7.4 Review

• 3

• 3x

• 6

• 15

Answer explanation

To find the greatest common monomial factor of 6x^2 and -15y, we identify the common factors. The coefficients 6 and 15 share a GCF of 3, and both terms have a common variable factor of x. Thus, the GCF is 3x.

• r

• 2

• s

• 2r

Answer explanation

To find the greatest common monomial factor of r^2 + 2rs, we look for the highest factor common to both terms. Both terms share 'r' as a factor, making 'r' the greatest common monomial factor.

• 6w

• 14w

Answer explanation

To find the greatest common monomial factor of 6w^3 and -14w^2, we identify the common factors. The coefficients 6 and 14 share a GCF of 2, and the variable part has a minimum power of w^2. Thus, the GCF is 2w^2.

• 6

• 3a

• 2b

• 18

Answer explanation

To find the greatest common monomial factor of 18a^2 and -6b, we look for the highest number that divides both coefficients (18 and 6), which is 6. Thus, the greatest common monomial factor is 6.

• 4

• x

• 4x

Answer explanation

To find the greatest common monomial factor of 4x^2 - 4x, factor out the common terms. Both terms share a factor of 4 and x, resulting in 4x as the greatest common monomial factor.

• 5q

• 10

• q

Answer explanation

To find the greatest common monomial factor of 5p^2q and 10q, we identify the common factors. Both terms share a factor of 5 and q. Thus, the greatest common monomial factor is 5q.

• 20b

• 100b

Answer explanation

To find the greatest common monomial factor of 10b^4, 100b^3, and -80b^2, we identify the common coefficients and the lowest power of b. The GCF is 10b^2, as 10 is the largest common factor and b^2 is the lowest power.

• 36n

Answer explanation

To find the greatest common monomial factor of -30n^5, 30n^4, and -36n^3, we identify the common coefficients and the lowest power of n. The GCF is 6n^3, as 6 is the highest common factor of the coefficients and n^3 is the lowest power.

• (x - 2)(x - 3)

• (x + 2)(x + 3)

• (x - 1)(x - 6)

• (x + 1)(x - 6)

Answer explanation

To factor the quadratic expression x^2 - 5x + 6, we look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 satisfy this, leading to the factors (x - 2)(x - 3).

• (p + 5)(p + 5)

• (p + 3)(p + 7)

• (p + 2)(p + 8)

• (p + 1)(p + 9)

Answer explanation

The expression p^2 + 10p + 25 can be factored as (p + 5)(p + 5) because it is a perfect square trinomial. The other options do not yield the original expression when multiplied.