Question

Which statements are true? Select each correct answer. Pick more then one

8x3−6x=2x3(4−3x3)

30x4−12x3=6x3(5x−2)

100x3+5=5x3(20x+1)

4x2+10x=2x(2x+5)


Which expressions are completely factored?

Select each correct answer.

18x4−12x2=6x(3x3−2x)

12x5+8x3=2x3(6x2+4)

24x6−18x5=6x5(4x−3)

20x3+12x2=4x2(5x+3)

Answer 1

1. Option B and D are correct.

2. Option C and D are correct.

Explanation:

i took the k12 test

Answer 2

1.

Option B and D are correct.

2.

Option C and D are correct.

Explanation:

1.

A.

Take RHS

`2x^3(4-3x^3)`

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

`8x^3-6x^6` ∵
`x^a \cdot x^b = x^(a+b)`

then;

`8x^3-6x \\eq 2x^3(4-3x^3)`

Similarly;

B.

`6x^3(5x-2)`

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

`30x^4-12x^3` ∵
`x^a \cdot x^b = x^(a+b)`

then;

`30x^4-12x^3 = 6x^3(5x-2)`

C.

`5x^3(20x+1)`

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

`100x^4+5x^3` ∵
`x^a \cdot x^b = x^(a+b)`

then;

`100x^3+5 \\eq 5x^3(20x+1)`

D.

`2x(2x+5)`

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

`4x^2+10x` ∵
`x^a \cdot x^b = x^(a+b)`

then;

`4x^2+10x = 2x(2x+5)`

2.

Completely factored states that an expression is completely factored when no further factor is possible.

C.

`24x^6-18x^5`

Take greatest common factor out
`6x^5`;

`6x^5(4x-3)`

`24x^6-18x^5 =6x^5(4x-3)`

D.

`20x^3+12x^2`

Take greatest common factor out
`4x^2`;

`4x^2(5x+3)`

`20x^3+12x^2 =4x^2(5x+3)`

Therefore, Only option C and D expressions are completely factored.