Factor completely x³ - 7x² + 2x + 40 given x = -2 is a root.

Mathematics

1 answer:

klemol [59]3 years ago

6 0

Answer:

(x +2)(x -4)(x -5)

Step-by-step explanation:

When you divide the cubic by (x +2), the factor that has -2 as a root, you get a quadratic with roots 4 and 5. Thus the factors are ...

(x +2)(x -4)(x -5)

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In the attachment, we have done the division using a graphing calculator. You can also do it by polynomial long division or by synthetic division. The resulting quadratic is ...

x^2 -9x +20 = (x -4)(x -5) . . . . . factor the quadratic

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Write a polynomial function of least degree with integral coefficients that has the

frutty [35]

A polynomial function of least degree with integral coefficients that has the

given zeros $f(x)=x^4+x^3+9x^2+9x$

Given

Given zeros are 3i, -1 and 0

complex zeros occurs in pairs. 3i is one of the zero

-3i is the other zero

So zeros are 3i, -3i, 0 and -1

Now we write the zeros in factor form

If 'a' is a zero then (x-a) is a factor

the factor form of given zeros

$\:\left(x-3i\right)\left(x-\left(-3i\right)\right)\left(x-0\right)\left(x-\left(-1\right)\right)\\\left(x-3i\right)\left(x+3i\right)\left(x-0\right)\left(x+1\right)$