Let `P(x) = x^3+5x^2+2x-8`.
- Show that `P(-2) = 0`. (1 mark)
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- Hence, factor the polynomial `P(x)` as `A(x)B(x)`, where `B(x)` is a quadratic polynomial. (2 marks)
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Show Worked Solution
| i. | `P(-2)` | `= (-2)^3+ 5(-2)^2+2(-2)-8` |
| `=-8+20-4-8` | ||
| `= 0` |
ii. `text{Since}\ \ P(-2)=0\ \ =>\ \ (x+2)\ text{is a factor of}\ P(x)`
`P(x)=A(x)B(x)=(x+2)*B(x)`
`text{Using long division:}\ P(x)-:(x+2)=B(x)`
`:.P(x)=(x+2)(x^2+3x-4)`