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alina1380 [7]
3 years ago
11

Please Help! Factor the following trinomial

x^2-24x+16" alt="9x^2-24x+16" align="absmiddle" class="latex-formula">
Please show work
Mathematics
2 answers:
Dmitrij [34]3 years ago
8 0

=> 9x² - 24x + 16

Split the middle term(term with x) in such a manner so that the product of those parts is equal to the product of term with x² and constant. Here, those parts are 12 & 12 as 12*12 = 9*16.

=> 9x² - 24x + 16

=> 9x² - (12 + 12)x + 16

=> 9x² - 12x - 12x + 16

=> 3x(3x - 4) - 4(3x - 4)

=> (3x - 4)(3x - 4)

Method 2

=> 9x² - 24x + 16

=> (3x)² - 2(3x*4) + 4²

=> (3x - 4)²

=> (3x - 4)(3x - 4)

Method 3

In case if you can't find the factors of the middle term.

Say f(x) = 0, find the zeroes using quadratic formula. Zeroes of this eqⁿ are [-(-24) ± √24²-4(9)(16)] / 2(9) = 4/3 & 4/3

Therefore, f(x) = (x - 4/3)(x - 4/3) = (3x - 4)(3x - 4)/9

Ignore the numeric constant.

f(x) = (3x - 4)(3x - 4)

AlexFokin [52]3 years ago
5 0

\huge\colorbox{pink}{Hey \: panda!}

The answer=>

For this,we need to know what's Middle splitting method

  • In order to factorize x² + bx + c we have to find numbers p and q such that p + q = b and pq = c. After finding p and q, we split the middle term in the quadratic as <em><u>px + qx and</u></em> get desired factors by grouping the terms.

Step-by-step explanation:

9x {}^{2}  - 24x + 16 \\  =  > 9x {}^{2}  - 12x - 12x + 16 \\  =  > 3x(3x - 4) - 4(3x - 4) \\  =  > (3x - 4)(3x - 4) \\ so... \\ x = eitherway \: 4

i.e

Alpha= Beta = 4

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\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}

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kifflom [539]

9514 1404 393

Answer:

  {Segments, Geometric mean}

  {PS and QS, RS}

  {PS and PQ, PR}

  {PQ and QS, QR}

Step-by-step explanation:

The three geometric mean relationships are derived from the similarity of the triangles the similarity proportions can be written 3 ways, each giving rise to one of the geometric mean relations.

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  short leg : hypotenuse = RP/PQ = PS/RP   ⇒   RP² = PS·PQ

  long leg : hypotenuse = RQ/QP = QS/RQ   ⇒   RQ² = QS·QP

I find it easier to remember when I think of it as <em>the segment from R is equal to the geometric mean of the two segments the other end is connected to</em>.

__

  segments PS and QS, gm RS

  segments PS and PQ, gm PR

  segments PQ and QS, gm QR

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