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3 years ago

How do you simplify this and write as a polynomial in standar form? (x-9)3x-7)+(3x^2-5x+2)

Mathematics

1 answer:

nasty-shy [4]3 years ago

6 0

Answer:

Standard form of $(x-9)(3x-7) + (3x^{2} - 5x+2)$ $=6x^{2} - 39x + 65$

Step-by-step explanation:

Here, the given expression is $(x-9)(3x-7) + (3x^{2} - 5x+2)$

Now, simplifying the above expression in parts, we get

$(x-9)(3x-7) = 3x^{2} - 7x -27x + 63 = 3x^{2} - 34x + 63$

hence, combining both parts:

$(x-9)(3x-7) + (3x^{2} - 5x+2)$ $=(3x^{2} -34x +63) + (3x^{2} - 5x+2)$

= $6x^{2} - 39x + 65$

The above expression is of the STANDARD FORM: $ax^{2} +bx + c$

Hence, the standard form of $(x-9)(3x-7) + (3x^{2} - 5x+2)$ $=6x^{2} - 39x + 65$

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Answer:

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$b=\left[\begin{array}{ccc}0\\1\end{array}\right]$

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c) $A=\left[\begin{array}{ccc}0&6\sqrt{2} &0\\\sqrt{3} &3\sqrt{3} &0\\2&-16&0\end{array}\right]$

$x=\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]$

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a) considering the equation:

Minimize $x_{1}^{2} +2x_{2}x^{2} +3x_{3}^{2}+(x_{1} -x_{2} +x_{3} -1)^{2} +(-x_{1} -4x_{2} +2)^{2}$

$A=\left[\begin{array}{ccc}1&2&3\\1&-1&1\end{array}\right]$ (matrix A)

vector b

$b=\left[\begin{array}{ccc}0\\1\end{array}\right]$

b) If Pxn is matrix B and p-vector d, we have:

minimize $(-6x_{2}+4)^{2} +(-4x_{1} +3x_{2} -1)+(x_{1} +8x_{2} -3)^{2}$

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$\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]$

$b=\left[\begin{array}{ccc}-4\\1\\3\end{array}\right]$

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c) minimize $2(-bx_{2}+4)^{2} +3(-4x_{1} +3x_{2} -1)^{2} +4(x_{1} -x_{2} -3)^{2} -(6\sqrt{2}x_{2} +4\sqrt{2} )^{2} +(-4\sqrt{3} x_{1} +3\sqrt{3}x_{2} -\sqrt{3})^{2} +(2x_{1} -16x_{2} -6)^{2}$

in matrix:

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$x=\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]$

$b=\left[\begin{array}{ccc}-\sqrt{2} \\\sqrt{3} \\6\end{array}\right]$

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3 years ago

How do you simplify this and write as a polynomial in standar form? (x-9)3x-7)+(3x^2-5x+2)​

How do you simplify this and write as a polynomial in standar form? (x-9)3x-7)+(3x^2-5x+2)