Question

Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial (x2 + x – 2) and got the expression below.

(2x)(x2) + (2x)(x) + (2x)(–2) + (3)(x2) + (3)(x) + (3)(–2)

Which is the simplified product?

2x3 + 6x2 – x – 6
2x3 + x2 – x – 6
2x3 + 5x2 – x – 6
2x3 – x2 – 7x – 6

Answer 1

Marta got the expression

$2x\cdot x^2 + 2x\cdot x + 2x\cdot (-2) + 3\cdot x^2 + 3\cdot x + 3\cdot (-2).$

First, note that

$2x\cdot x^2=2x^3,\\2x\cdot x=2x^2,\\2x\cdot (-2)=-4x,\\3\cdot x^2=3x^2,\\ 3\cdot x=3x,\\3\cdot (-2)=-6.$

Then add terms with the same degree:

$2x^2+3x^2=5x^2,\\-4x+3x=-x.$

At last,

$(2x+3)(x^2 + x - 2)=2x^3+5x^2-x-6.$

Answer: correct choice is C.

Answer 2

The resultant product of the given polynomials is $2x^3+5x^2-x-6$. Option C is correct.

Given information:

Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial $(x^2 + x - 2)$.

The resultant of the above product is $(2x)(x^2) + (2x)(x) + (2x)(-2) + (3)(x^2) + (3)(x) + (3)(-2)$.

Solve the given product as,

$(2x+3)(x^2+x-2)=(2x)(x^2) + (2x)(x) + (2x)(-2) + (3)(x^2) + (3)(x) + (3)(-2)\\=2x^3+2x^2-4x+3x^2+3x-6\\=2x^3+5x^2-x-6$

Therefore, the resultant product of the given polynomials is $2x^3+5x^2-x-6$. Option C is correct.

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https://brainly.com/question/23675883