Question

Match each trinomial to its factored form. (y - 2)(3y + 4) 3y2 + 2y - 8 (y + 2)(3y - 4) 3y2 + 13y - 10 (3y + 2)(y - 5) 3y2 - 13y - 10 (3y - 2)(y + 5) 3y2 - 2y - 8 arrowBoth arrowBoth arrowBoth arrowBoth

Answer 1

`3y^2 + 2y - 8=(3y-4)(y+2)`

`3y^2 + 13y - 10=(3y-2)(y+5)`

`3y^2 - 13y - 10=(3y+2)(y-5)`

`3y^2 - 2y - 8=(3y+4)(y-2)`

Explanation:

Given trinomial are

`3y^2 + 2y - 8\\3y^2 + 13y - 10\\3y^2 - 13y - 10\\3y^2 - 2y - 8`.

we have to convert these in factored form

`3y^2 + 2y - 8=3y^2+6y-4y-8`

=
`3y(y+2)-4(y+2)`

=
`(3y-4)(y+2)`

`3y^2 + 13y - 10=3y^2+15y-2y-10`

=
`3y(y+5)-2(y+5)`

=
`(3y-2)(y+5)`

`3y^2 - 13y - 10=3y^2-15y+2y-10`

=
`3y(y-5)+2(y-5)`

=
`(3y+2)(y-5)`

`3y^2 - 2y - 8=3y^2-6y+4y-8`

=
`3y(y-2)+4(y-2)`

=
`(3y+4)(y-2)`

Answer 2

Match each trinomial to its factored form:

1.
`(y-2)(3y+4)`

Multiplying each term in the first expression by each term in a second expression.

`y(3y+4) -2(3y+4)`

Using distributive property:
`a\cdot (b+c) = a\cdot b+ a\cdot c`

`(3y^2 + 4y) -(6y + 8)`

Remove the parenthesis, we have;

`3y^2 + 4y -6y -8`

combine like term ;

`3y^2-2y -8`

2.
`(y+2)(3y-4)`

Multiplying each term in the first expression by each term in a second expression.

`y(3y-4) +2(3y-4)`

Using distributive property:
`a\cdot (b+c) = a\cdot b+ a\cdot c`

`(3y^2 - 4y) + (6y - 8)`

Remove the parenthesis, we have;

`3y^2 - 4y + 6y - 8`

combine like term ;

`3y^2 + 2y -8`

3.
`(3y+2)(y-5)`

Multiplying each term in the first expression by each term in a second expression.

`3y(y-5) +2(y-5)`

Using distributive property:
`a\cdot (b+c) = a\cdot b+ a\cdot c`

`(3y^2 - 15y) + (2y - 10)`

Remove the parenthesis, we have;

`3y^2 - 15y + 2y - 10`

combine like term ;

`3y^2 -13y -10`

4.
`(3y-2)(y+5)`

Multiplying each term in the first expression by each term in a second expression.

`3y(y+5) -2(y+5)`

Using distributive property:
`a\cdot (b+c) = a\cdot b+ a\cdot c`

`(3y^2 + 15y) - (2y + 10)`

Remove the parenthesis, we have;

`3y^2+ 15y - 2y - 10`

combine like term ;

`3y^2 + 13y -10`

Column 1 Column 2

`(y-2)(3y+4)`
`3y^2-2y -8`

`(y+2)(3y-4)`
`3y^2+ 2y -8`

`(3y+2)(y-5)`
`3y^2 -13y -10`

`(3y-2)(y+5)`
`3y^2 + 13y -10`