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lina2011 [118]
3 years ago
7

Explain in easy terms, how the signs of the last terms of the two binomial factors of a trinomial are determined?

Mathematics
1 answer:
shutvik [7]3 years ago
5 0

Explanation:

It helps to understand the process of multiplying the binomials. Consider the simple case ...

  (x +a)(x +b)

The product is ...

  (x +a)(x +b) = x² +(a+b)x + ab

If the <em>constant</em> term (ab) is <em>negative</em>, the signs of (a) and (b) are <em>different</em>.

If the constant term (ab) is <em>positive</em>, the signs of (a) and (b) will both match the sign of the coefficient of the linear term (a+b).

___

Of course, the sum (a+b) will have the sign of the (a) or (b) value with the largest magnitude, so when the signs of (a) and (b) are different, the factor with the largest magnitude will have the sign of (a+b), the x-coefficient.

<u>Example</u>:

  x² -x -6

 -6 tells you the factors will have different signs. -x tells you the one with the largest magnitude will be negative.

  -6 = -6×1 = -3×2 = ... (other factor pairs have a negative factor with a smaller magnitude)

 The sums of these factor pairs are -5 and -1. We want the factor pair that has a sum of -1, the coefficient of x in the trinomial.

  x² -x -6 = (x -3)(x +2)

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OLEGan [10]

Answer:

PQ = 3.58, and RQ = 10.4

Step-by-step explanation:

We are given the hypotenuse of the triangle, and an angle. Use sin and cos to solve.  

Hypotenuse = 11,

Opposite side is PQ

Adjacent side is RQ

x = 19

Sin x  = (opposite side)/(hypotenuse)

Cos x = (adjacent side)/(hypotenuse)

For PQ, this is the side opposite to the angle, so use sin,

Sin 19 = x/11

   11(Sin 19) = x

        3.58 = x        (rounded to the nearest hundredth)            

For RQ, this is the side adjacent to the angle, so use cos,

Cos 19 = x/11

   11(Cos 19) = x

        10.4 = x        (rounded to the nearest hundredth)        

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3 years ago
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goldenfox [79]

Answer:

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Step-by-step explanation:

hope this helps:)

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Answer:

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I'm sorry if I misunderstood.

Good luck mate! :)

Please add Brainliest if you'd like, not that it matters.

Remember to try your best every day!

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