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3 years ago

2. Explain and correct the error made by a student who simplified this expression.

Mathematics

1 answer:

Ira Lisetskai [31]3 years ago

6 0

Answer:

what this student did was distribute the x to all 3 numbers when what they should have done was just combine 7x and -2x, and the answer should be 5x +8

Step-by-step explanation:

By the student placing x on the outside they are making the equation seem as if 8 also had an x. However if we look at the original problem 8 does not have any variable so right away that was their first mistake. Instead they had to find the numbers that had similar values. In this case it is negative 2x and 7x. We combine those two to get 5x+8 we cannot combine these two because as said previously 8 doesnt have a variable. so the answer stays with the expression 5x+8

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GalinKa [24]

Answer:

$\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }$

Step-by-step explanation:

Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).

$\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}$

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$f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240$

We identify the coefficients for the like terms, it comes

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$f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}$

And we can write in $\mathbb{C}$

$f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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