Mathematics, 13.07.2019 22:30 ewaltz74

What is the completely factored form of f(x)=x3+5x2+4x−6? f(x)=(x−3)(x−(−1+i3√−(−1−i3√)) f(x)=(x+3)(x−(−1+i3√−(−1−i3√)) f(x)=(x+3)(x−(−1+3√−(−1−3√)) f(x)=(x−3)(x−(−1+3√−(−1−3√))

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Answer from: apodoltsev2021

The factored type is the product of constants and two-dimensional terms, that is the root of a function as well as the graph's x-intercepts, and the further calculation can be defined as follows:

Given:

$\bold{f(x)=x^3+5x^2+4x-6}$

To find:

factored form=?

Solution:

$\bold{f(x)=x^3+5x^2+4x-6}$

putting the value x=-1,-2,-3...... to find the function value 0.

$\to \bold{f(-1)=-1^3+5(-1)^2+4(-1)-6}\\\\$

$\bold{=-1+5\times 1+4 \times (-1)-6}\\\\ \bold{= -1+5-4-6} \\\\ \bold{=-6}\\\\$

$\to \bold{f(-2)=-2^3+5(-2)^2+4(-2)-6}$

$\bold{=-8+5\times 4+4 \times(- 2)-6}\\\\\bold{= -8+20-8-6}\\\\\bold{=-2}\\\\$

$\to \bold{f(-3)=-3^3+5(-3)^2+4(-3)-6}$

$\bold{=-27+5\times 9+4 \times(- 3)-6}\\\\\bold{= -27+45-12-6}\\\\\bold{=0}\\\\$

Therefore, $\bold{(x+3)}$ is the factor of the function.

Let $\bold{(x+3)}$ divide by the function:

$\to \bold{\frac{x^3+5x^2+4x-6}{(x+3)}= x^2+2x-2}$

compare the value $\bold{x^2+2x-2}$ by the standard equation $\bold{ax^2+bx+c=0}$ so,

$\bold{a=1}\\\\\bold{b=2}\\\\\bold{c=-2}\\\\$

Putting value into the quadratic equation formula:

$\bold{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}$

$\bold{x=\frac{-(2) \pm \sqrt{(2)^2-4\times 1 \times -2}}{2\times 1}}\\\\\bold{x=\frac{-2 \pm \sqrt{4+8}}{2}}\\\\\bold{x=\frac{-2 \pm \sqrt{12}}{2}}\\\\\bold{x=\frac{-2 \pm 2\sqrt{3}}{2}}\\\\\bold{x=\frac{2(-1 \pm \sqrt{3})}{2}}\\\\\bold{x=(-1 \pm \sqrt{3})}\\\\\bold{x=(-1 + \sqrt{3}) (-1 -\sqrt{3})}\\\\$

Adding the factor value that is $\bold{(x+3)}$ so, the value is " $\bold{(x+3)(-1+\sqrt{3})(-1-\sqrt{3}) }$ "

So, the final answer is " $\bold{f(x)=(x+3)(x-(-1+\sqrt{3}))(x-(-1-\sqrt{3}))}$ "

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Answer from: doritasanchez

$f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)$

Synthetic division yields

-3 | 1   5   4   -6
.    |      -3 -6    6
- - - - - - - - - - - - -
.    | 1   2 -2    0

which translates to

$\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2$

with remainder 0. Now by the quadratic formula,

$x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3$

and so

$f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))$

Answer from: Quest

-4

step-by-step explanation:

(-4+8)=-(4-8)=-8+4=-4

Answer from: Quest

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

The graph below shows the value of a $100 deposited into three different accounts over a period of 2

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What is the completely factored form of f(x)=x3+5x2+4x−6? f(x)=(x−3)(x−(−1+i3√−(−1−i3√)) f(x)=(x+3)...

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