Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Select ALL the correct answers.

Select all the expressions that are equivalent to the polynomial below.

[tex]\[ -15x^2 - 29x - 12 \][/tex]

A. [tex]\((-7x^2 - 21x + 13) - (8x^2 + 8x + 25)\)[/tex]

B. [tex]\(-2(4x - 15) - 3(5x^2 + 7x + 6)\)[/tex]

C. [tex]\((-19x^2 - 4x - 7) + (4x^2 + 25x - 5)\)[/tex]

D. [tex]\((-17x^2 + 2x - 3) + (2x^2 - 31x - 9)\)[/tex]

E. [tex]\(-2(7x + 1) - 5(3x^2 + 3x + 2)\)[/tex]

F. [tex]\((5x^2 - 10x + 8) - (10x^2 + 19x + 20)\)[/tex]

Sagot :

GinnyAnswer
Let's analyze each expression to see which of them are equivalent to the polynomial [tex]\(-15x^2 - 29x - 12\)[/tex].

### Expression 1
[tex]\[ \left(-7x^2 - 21x + 13\right) - \left(8x^2 + 8x + 25\right) \][/tex]
Combine and simplify:
[tex]\[ = (-7x^2 - 21x + 13) - 8x^2 - 8x - 25 \][/tex]
[tex]\[ = -7x^2 - 21x + 13 - 8x^2 - 8x - 25 \][/tex]
[tex]\[ = -15x^2 - 29x - 12 \][/tex]
The simplified expression matches the given polynomial. Thus, Expression 1 is correct.

### Expression 2
[tex]\[ -2(4x - 15) - 3(5x^2 + 7x + 6) \][/tex]
Distribute and simplify:
[tex]\[ = -2(4x) + 30 - 3(5x^2) - 3(7x) - 3(6) \][/tex]
[tex]\[ = -8x + 30 - 15x^2 - 21x - 18 \][/tex]
[tex]\[ = -15x^2 - 29x + 12 \][/tex]
The simplified form does not match the given polynomial. Thus, Expression 2 is not correct.

### Expression 3
[tex]\[ \left(-19x^2 - 4x - 7\right) + \left(4x^2 + 25x - 5\right) \][/tex]
Combine and simplify:
[tex]\[ = -19x^2 - 4x - 7 + 4x^2 + 25x - 5 \][/tex]
[tex]\[ = -15x^2 + 21x - 12 \][/tex]
The simplified form does not match the given polynomial. Thus, Expression 3 is not correct.

### Expression 4
[tex]\[ \left(-17x^2 + 2x - 3\right) + \left(2x^2 - 31x - 9\right) \][/tex]
Combine and simplify:
[tex]\[ = -17x^2 + 2x - 3 + 2x^2 - 31x - 9 \][/tex]
[tex]\[ = -15x^2 - 29x - 12 \][/tex]
The simplified expression matches the given polynomial. Thus, Expression 4 is correct.

### Expression 5
[tex]\[ -2(7x + 1) - 5(3x^2 + 3x + 2) \][/tex]
Distribute and simplify:
[tex]\[ = -2(7x) - 2(1) - 5(3x^2) - 5(3x) - 5(2) \][/tex]
[tex]\[ = -14x - 2 - 15x^2 - 15x - 10 \][/tex]
[tex]\[ = -15x^2 - 29x - 12 \][/tex]
The simplified expression matches the given polynomial. Thus, Expression 5 is correct.

### Expression 6
[tex]\[ \left(5x^2 - 10x + 8\right) - \left(10x^2 + 19x + 20\right) \][/tex]
Combine and simplify:
[tex]\[ = 5x^2 - 10x + 8 - 10x^2 - 19x - 20 \][/tex]
[tex]\[ = -5x^2 - 29x - 12 \][/tex]
The simplified form does not match the given polynomial. Thus, Expression 6 is not correct.

### Conclusion
The expressions equivalent to the given polynomial [tex]\(-15x^2 - 29x - 12\)[/tex] are:

[tex]\[ \boxed{1, 4, 5} \][/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.