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Factor the expression 10d² - 6d + 35d - 21 by grouping.

User Kalhartt
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Final answer:

To factor the expression by grouping, we first arrange the terms into pairs with common factors, factor those out, and then factor out the common binomial. After factoring, we get (5d - 3)(2d + 7) and verify that this is correct by expanding and checking against the original expression.

Step-by-step explanation:

To factor the expression 10d² - 6d + 35d - 21 by grouping, we need to rearrange the terms to group them into pairs that share a common factor. Rearranging gives us 10d² + 35d - 6d - 21. Now, we can factor out the common factors from each pair:

  • From the first pair, 10d² + 35d, we factor out 5d, resulting in 5d(2d + 7).
  • From the second pair, -6d - 21, we factor out -3, resulting in -3(2d + 7).

Both groups now share the common factor (2d + 7), so we can factor that out:

(5d - 3)(2d + 7)

Check the answer to see if it is reasonable by expanding the factored form to see if it equals the original expression:

5d(2d) + 5d(7) - 3(2d) - 3(7) = 10d² + 35d - 6d - 21

This confirms that our factoring by grouping is correct.

User Shanice
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