https://file.aiquickdraw.com/mathbot/file/17290995226446ekno8yu.jpg

Let's break down and solve the problems shown in the image step by step.

### Problem 1: Add the polynomials
\[
(2x - 5) + (4x^2 - 1)
\]

We can rearrange the terms:
\[
(4x^2) + (2x) + (-5 - 1)
\]
Simplifying:
\[
4x^2 + 2x - 6
\]
Thus, the coefficients for the standard form \( Cx^2 + Dx + E \) are:
- \( C = 4 \)
- \( D = 2 \)
- \( E = -6 \)

### Problem 2: Multiply the polynomials
\[
(x + 4)(x^2 + 6x - 3)
\]

To solve this, we distribute \(x\) and \(4\) to each term in the second polynomial:
\[
x(x^2 + 6x - 3) = x^3 + 6x^2 - 3x
\]
\[
4(x^2 + 6x - 3) = 4x^2 + 24x - 12
\]

Now combine like terms:
\[
x^3 + (6x^2 + 4x^2) + (-3x + 24x) + (-12)
\]
\[
x^3 + 10x^2 + 21x - 12
\]

Thus, the coefficients for the standard form \(Ax^3 + Bx^2 + Cx + D\) are:
- \( A = 1 \)
- \( B = 10 \)
- \( C = 21 \)
- \( D = -12 \)

Let me know if you'd like further details or have any questions!

Here are 5 questions that build on this:
1. Can you explain how to combine like terms when adding polynomials?
2. How do you apply the distributive property in polynomial multiplication?
3. What happens when you multiply two binomials together?
4. How can you identify the degree of a polynomial after addition or multiplication?
5. How would you approach simplifying higher-degree polynomials?

**Tip:** When adding or multiplying polynomials, it's important to align terms with the same powers of \(x\) before combining them.

Add the polynomials (2x - 5) + (4x^2 - 1) and multiply the polynomials (x + 4)(x^2 + 6x - 3).

Learn how to add the polynomials (2x - 5) + (4x^2 - 1) and multiply the polynomials (x + 4)(x^2 + 6x - 3) with step-by-step solutions. This problem covers essential algebraic concepts like polynomial addition, the distributive property, and combining like terms. Suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation