1 of 8 0-day streak

Determine parameters in a polynomial identity

Question 1 of 8

No calculator

For every real value of \(x\), the expressions below are equal

P(x)=-2x^3 - 3x - 5

Q(x)=-2x^3 - 3x^2 + px^2 - 4x + qx - 5

The required identity is \(P(x)=Q(x)\)

For a numerical check, evaluate the displayed expressions at \(x=0\)

(a)1 mark

Solve the coefficient conditions for the unknown parameters

Select the coefficient condition that uses the identity correctly

x^3:\;-2=-2\qquad x^2:\;-3 + p=0\qquad x:\;-4 + q=-3\qquad 1:\;-5=-5

\(P(0)=Q(0)\) alone proves \(P(x)=Q(x)\) for every real \(x\)

x^3:\;-2=-3 + p\qquad x^2:\;-3 + p=-4 + q\qquad x:\;-4 + q=-5\qquad 1:\;-5=-2

(b)2 marks

Solve the coefficient conditions and enter the values of \(p, q\)

\(p\) \(q\)

Evaluate the displayed polynomial at \(x=0\) and enter \(P(0)\)

\(P(0)\)