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Let's transform the given quadratic inequalities to standard form:

### 1. \( 2 + x^2 > 2x \)
To transform this into standard form, move all terms to one side of the inequality:
\[
x^2 - 2x + 2 > 0
\]
The standard form of the inequality is:
\[
x^2 - 2x + 2 > 0
\]

### 2. \( 3b^2 - 5b < 8 \)
Similarly, move all terms to one side of the inequality:
\[
3b^2 - 5b - 8 < 0
\]
The standard form of the inequality is:
\[
3b^2 - 5b - 8 < 0
\]

Both inequalities are now in the standard quadratic form \( ax^2 + bx + c \, [ \text{inequality} ] \, 0 \).

Would you like further details or explanations on any part of this?

Here are 5 questions to explore further:
1. How do you solve a quadratic inequality?
2. What is the graphical interpretation of quadratic inequalities?
3. What is the significance of the discriminant in quadratic inequalities?
4. How can you determine the solution intervals for these inequalities?
5. What role do critical points play in solving quadratic inequalities?

**Tip**: When solving quadratic inequalities, it’s useful to first solve the corresponding equation (by setting the inequality to 0) and then analyze the sign changes over different intervals.

Transform the following quadratic inequalities to standard form: 1. 2 + x^2 > 2x 2. 3b^2 - 5b < 8

Learn how to transform quadratic inequalities like 2 + x^2 > 2x and 3b^2 - 5b < 8 into their standard forms. Understand key algebraic concepts with step-by-step solutions. Ideal for students in Grades 9-11.

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