Factorising Algebraic Expressions (with negative common factors)

What is the correct factorization of −2𝑥−6?

(taking out the negative HCF)

• −2(x+3)

• −6(x+2)

• x(−2−6)

• −6(2x+1)

Answer explanation

Explanation: The common factor between -2x and -6 is -2. Dividing each term by -2 results in −2(𝑥+3).

What is the correct factorization of −4𝑎+12?

• −4(a−3)

• −12(a−4)

• 𝑎(−4+12)

• −12(4a+1)

Answer explanation

Explanation: The common factor between -4a and 12 is -4. Dividing each term by -4 results in −4(𝑎−3).

What is the correct factorization of −6𝑐−18?

• −18(6c+1)

• c(−6−18)

• −18(c+6)

• −6(c+3)

Answer explanation

Explanation: The common factor between -6c and -18 is -6. Dividing each term by -6 results in −6(𝑐+3).

What is the correct factorization of −8𝑥+24?

• −8(x−3)

• −24(x−8)

• x(−8+24)

• −24(8x+1)

Answer explanation

Explanation: The common factor between -8x and 24 is -8. Dividing each term by -8 results in −8(𝑥−3).

What is the correct factorization of −10𝑎−30?

• −30(a+10)

• a(−10−30)

• −10(a+3)

• −30(10a+1)

Answer explanation

Explanation: The common factor between -10a and -30 is -10. Dividing each term by -10 results in −10(𝑎+3).

What is the correct factorization of 4𝑦−12? (take a negative common factor)

• −12(y−4)

• −4(y−3)

• y(4−12)

• −12(4y+1)

Answer explanation

Explanation: The common factor between 4y and -12 is -4. Dividing each term by -4 results in −12(𝑦−4).

What is the correct factorization of 6𝑏−18? (take a negative common factor)

• b(6−18)

• −18(6b+1)

• −18(b−6)

• −6(b−3)

Answer explanation

Explanation: The common factor between 6b and -18 is -6. Dividing each term by -6 results in −6(𝑏−3).

What is the correct factorization of 8𝑑−24? (Take out a negative common factor)

• −24(d−8)

• d(8−24)

• −8(d−3)

• −24(8d+1)

Answer explanation

Explanation: The common factor between 8d and -24 is -8. Dividing each term by -8 results in −8(𝑑−3).