Steven will factor the expression 42xyz + 56xy – 7x by dividing each term by a common factor. Which possible common factor could Steven use? (choose 2)
One possible common factor that Steven could use is x. Another possible common factor that Steven could use is 7.
To find the common factor that Steven could use to factor the expression 42xyz + 56xy - 7x, we need to look for the greatest common factor (GCF) among the terms. The possible common factors that can be used are:
1. 7 - This is the factor that can be divided from all the terms: 7 divides into 42, 56, and 7.
2. x - This is another factor that can be divided from all the terms: x divides into x, xy, and x.
So, the possible common factors that Steven could use are 7 and x.
To find the possible common factors that Steven could use to factor the expression 42xyz + 56xy - 7x, we need to determine the highest common factor (HCF) of the coefficients of each term.
The coefficients in this expression are 42, 56, and -7.
Step 1: Find the factors of each coefficient.
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of -7: 1, -1, 7, -7
Step 2: Determine the common factors shared by all three coefficients.
Considering the common factors among the coefficients - 42, 56, and -7, we find that the possible common factors are:
1. The number 1 is a factor of all three coefficients.
2. The number 7 is another common factor, since it can be divided evenly into 42, 56, and -7.
Therefore, the two possible common factors that Steven could use to factor the expression are 1 and 7.