Question

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

Answer 1

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;

$8x^3-6x \neq 2x^3(4-3x^3)$

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;

$100x^3+5 \neq 5x^3(20x+1)$

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.

Answer 2

True statements : 2nd one and 4th one

factored completely : 3rd one and 4th one