Foundations & Pre-Calculus 10 H
Worksheet (Common factors of a polynomial)
YOU MUST SHOW YOUR WORK WHENEVER POSSIBLE!
1. a) Factor the terms in each set and then identify the greatest common factor.
i) 6, 15n
ii) 4m, m2
b) Use the greatest common factors from above to factor each expression.
i) 15n + 6
ii) 6 – 15n
iii) 4m + m2
3. Factor each binomial.
a) 5y + 10
iv) m2 – 4m
b) 6 + 12x2
c) 4s2 + 14s
d) y + y2
e) 9b2 – 12b3
f) 48s3 – 12
g) 3x2 + 6x4
h)  a 2  a 3
4. Factor each trinomial.
a) 8 + 10x + 6x2
b) 3x2 + 12x – 6
c) 4 – 6y – 8y2
d)  9  12b  6b 2
e) 5 + 15m2 – 10m3
f) 27n + 36 – 18n3
g)  3c 2  13c 4  12c 3
h) s4 + s2 – 4s
5. Here are a student’s solution for factoring a polynomial. Identify the error in the solution and then write a
correct solution.
Factor: 3m 2  9m 3  3m
Solution: 3mm  3m 2 
6. Simplify each expression by combining like terms, then factor.
a) x 2  6 x  7  x 2  2 x  3
b)  7n 3  5n 2  2n  n 2  n 3  12n
7. a) Factor the terms in each set and then identify the greatest common factor.
i) 4s 2t 2 , 12s 2t 3 , 36st 2
ii) 12 x 3 y 2 , 12 x 4 y 3 , 36 x 2 y 4
b) Use the greatest common factors from above to factor each expression.
i) 12s 2t 3  4s 2t 2  36st 2
ii)  36 x 2 y 4  12 x 4 y 3  12 x 3 y 2
8. Factor each trinomial. Check by expanding.
a) 25xy  15x 2  30 x 2 y 2
c) 7r 3 s 3  14r 2 s 2  21rs 2
b) 9 p 4 q 2  6 p 3q 3  12 p 2 q 4
d) 51m 2 n  39mn2  72mn
9. A diagonal of a polygon is a line segment joining non-adjacent vertices.
a) How many diagonals can be drawn from one vertex of a pentagon? A hexagon?
b) Suppose the polygon has n sides. How many diagonals can be drawn from one vertex?
c) The total number of diagonals of a polygon with n sides is
Explain why it is reasonable.
*10.
𝑛2
2
−
3𝑛
2
. Factor this formula.