https://file.aiquickdraw.com/mathbot/file/17259703020534tdswqr5.jpg

The equation provided in the image is:

\[
y = (x - 2)(x - 1)(2x^2 + 3) + 4
\]

To find the value of \( y \) when \( x = 1 \), we substitute \( x = 1 \) into the equation:

\[
y = (1 - 2)(1 - 1)(2(1)^2 + 3) + 4
\]

Let's break it down:

1. \( (1 - 2) = -1 \)
2. \( (1 - 1) = 0 \)
3. \( 2(1)^2 + 3 = 2 + 3 = 5 \)

Now, using these results in the equation:

\[
y = (-1)(0)(5) + 4
\]

Since \( (-1)(0)(5) = 0 \), we have:

\[
y = 0 + 4 = 4
\]

Thus, the value of \( y \) when \( x = 1 \) is \( y = 4 \).

Would you like further details or explanations on any steps?

Here are 5 questions related to this problem:
1. What happens to the equation if we expand all terms?
2. How do roots of the equation affect the behavior of \( y \)?
3. How can we find the critical points of this equation?
4. What is the behavior of \( y \) for larger values of \( x \)?
5. Can this equation have complex solutions for certain \( x \) values?

**Tip:** When simplifying equations, zero factors eliminate terms early, saving computation time.

If y = (x - 2)(x - 1)(2x^2 + 3) + 4, what is the value of y when x = 1?

Discover how to solve the polynomial equation y = (x - 2)(x - 1)(2x^2 + 3) + 4 by substituting x = 1. This step-by-step explanation demonstrates key algebraic concepts like the zero-product property and polynomial expansion, perfect for students in Grades 8-10.

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