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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)

Respuesta :

Answer:

1.

Option B and D are correct.

2.

Option C and D are correct.

Step-by-step explanation:

1.

A.

Take RHS

[tex]2x^3(4-3x^3)[/tex]

Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]

[tex]8x^3-6x^6[/tex]                ∵[tex]x^a \cdot x^b = x^{a+b}[/tex]

then;

[tex]8x^3-6x \neq 2x^3(4-3x^3)[/tex]

Similarly;

B.

[tex]6x^3(5x-2)[/tex]

Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]

[tex]30x^4-12x^3[/tex]                ∵[tex]x^a \cdot x^b = x^{a+b}[/tex]

then;

[tex]30x^4-12x^3 = 6x^3(5x-2)[/tex]

C.

[tex]5x^3(20x+1)[/tex]

Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]

[tex]100x^4+5x^3[/tex]                ∵[tex]x^a \cdot x^b = x^{a+b}[/tex]

then;

[tex]100x^3+5 \neq 5x^3(20x+1)[/tex]

D.

[tex]2x(2x+5)[/tex]

Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]

[tex]4x^2+10x[/tex]                ∵[tex]x^a \cdot x^b = x^{a+b}[/tex]

then;

[tex]4x^2+10x = 2x(2x+5)[/tex]

2.

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

C.

[tex]24x^6-18x^5[/tex]

Take greatest common factor out [tex]6x^5[/tex];

[tex]6x^5(4x-3)[/tex]

[tex]24x^6-18x^5 =6x^5(4x-3) [/tex]

D.

[tex]20x^3+12x^2[/tex]

Take greatest common factor out [tex]4x^2[/tex];

[tex]4x^2(5x+3)[/tex]

[tex]20x^3+12x^2 =4x^2(5x+3)[/tex]

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





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