2 + 3y – 2
d) 3y + 7y2 + 1 – y – 2y – 3y2
4y2 + 1
b) –5 – 3 – k – 5k
–8 – 6k
d) 3p – 6 – 4p + 6
–p
4. Simplify each polynomial.
a) 3a2 – 2a – 4 + 2a – 3a2 + 5
b) 7z – z2 + 3 + z2 – 7
7z – 4
1
c) d2 + 3d + 1 + 4d2 + 2
d) –6x2 + 10x – 4 + 4 – 12x – 7x2
–13x2 – 2x
5d2 + 3d + 3
5. Identify the equivalent polynomials. Justify your responses.
a) –5y2 – 3y – 4
b) 10x – 1
c) 1 + x – x2
d) 2y2 – 4 – 16 – 7y2 – 3y + 16
e) –7 + 5x – 7x – 8 + 14 + 12x
f) 5x2 + 7 + 4x – 6x2 – 6 – x – 2x
a and d; b and e; c and f; each has the same terms with the same
coefficients, variables raised to the same exponent.
6. Write a polynomial to represent the perimeter of each rectangle.
a)
b)
4x + 12
12x
Math 9
Ch 5.3 Polynomial Bellwork.
Name:______Key_______
Adding Polynomials
1. Simplify.
a) (– 4h + 1) + (6h + 3)
b) (2a2 + a) + (–5a2 + 3a)
–3a2 + 4a
2h + 4
c) (3y2 – 2y + 5) + (–y2 + 6y + 3)
d) (3 – 2y + y2) + (–1 + y – 3y2)
2 – y – 2y2
2y2 + 4y + 8
2. Add these polynomials.
a) (x – 5) + (2x + 2)
b) (b2 + 3b) + (b2 – 3b)
3x – 3
c) (y2 + 6y) + (–7y2 + 2y)
2b2
d) (5n2 + 5) + (–1 – 3n2)
–6y2 + 8y
2n2 + 4
3. Add these polynomials.
a) (–7x + 5)
+ (2x – 8)
b) (4x2 – 3)
+ (–8x2 – 1)
–5x – 3
–4x2 – 4
c)
(x2 – 4x + 3)
+ (–x2 – 2x – 3)
–6x
d) (3x2 – 4x + 1)
+ (–2x2 + 4x + 1)
x2
+2
4. Add.
a) (y2 + 6y – 5) + (–7y2 + 2y – 2)
b)
(–2n + 2n2 + 2) + (–1 – 7n2 + n)
–6y2 + 8y – 7
–n – 5n2 + 1
c) (3m2 + m) + (–10m2 – m – 2)
d)
(–3d2 + 2) + (–2 – 7d2 + d)
–7m2 – 2
–10d2 + d
5. For each shape below, write the perimeter as a sum of polynomials and in simplest
form.
i)
ii)
(2n + 2) + (n + 1) + (2n + 2) + (n + 1)
= 6n + 6
(3p + 4) + (3p + 4) + (3p + 4)
= 9p + 12
6. The sum of two polynomials is 4r + 5 – 3r2. One polynomial is –8 – 2r2 + 2r; what is
the other polynomial? Explain how you found your answer.
(–8 – 2r2 + 2r) + (
) = 4r + 5 – 3r2
(4r + 5 – 3r2) – (–8 – 2r2 + 2r) = 13 – r2 + 2r
Math 9
Ch 5.4 Polynomial Bellwork.
Name:_____Key______
Subtracting Polynomials
1. Simplify.
a) (4x + 2) – (2x + 1)
2x + 1
c) (4x + 2) – (2x – 1)
2x + 3
b) (4x + 2) – (–2x +1)
6x + 1
d) (4x + 2) – (–2x – 1)
6x + 3
2. Simplify.
a) (2s2 + 3s + 6) – (s2 + s + 2)
s2 + 2s + 4
c) (–2s2 + 3s + 6) – (–s2 + s + 2)
–s2 + 2s + 4
b) (2s2 + 3s – 6) – (s2 + s – 2)
s2 + 2s – 4
d) (2s2 – 3s + 6) – (s2 – s + 2)
s2 – 2s + 4
3. The difference between two polynomials is (5x + 3). One of the two polynomials is
(4x + 1 – 3x2). What is the other polynomial? Explain how you found your answer.
There are two possible answers.
(4x + 1 – 3x2) – (______) = (5x + 3), or (______) – (4x + 1 – 3x2) = (5x + 3)
(4x + 1 – 3x2) – (5x + 3) = (______) = –3x2 – x – 2, or
(______) = (5x + 3) + (4x + 1 – 3x2) = –3x2 + 9x + 4
4. A student subtracted
(3y2 + 5y + 2) – (4y2 + 3y + 2) like this:
= 3y2 – 5y – 2 – 4y2 – 3y – 2
= 3y2 – 4y2 – 5y – 3y – 2 – 2
= –y2 – 8y – 4
a) Explain why the student’s solution is incorrect.
b) What is the correct answer? Show your work.
a) The student is incorrect because he changed the signs in the first polynomial.
b) (3y2 + 5y + 2) – (4y2 + 3y + 2)
= 3y2 + 5y + 2 – 4y2 – 3y – 2
= 3y2 – 4y2 + 5y – 3y + 2 – 2
= –y2 + 2y
5. Subtract.
a) (mn – 5m – 7) – (–6n + 2m + 1)
= mn – 7m – 8 + 6n
b) (2a + 3b – 3a2 + b2) – (–a2 + 8b2 + 3a – b)
= –a + 4b – 2a2 – 7b2
c) (xy – x – 5y + 4y2) – (6y2 + 9y – xy)
= 2xy – x – 14y – 2y2