Questions: P(x)=6x^4-12x^2+9x-18; 1.5 and 2 Evaluate the function for the lower bound, 1.5. P(1.5)= (Type an integer or decimal rounded to the nearest hundredth as needed.

Solution Steps

To evaluate the polynomial function \( P(x) = 6x^4 - 12x^2 + 9x - 18 \) at \( x = 1.5 \), we will substitute \( x = 1.5 \) into the polynomial and compute the result.

We need to evaluate the polynomial function \( P(x) = 6x^4 - 12x^2 + 9x - 18 \) at \( x = 1.5 \).

Substituting \( x = 1.5 \) into the polynomial gives: \[ P(1.5) = 6(1.5)^4 - 12(1.5)^2 + 9(1.5) - 18 \]

Calculating each term:

• \( (1.5)^4 = 5.0625 \)
• \( (1.5)^2 = 2.25 \)

Now substituting these values: \[ P(1.5) = 6(5.0625) - 12(2.25) + 9(1.5) - 18 \] Calculating each term:

• \( 6(5.0625) = 30.375 \)
• \( 12(2.25) = 27 \)
• \( 9(1.5) = 13.5 \)

Putting it all together: \[ P(1.5) = 30.375 - 27 + 13.5 - 18 \]

Now, performing the final calculation: \[ P(1.5) = 30.375 - 27 + 13.5 - 18 = -1.125 \]

Final Answer