Factor 8x^3 + 12x^2.

Factor 8x^3 + 12x^2.

• A. 2x^2(4x + 6)
• B. 8x^3 + 12x^2
• C. 4x^2(2x + 3)
• D. 8x^2( x + 1.5)

Answer: (C)

Pull out the greatest common factor. Both terms share a factor of x^2 and a numeric factor of 4, so you factor 4x^2 from the expression. Dividing each term by 4x^2 gives 2x + 3, so the factorization is 4x^2(2x + 3). This form is the simplest and most useful because it shows the exact common factor and leaves a binomial with integer coefficients. If you pull out only 2x^2, you’d get 2x^2(4x + 6), which is the same after factoring a 2 from the inside to get 4x^2(2x + 3). The version with decimals like 8x^2(x + 1.5) is mathematically correct but less tidy; standard practice favors the integer-coefficient, fully factored form.

Pull out the greatest common factor. Both terms share a factor of x^2 and a numeric factor of 4, so you factor 4x^2 from the expression. Dividing each term by 4x^2 gives 2x + 3, so the factorization is 4x^2(2x + 3). This form is the simplest and most useful because it shows the exact common factor and leaves a binomial with integer coefficients.

If you pull out only 2x^2, you’d get 2x^2(4x + 6), which is the same after factoring a 2 from the inside to get 4x^2(2x + 3). The version with decimals like 8x^2(x + 1.5) is mathematically correct but less tidy; standard practice favors the integer-coefficient, fully factored form.