1 of 8 0-day streak

Determine parameters in a polynomial identity

Question 1 of 8

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

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

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

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

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

(a)1 mark

Which parameter values make the stated equality true for every real input?

Select the coefficient condition that uses the identity correctly

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

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

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

(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 \(P(0)\)

\(P(0)\)