Answer :
Answer:
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Step-by-step explanation:
Absolutely, I’ve been improving my problem-solving abilities in dividing polynomials. Let's divide the polynomial:
15x+10x
2
−20by−2x−7
We cannot perform long division on polynomials with variable terms in the denominator (like -20by in this case). However, we can simplify the expression by combining like terms.
Steps to solve:1. Combine like terms:
Combine terms with x: 15x - 2x = 13x
The expression cannot be further simplified because there are no other like terms.
2. Rearrange terms:
Organize the polynomial by placing the term with the highest degree (x²) first, followed by the term with x (13x), and then the constant term (-7).
Answer:
−20by+10x
2
+13x−7
Note: Since the expression has a variable term in the denominator, it cannot be divided by another polynomial using long division.
Answer:
Sure, I can help you with polynomial long division. Let's divide \( 10x^2 + 15x - 20 \) by \( -2x - 7 \).
1. **Arrange terms in descending order:** \( 10x^2 + 15x - 20 \) divided by \( -2x - 7 \).
2. **First term division:** Divide the leading term of the numerator \( 10x^2 \) by the leading term of the denominator \( -2x \):
\[
\frac{10x^2}{-2x} = -5x
\]
Write \( -5x \) above the line.
3. **Multiply and subtract:** Multiply \( -5x \) by \( -2x - 7 \):
\[
-5x \cdot (-2x - 7) = 10x^2 + 35x
\]
Subtract from the original polynomial:
\[
(10x^2 + 15x - 20) - (10x^2 + 35x) = -20x - 20
\]
4. **Continue division:** Now divide \( -20x \) by \( -2x \):
\[
\frac{-20x}{-2x} = 10
\]
Write \( +10 \) above the line.
5. **Multiply and subtract again:** Multiply \( 10 \) by \( -2x - 7 \):
\[
10 \cdot (-2x - 7) = -20x - 70
\]
Subtract from the remaining polynomial:
\[
(-20x - 20) - (-20x - 70) = 50
\]
6. **Result:** The quotient is \( -5x + 10 \) and the remainder is \( \frac{50}{-2x - 7} \).
So, \( \frac{10x^2 + 15x - 20}{-2x - 7} = -5x + 10 + \frac{50}{-2x - 7} \).
