Question

factoring polynomials worksheet

1. factor out the greatest common factor in the following questions. 4 marks

a. 6x²+12x
b. 8x+24
c. 3x²+12x+18
d. 4pn+2n+8p

1. expand and simplify the following polynomials. 4 marks

a. (x+9)(x+2)
b. (x+3)²
c. (x+3)(x-2)
d. (3x-4)(2x+3)

1. fully factor the following perfect square trinomials. show your work. 5 marks

a. x²+6x+1
b. x²+6x+121
c. 25n²+30n+9
d. 9h²+12h+4
e. 3k² - 24k + 48

1. factor the following trinomials in the form on x²+bx+c 4 marks

a. x²+12x+27
b. x²+7x+30
c. x²+5x+6
d. 3x²+12x+9

1. a rectangle has an area x²+8x+15 5 marks

a. factor the trinomial
b. calculate the actual dimensions if x=4cm

Explanation:

Let's solve question 1a as an example (factoring out the greatest common factor from \(6x^2 + 12x\)):

Step1: Identify the GCF of coefficients and variables

The coefficients are 6 and 12. The GCF of 6 and 12 is 6. For the variable part, \(x^2\) and \(x\) have a GCF of \(x\) (since \(x\) is the lowest power of \(x\) present). So the overall GCF is \(6x\).

Step2: Factor out the GCF

Divide each term in \(6x^2 + 12x\) by \(6x\):
\(\frac{6x^2}{6x} = x\) and \(\frac{12x}{6x} = 2\).
So, \(6x^2 + 12x = 6x(x + 2)\).

Step1: Find GCF of 8 and 24

The GCF of 8 and 24 is 8. There's no variable in the second term, so we factor out 8.

Step2: Factor out 8

Divide \(8x\) by 8: \(\frac{8x}{8}=x\), divide \(-24\) by 8: \(\frac{-24}{8}=-3\).
So, \(8x - 24 = 8(x - 3)\).

Step1: Determine GCF of 3, 12, 18

The GCF of 3, 12, and 18 is 3.

Step2: Factor out 3

Divide each term by 3: \(\frac{3x^2}{3}=x^2\), \(\frac{12x}{3}=4x\), \(\frac{18}{3}=6\).
So, \(3x^2 + 12x + 18 = 3(x^2 + 4x + 6)\).

Answer:

\(6x(x + 2)\)

For question 1b (\(8x - 24\)):