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Reptile [31]
2 years ago
7

Divide using synthetic division, and write a summary statement in fraction form 2x^3-3x^2-5x+4/x-2

Mathematics
2 answers:
Tems11 [23]2 years ago
7 0
I’m not sure if this is how you’re supposed to write the summary statement, but I got the answer of (2x+3)(x-1)(-2/(x-2)) (see photo to see my work

choli [55]2 years ago
6 0

Answer:

2x²+ x - 3 + \frac{(-2)}{x-2}

Step-by-step explanation:

We have to divide the polynomial (2x³- 3x²- 5x + 4) by (x - 2) using synthetic division.

2  |   2     -3    -5     4

       ×      4      2    -6        

     -------------------------

       2      1      -3     -2

Now we will form the expression in the form of fraction again

2x²+ 1.(x) - 3 + \frac{(-2)}{x-2}

Therefore, 2x²+ x - 3 + \frac{(-2)}{x-2} will be the answer.

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Given: △ACM, m∠C=90°, CP ⊥ AM
larisa86 [58]

Answer:  The answer is 3\dfrac{4}{7}.

Step-by-step explanation:  Given in the question that ΔAM is a right-angled triangle, where ∠C = 90°, CP ⊥ AM, AC : CM = 3 : 4 and MP - AP = 1. We are to find AM.

Let, AC = 3x and CM = 4x.

In the right-angled triangle ACM, we have

AM^2=AC^2+CM^2=(3x)^2+(4x)^2=9x^2+16x^2=25x^2\\\\\Rightarrow AM=5x.

Now,

AM=AP+PM=AP+(AP+1)\\\\\Rightarrow 2AP=AM-1\\\\\Rightarrow 2AP=5x-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(A)

Now, since CP ⊥ AM, so ΔACP and ΔMCP are both right-angled triangles.

So,

CP^2=AC^2-AP^2=CM^2-MP^2\\\\\Rightarrow (3x)^2-AP^2=(4x)^2-(AP+1)^2\\\\\Rightarrow 9x^2-AP^2=16x^2-AP^2-2AP-1\\\\\Rightarrow 2AP=7x^2-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(B)

Comparing equations (A) and (B), we have

5x-1=7x^2-1\\\\\Rightarrow 5x=7x^2\\\\\Rightarrow x=\dfrac{5}{7},~\textup{since }x\neq 0.

Thus,

AM=5\times\dfrac{5}{7}=\dfrac{25}{7}=3\dfrac{4}{7}.

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