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¿Cuál es el producto de calcular [tex] \left(5x^2 - 3x + 6\right) \cdot (7x + 2) [/tex]?

Seleccione una:

A. [tex] 35x^3 + 11x^2 + 36x + 12 [/tex]

B. [tex] 35x^3 - 11x^2 + 36x + 12 [/tex]

C. [tex] -35x^3 - 11x^2 - 36x + 12 [/tex]

D. [tex] -35x^3 - 11x^2 + 36x + 12 [/tex]

Answer :

To solve the problem of calculating [tex]\((5x^2 - 3x + 6)(7x + 2)\)[/tex], we'll use the distributive property to expand the expression step by step.

1. Distribute each term in the first polynomial by each term in the second polynomial:

- Multiply [tex]\(5x^2\)[/tex] by each term in [tex]\(7x + 2\)[/tex]:
- [tex]\(5x^2 \cdot 7x = 35x^3\)[/tex]
- [tex]\(5x^2 \cdot 2 = 10x^2\)[/tex]

- Multiply [tex]\(-3x\)[/tex] by each term in [tex]\(7x + 2\)[/tex]:
- [tex]\(-3x \cdot 7x = -21x^2\)[/tex]
- [tex]\(-3x \cdot 2 = -6x\)[/tex]

- Multiply [tex]\(6\)[/tex] by each term in [tex]\(7x + 2\)[/tex]:
- [tex]\(6 \cdot 7x = 42x\)[/tex]
- [tex]\(6 \cdot 2 = 12\)[/tex]

2. Combine all these terms together:

[tex]\[
35x^3 + 10x^2 - 21x^2 - 6x + 42x + 12
\][/tex]

3. Combine like terms:

- The [tex]\(x^2\)[/tex] terms: [tex]\(10x^2 - 21x^2 = -11x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(-6x + 42x = 36x\)[/tex]

4. Write the final expression:

[tex]\[
35x^3 - 11x^2 + 36x + 12
\][/tex]

Therefore, the product of [tex]\((5x^2 - 3x + 6)(7x + 2)\)[/tex] is [tex]\(35x^3 - 11x^2 + 36x + 12\)[/tex].

This matches option b: [tex]\(35x^3 - 11x^2 + 36x + 12\)[/tex].

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