1 of 8 0-day streak

Solve a higher-degree polynomial equation or inequality

Question 1 of 8

No calculator

Consider this polynomial equation for real x

\left(x + 3\right)\left(x + 2\right)\left(x\right)\left(x - 5\right) = 0

Use exact values. Write the comparison with zero, factorise completely, and verify the real roots

Let \(F(x)\) denote the left side minus the right side of the displayed comparison. Root and multiplicity entries refer to \(F(x)=0\); enter distinct roots in increasing order. For an inequality, its final solution is the full set of inputs satisfying the original comparison

(a)1 mark

Identify the complete zero-form factorisation before solving

\left(x + 3\right)=1

\left(x + 3\right)\left(x + 2\right)\left(x\right)=0

\left(x + 3\right)\left(x + 2\right)\left(x\right)\left(x - 5\right)=0

(b)8 marks

Enter the critical roots and their multiplicities

\(r_{1}\) \(m_{1}\) \(r_{2}\) \(m_{2}\) \(r_{3}\) \(m_{3}\) \(r_{4}\) \(m_{4}\)