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Irina18 [472]
3 years ago
12

How do i get the factor of 3p2-2p-5

Mathematics
2 answers:
tensa zangetsu [6.8K]3 years ago
5 0
3p² - 2p - 5 = 0

3p² + 3p - 5p - 5 = 0

3p(p + 1) -5(p + 1) = 0

(3p - 5)(p + 1) = 0

p = 5/3 or -1

Hope this helps!
Reika [66]3 years ago
5 0

The first term is, <span> <span>3p2</span> </span> its coefficient is <span> 3 </span>.
The middle term is, <span> -2p </span> its coefficient is <span> -2 </span>.
The last term, "the constant", is <span> -5 </span>

Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 3</span> • -5 = -15</span> 

Step-2 : Find two factors of  -15  whose sum equals the coefficient of the middle term, which is  <span> -2 </span>.

<span><span>     -15   +   1   =   -14</span><span>     -5   +   3   =   -2   That's it</span></span>


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  3 
                     <span>3p2 - 5p</span> + 3p - 5

Step-4 : Add up the first 2 terms, pulling out like factors :
                    p • (3p-5)
              Add up the last 2 terms, pulling out common factors :
                     1 • (3p-5)
Step-5 : Add up the four terms of step 4 :
                    (p+1)  •  (3p-5)
             Which is the desired factorization

Final result : (3p - 5) • (p + 1) <span>
</span>
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determine the point of intersection of the following pair of lines ............2x-3y-4=-13 and 5x=-2y+25. 3x+2y-7=0 and 2x=12-5y
grandymaker [24]

Answer:

  1. (x, y) = (3, 5)
  2. (x, y) = (1, 2)

Step-by-step explanation:

A nice graphing calculator app makes these trivially simple. (See the first two attachments.) It is available for phones, tablets, and as a web page.

__

The usual methods of solving a system of equations involve <em>elimination</em> or <em>substitution</em>.

There is another method that is relatively easy to use. It is a variation of "Cramer's Rule" and is fully equivalent to <em>elimination</em>. It makes use of a formula applied to the equation coefficients. The pattern of coefficients in the formula, and the formula itself are shown in the third attachment. I like this when the coefficient numbers are "too messy" for elimination or substitution to be used easily. It makes use of the equations in standard form.

_____

1. In standard form, your equations are ...

  • 2x -3y = -9
  • 5x +2y = 25

Then the solution is ...

  x=\dfrac{-3(25)-(2)(-9)}{-3(5)-(2)(2)}=\dfrac{-57}{-19}=3\\\\y=\dfrac{-9(5)-(25)(2)}{-19}=\dfrac{-95}{-19}=5\\\\(x,y)=(3,5)

__

2. In standard form, your equations are ...

  • 3x +2y = 7
  • 2x +5y = 12

Then the solution is ...

  x=\dfrac{2(12)-5(7)}{2(2)-5(3)}=\dfrac{-11}{-11}=1\\\\y=\dfrac{7(2)-12(3)}{-11}=\dfrac{-22}{-11}=2\\\\(x,y)=(1,2)

_____

<em>Note on Cramer's Rule</em>

The equation you will see for Cramer's Rule applied to a system of 2 equations in 2 unknowns will have the terms in numerator and denominator swapped: ec-bf, for example, instead of bf-ec. This effectively multiplies both numerator and denominator by -1, so has no effect on the result.

The reason for writing the formula in the fashion shown here is that it makes the pattern of multiplications and subtractions easier to remember. Often, you can do the math in your head. This is the method taught by "Vedic maths" and/or "Singapore math." Those teaching methods tend to place more emphasis on mental arithmetic than we do in the US.

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In total Christine hiked 14.75

So, 16 - 14.75 = 1.25

Overall, Brian hiked 1.25 more miles than Christine.

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