How do you factor the expression #14m^2 + 55m + 21 #?

Answer 1

(7m + 3)(2m + 7)

Use the new AC Method to factor trinomials (Socratic Search). #y = 14m^2 + 55m + 21 =# 14( x + p)(x + q) Converted trinomial: #y' = m^2 + 55m + 294 =# (m + p')(m + q'). Since ac > 0, p' and q' have same sign. Compose factor pairs of (ac = 294) -->... (3, 98)(6, 49). This last sum is (6 + 49 = 55 = b). Then, p' = 6 and q' = 49. Back to original y, we have:#p = (p')/a = 6/14 = 3/7#, and #q = (q')/a = 49/14 = 7/2#. Factored form: #y = 14(m + 3/7)(m + 7/2) = (7m + 3)(2m + 7)#

NOTE : This method avoids the lengthy factoring by grouping

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Answer 2

To factor the expression (14m^2 + 55m + 21), you can use the factoring by grouping method. Here's how you can do it:

  1. Multiply the coefficient of (m^2) (14) by the constant term (21). This gives you (14 \times 21 = 294).
  2. Find two numbers that multiply to 294 and add to the coefficient of (m) term (55). The numbers are 42 and 7.
  3. Rewrite the middle term (55m) using these two numbers: (55m = 42m + 13m).
  4. Group the terms: (14m^2 + 42m + 13m + 21).
  5. Factor by grouping: (14m(m + 3) + 7(3m + 7)).
  6. Factor out the common factors: (14m(m + 3) + 7(3m + 7)).
  7. The factored expression is ( (14m + 7)(m + 3)).
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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