Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( P(x) = 6x^2 - 9x - 15 \)
Solution
Calculate or simplify the expression \( 3(2x-5)(x+1) \).
Simplify the expression by following steps:
- step0: Solution:
\(3\left(2x-5\right)\left(x+1\right)\)
- step1: Multiply the terms:
\(\left(6x-15\right)\left(x+1\right)\)
- step2: Apply the distributive property:
\(6x\times x+6x\times 1-15x-15\times 1\)
- step3: Multiply the terms:
\(6x^{2}+6x-15x-15\)
- step4: Subtract the terms:
\(6x^{2}-9x-15\)
The expanded form of \( P(x) = 3(2x-5)(x+1) \) is \( 6x^2 - 9x - 15 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
Did you know that this polynomial can be expanded to reveal its full form? By multiplying it out, you’ll get \( P(x) = 3(2x^2 - 10x + 2x - 5) \), which simplifies down to \( P(x) = 6x^2 - 24x - 15 \). This is a great way to better understand the behavior of the polynomial and its roots! Now, speaking of roots, you can easily find them by setting \( P(x) = 0 \). This means solving \( 3(2x-5)(x+1) = 0 \). Hence, the roots occur when either \( 2x-5 = 0 \) or \( x+1 = 0 \). So, those roots are \( x = 2.5 \) and \( x = -1 \)! An exciting hunt, isn’t it?
