Question

What are the roots of the polynomial equation x^4+x^3=4x^2+4x?
–2, –1, 0, 2
–2, 0, 1, 2
–1, 0
0, 1

Answer 1

you could write everything on one side and try to factor

Answer 2

x^4+x^3=4x^2+4x
x^4 + x^3 - 4x^2 - 4x = 0

take out the common factor x
x(x^3 + x^2 - 4x - 4) = 0

so what is one root?

Answer 3

when two expression are multiplied and the result is zero then either one = zero
right?

Answer 4

yes, so it would be D?

Answer 5

dont jump to conclusions
all we can say is that x = 0
one root is 0

Answer 6

- so it could be any of the 4 options
now we can look to see if we can factor the cubic in the parentheses

Answer 7

x^3 + x^2 - 4x - 4 = 0

Answer 8

we can factor this by grouping
can you factor the first 2 terms x ^3 and x^2
- what is the highest common factor of these 2?

Answer 9

what is the highest thing which divides into x^3 and x^2?

Answer 10

is it x or is it x^2?

Answer 11

it would be x^2

Answer 12

yes
so it factors to x^2(x + 1)

OK with that?

Answer 13

yes

Answer 14

right so so far we have
x^1(x + 1) - 4x - 4 = 0

it would be nice if we could get another (x + 1) so we could factor further and we can do this by taking out -4 from the lat 2 terms
so we get

x^2( x + 1) - 4(x + 1) = 0

taking out the x+ 1

(x^2 - 4)(x + 1) = 0


do you follow that ok?

Answer 15

sure do :)

Answer 16

great so now we have
x^2 - 4 = 0 and x + 1 = 0

x = 2 , -2 and -1


so final answer is
2, -2, -1 and 0

Answer 17

A is correct

Answer 18

Thank you for explaining this to me!!!

Answer 19

yw

Answer 20

its always worth checking to see if you can factor by grouping

Answer 21

you cant always do it of course