Question

10 fill in the blank 1 point
find the greatest common factor (gcf) of 6, 8, 16.
choose your answer...

11 fill in the blank 1 point
find the greatest common factor (gcf) of ( 21xy^4 ), ( 42x^2y^2 ), ( 9x^4y ).
choose your answer...

12 fill in the blank 1 point
solve the equation by factoring: ( x^2 - 10x + 24 = 0
choose your answer...

Explanation:

Question 10

Step1: Factor each number

Factor of \(6 = 2\times3\)
Factor of \(8 = 2\times2\times2\)
Factor of \(16 = 2\times2\times2\times2\)

Step2: Identify common factors

The common prime factor among 6, 8, and 16 is 2.

Step1: Factor coefficients and variables

• Coefficients: \(21 = 3\times7\), \(42 = 2\times3\times7\), \(9 = 3\times3\)
• For \(x\): The lowest power of \(x\) is \(x^1\) (from \(21xy^4\))
• For \(y\): The lowest power of \(y\) is \(y^1\) (from \(9x^4y\))

Step2: Determine GCF

The common factor for coefficients is 3, for \(x\) is \(x\), and for \(y\) is \(y\). So GCF is \(3xy\).

Step1: Factor the quadratic

We need two numbers that multiply to 24 and add to -10. The numbers are -4 and -6.
So \(x^2 - 10x + 24=(x - 4)(x - 6)\)

Step2: Solve for x

Set each factor to zero:
\(x - 4 = 0\) gives \(x = 4\)
\(x - 6 = 0\) gives \(x = 6\)

Answer:

2

Question 11