Question

Factor the following trinomial completely: -3x^3 + 66x^2 - 363x
A. -3x(x - 11)(x + 11)
B. -3x(x - 11)^2
C. 3x(x - 11)(x + 11)
D. 3x(x - 11)^2

Answer 1

@dan815

Answer 2

@Preetha

Answer 3

@amistre64

Answer 4

@Michele_Laino

Answer 5

hint: \(\large {
-3x^3 + 66x^2 - 363x\implies
\begin{array}{cccllll}
-3x(x^2&-22x&+121)\\
&-11-11&-11\cdot -11
\end{array}
}\)

Answer 6

Okay so what should I do with that next

Answer 7

hint:
the polynomial:
\[{x^2} - 22x + 121\]
is a perfect square

Answer 8

for example:
\[\Large {\left( {x - a} \right)^2} = {x^2} - 22x + 121\]
what is a?

Answer 9

How would I find that?

Answer 10

hint:
\[\Large {\left( {x - a} \right)^2} = {x^2} - 2ax + {a^2}\]

Answer 11

so we can write:
\[\Large {x^2} - 2ax + {a^2} = {x^2} - 22x + 121\]

Answer 12

using the principle of identity of polynomial, we can write:
\[\Large \begin{gathered}
- 2a = - 22 \hfill \\
{a^2} = 121 \hfill \\
\end{gathered} \]
so, what is a?

Answer 13

11!

Answer 14

ok!

Answer 15

so the requested factorization, is:
\[ \Large - 3x\left( {{x^2} - 22x + 121} \right) = - 3x{\left( {x - 11} \right)^2}\]

Answer 16

is it ok?

Answer 17

Yes!

Answer 18

ok!

Answer 19

So it's B

Answer 20

That's right!

Answer 21

Awesome thanks! could you help with another problem? I'll put it in a new question and tag you

Answer 22

ok!