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 - 5x^2 + 3x + 10

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

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

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

(a)1 mark

Find the parameter values that make the two polynomial expressions identical

Select the coefficient condition that uses the identity correctly

x^3:\;2=2\qquad x^2:\;-5=-5\qquad x:\;4 + p=3\qquad 1:\;5 + q=10

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

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

\(P(0)\)