Question

Factor completely. 12x4+18x3+45x2 Enter your answer in the box.

What are the roots of the polynomial equation?

x2+6x−72=0


Enter your answers in the boxes.

x=
or x=

Boris solves the system of equations using the linear combination method.

3x+4y=−87x−3y=6

Which steps would allow him to eliminate the y terms in the system of equations?

Multiply 3x+4y=−8

by 7. Multiply 7x−3y=6 by −3
. Add the resulting equations together.
Multiply 3x+4y=−8
by 4. Multiply 7x−3y=6
by 3. Add the resulting equations together.
Multiply 3x+4y=−8
by −3 . Multiply 7x−3y=6
by 7. Add the resulting equations together.
Multiply 3x+4y=−8
by 3. Multiply 7x−3y=6 by 4. Add the resulting equations together.

Answer 1

QUESTION 1

The given expression is

`12x^4+18x^3+45x^2`

The greatest common factor is
`3x^2`.

We factor to obtain;

`3x^2(4x^2+6x+15)`

QUESTION 2

The given quadratic equation is

`x^2+6x-72=0`

We split the middle term to obtain

`x^2+12x-6x-72=0`

Factor by grouping;

`x(x+12)-6(x+12)=0`

`(x+12)(x-6)=0`

Use zero product property;

`(x+12)=0\:\:or\:\:(x-6)=0`

`x=-12\:\:or\:\:x=6`

QUESTION 3

The given system of equation is

`3x+4y=-8`

`7x-3y=6`

If we multiply
`3x+4y=-8` by 3, we obtain;

`9x+12y=-24`

If we multiply
`7x-3y=6` by 4 we obtain;

`28x-12y=24`

Adding the last two equations will give us;

`37x=0`

The y-variable is eliminated.

Answer:Multiply 3x+4y=−8

by 3. Multiply 7x−3y=6 by 4. Add the resulting equations together.