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a_sh-v [17]
3 years ago
13

Given the function f(x)=x^4+3x^3-7x^2-27x-18 , factor completely

Mathematics
1 answer:
Dmitry [639]3 years ago
6 0

Answer:

(x - 3), (x + 2), (x + 1) and (x + 3)

Step-by-step explanation:

Using synthetic division, I'd begin by testing various factors of -18 to determine whether any of them will divide into f(x)=x^4+3x^3-7x^2-27x-18 with no remainder.  Note that possible factors of -18 are ±1, ±2, ±3, ±6, ±18.

Let's arbitrarily start with -3.  In synthetic division, will the divisor yield a zero remainder ( which would tell us that -3 is a root of f(x)=x^4+3x^3-7x^2-27x-18 and that (x + 3) is a factor)?

-3   )   1    3    -7    -27    -18

              -3    0      21    +18

     ------------------------------------

         1      0    -7     -6      0  

Since the remainder is zero, -3 is a root and (x + 3) is a factor.  The coefficients of the quotient are shown above:  1  0  -7  -6.  Possible factors of 6 include ±1, ±2, ±3, ±6.  Arbitrarily choose 2.  Is this a root or not?

2    )    1     0     -7    -6

                 2     4     -6

      --------------------------

          1       2     -3    -12    

Here the remainder is not zero, so +2 is not a root and (x - 2) is not a factor.

Continuing to use synthetic division, I find that -1 is a root and (x + 1) is a factor, because the remainder of synth. div. is zero.  The coefficients of the quotient are 1, -1 and -6, which represents the quadratic y = x^2 - x - 6, whose factors are (x - 3)(x + 2).

Thus, the four factors of the original polynomial are (x - 3), (x + 2), (x + 1) and (x + 3).

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Step-by-step explanation: Once you subtract 4 from both sides, in order to solve for y (as the equation needs to be in the slope-intercept form, otherwise known as y=mx+b), you end up with y=x-2, which is the right answer. It is the correct answer because the y-intecept shown in the equation matches what is on the graph, in addition to the fact that the slope is just x.

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8090 [49]
D) Definition of Equilateral Triangle
e) Vertical Angles
f1) ΔTVS <span>≅ </span>ΔUVR
f2) Side Angle Side Postulate
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4 0
3 years ago
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kati45 [8]

Answer:

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Step-by-step explanation:

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7 0
2 years ago
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What other information do you need in order to prove the triangles congruent using the SAS congruence postulate
iren [92.7K]

AC is perpendicular to BD.

<h3>Further explanation</h3>
  • We observe that both the ABC triangle and the ADC triangle have the same AC side length. Therefore we know that \boxed{ \ \overline{AC} \cong \overline{AC} \ } is reflexive.
  • The length of the base of the triangle is the same, i.e., \boxed{ \ \overline{BC} = \overline{CD} \ }.
  • In order to prove the triangles congruent using the SAS congruence postulate, we need the other information, namely \boxed{ \ AC \bot BD \ }. Thus we get ∠ACB = ∠ACD = 90°.

Conclusions for the SAS Congruent Postulate from this problem:

  • \boxed{ \ \overline{BC} = \overline{CD} \ }
  • ∠ACB = ∠ACD
  • \boxed{ \ \overline{AC} = \overline{AC} \ }

- - - - - - - - - -

The following is not other or additional information along with the reasons.

  • ∠CBA = ∠CDA no, because that is AAS with ∠ACB = ∠ACD and \boxed{ \ \overline{AC} \cong \overline{AC} \ }
  • ∠BAC = ∠DAC no, because that is ASA with \boxed{ \ \overline{AC} \cong \overline{AC} \ } and ∠ACB = ∠ACD.
  • \boxed{ \ \overline{BC} = \overline{CD} \ } no, because already marked.

- - - - - - - - - -

Notes

  • The SAS (Side-Angle-Side) postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.
  • The ASA (Angle-Side-Angle) postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles.  
  • The SSS (Side-Side-Side) postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.
  • The AAS (Angle-Angle-Side) postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.  
<h3>Learn more</h3>
  1. Which shows two triangles that are congruent by ASA?  brainly.com/question/8876876  
  2. Which shows two triangles that are congruent by AAS brainly.com/question/3767125
  3. About vertical and supplementary angles brainly.com/question/13096411  
9 0
3 years ago
Read 2 more answers
PLs answer fast i need this questions answer
Mashutka [201]

Answer:

x=6

Step-by-step explanation:

Given equation:

x-\left(2x-\dfrac{3x-4}{7}\right)=\dfrac{4x-27}{3}-3

Expand the left side:

\implies x-2x+\dfrac{3x-4}{7}=\dfrac{4x-27}{3}-3

Let all terms on the left side have the same denominator of 7:

\implies \dfrac{7x}{7}-\dfrac{14x}{7}+\dfrac{3x-4}{7}=\dfrac{4x-27}{3}-3

Join the terms on the left side:

\implies \dfrac{7x-14x+3x-4}{7}=\dfrac{4x-27}{3}-3

\implies \dfrac{-4x-4}{7}=\dfrac{4x-27}{3}-3

Let all the terms on the right side have the same denominator of 3:

\implies \dfrac{-4x-4}{7}=\dfrac{4x-27}{3}-\dfrac{9}{3}

Join the terms on the right side:

\implies \dfrac{-4x-4}{7}=\dfrac{4x-27-9}{3}

\implies \dfrac{-4x-4}{7}=\dfrac{4x-36}{3}

Cross multiply:

\implies 3(-4x-4)=7(4x-36)

Expand:

\implies -12x-12=28x-252

Add 12x to both sides:

\implies -12=40x-252

Add 252 to both sides:

\implies 240=40x

Divide both sides by 40:

\implies 6=x

\implies x=6

6 0
1 year ago
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