The expression x3 – 64 can be written as (x)3 – (4)3. What is the factorization of x3 – 64?

Mathematics

1 answer:

Bumek [7]3 years ago

4 0

Answer:

Step-by-step explanation:

(x - 4) because a = x and b = 4, subsitute into (a - b)

(x2 + 4x + 16) because if a = x and b = 4, you subsitute them into (a2 + ab + b2) to get your answer

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find the zeros of 2x^2 - 16x + 27 using the quadratic formula. be sure to simplify the expression. Can someone please show me ho

____ [38]

For a quadratic of the form $f(x)=ax^2+bx+c$ , we have the quadratic formula
$x=\dfrac{-b \pm \sqrt{b^2 -4ac} }{2a}$ ,
where a is the coefficient (number before the variable) of the squared term, b is the coefficient of the linear term, and c is the constant term.

So, given $2x^2-16x+27=0$ , we can get that $a=2, \ b=-16$ , and $c=27$ . We substitute these numbers into the quadratic formula above.

$x=\dfrac{-(-16) \pm \sqrt{(-16)^2 -4(2)(27)} }{2(2)}$

$x=\dfrac{16 \pm \sqrt{(256 -216)} }{4}$

$x=\dfrac{16 \pm \sqrt{40} }{4}$

$x=\dfrac{16 \pm 2\sqrt{10} }{4}$

$x=4+ \frac{\sqrt{10}}{2}, \ x=4- \frac{\sqrt{10}}{2}$

This is our final answer.

If you've never seen the quadratic formula, you can derive it by completing the square for the general form of a quadratic. Note that the $\pm$ symbol (read: plus or minus) represents the two possible distinct solutions, except for zero under the radical, which gives only one solution.