Question

3 fill in the blank 1 point simplify. write your answer in standard form. $(-10x - 3)(3x + 1)$ note: type your answer as is. ex. 2x^3 - x^2 + x - 7 for $2x^3 - x^2 + x - 7$. do not use any spaces in your answer. type your answer... 4 fill in the blank 1 point expand. write your answer in standard form. $(3x^2 - 2x + 1)(x^2 - 5x - 1$

Explanation:

Question 3

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
$$(-10x)(3x) + (-10x)(1) + (-3)(3x) + (-3)(1)$$

Step2: Simplify each product

Calculate each term:
$$-30x^2 - 10x - 9x - 3$$

Step3: Combine like terms

Combine the linear terms ($-10x$ and $-9x$):
$$-30x^2 - 19x - 3$$

Step1: Distribute each term in the first trinomial

Multiply \(3x^2\) by each term in \((x^2 - 5x - 1)\), \(-2x\) by each term, and \(1\) by each term:
$$3x^2(x^2) + 3x^2(-5x) + 3x^2(-1) - 2x(x^2) - 2x(-5x) - 2x(-1) + 1(x^2) + 1(-5x) + 1(-1)$$

Step2: Simplify each product

Calculate each term:
$$3x^4 - 15x^3 - 3x^2 - 2x^3 + 10x^2 + 2x + x^2 - 5x - 1$$

Step3: Combine like terms

Combine \(x^4\) terms: \(3x^4\)
Combine \(x^3\) terms: \(-15x^3 - 2x^3 = -17x^3\)
Combine \(x^2\) terms: \(-3x^2 + 10x^2 + x^2 = 8x^2\)
Combine \(x\) terms: \(2x - 5x = -3x\)
Constant term: \(-1\)
So the polynomial becomes:
$$3x^4 - 17x^3 + 8x^2 - 3x - 1$$

Answer:

-30x^2-19x-3

Question 4 (assuming the second binomial is \((x^2 - 5x - 1)\) as the original seems cut off, but proceeding with that)