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Which binomials have a GCF of 2a^3? SELECT

TWO (circle your answers) (16 points)
a)
b
d e)
f)
g)
a^4 + 2a^3
4a^t + 8a^3
10a^4 + 8a^3
10a^2 + 4a^3
8a^6 - 6а^3
6á^4 + 18a^3
2a^3 - 2a^2

1 answer

To find the binomials that have a greatest common factor (GCF) of \( 2a^3 \), we can factor \( 2a^3 \) out of each binomial and see if all terms in the binomial include \( 2a^3 \) as a factor.

  1. \( a) \quad a^4 + 2a^3 \)

    • GCF is not \( 2a^3 \). GCF is \( a^3 \).

  2. \( b) \quad 4a^4 + 8a^3 \)

    • GCF is \( 4a^3 \). Not \( 2a^3 \).

  3. \( c) \quad 10a^4 + 8a^3 \)

    • GCF is \( 2a^3 \). This is a candidate.

  4. \( d) \quad 10a^2 + 4a^3 \)

    • GCF is \( 2a^2 \). Not \( 2a^3 \).

  5. \( e) \quad 8a^6 - 6a^3 \)

    • GCF is \( 2a^3 \). This is a candidate.

  6. \( f) \quad 6a^4 + 18a^3 \)

    • GCF is \( 6a^3 \). Not \( 2a^3 \).

  7. \( g) \quad 2a^3 - 2a^2 \)

    • GCF is \( 2a^2 \). Not \( 2a^3 \).

From this analysis, the two binomials that have a GCF of \( 2a^3 \) are:

  • \( c) \quad 10a^4 + 8a^3 \)
  • \( e) \quad 8a^6 - 6a^3 \)

So, the correct selections are (c) and (e).