Question

2 multiple choice 1 point simplify. write your answer in standard form. \\((3x^5 - 2x^4 - 5) - (2x^4 + x^2 - 10)\\) \\(\bigcirc\\ 3x^5 - 4x^4 - x^2 + 5\\) \\(\bigcirc\\ 3x^4 + x^2 + 15\\) \\(\bigcirc\\ 3x^5 - 10x^2 - 5x + 10\\) \\(\bigcirc\\ 3x^5 - 4x^4 + x^2 - 15\\) 3 fill in the blank 1 point simplify. write your answer in standard form. \\((-10x - 3)(3x + 1)\\)

Explanation:

Question 2 (Multiple Choice)

Step1: Distribute the negative sign

To simplify \((3x^5 - 2x^4 - 5) - (2x^4 + x^2 - 10)\), we first distribute the negative sign to each term inside the second parentheses:
\(3x^5 - 2x^4 - 5 - 2x^4 - x^2 + 10\)

Step2: Combine like terms

• For the \(x^5\) term: \(3x^5\) (no other \(x^5\) terms)
• For the \(x^4\) terms: \(-2x^4 - 2x^4 = -4x^4\)
• For the \(x^2\) term: \(-x^2\) (no other \(x^2\) terms)
• For the constant terms: \(-5 + 10 = 5\)

Putting it all together, we get \(3x^5 - 4x^4 - x^2 + 5\).

Step1: Use the distributive property (FOIL method)

To simplify \((-10x - 3)(3x + 1)\), we use the FOIL method (First, Outer, Inner, Last):

• First: \(-10x \cdot 3x = -30x^2\)
• Outer: \(-10x \cdot 1 = -10x\)
• Inner: \(-3 \cdot 3x = -9x\)
• Last: \(-3 \cdot 1 = -3\)

Step2: Combine like terms

Now, we combine the like terms (the \(x\) terms):
\(-30x^2 - 10x - 9x - 3 = -30x^2 - 19x - 3\)

Answer:

A. \(3x^5 - 4x^4 - x^2 + 5\)

Question 3 (Fill in the Blank)