Answered

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)

Verified Answer :

Answer:

1.

Option B and D are correct.

2.

Option C and D are correct.

Step-by-step 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.