Hint
Retain signs inside every bracket. Expand and collect \(\displaystyle x^{2}\) terms.
Worked solution
(a)
\(x^{2} - 12 x + 11\) multiplied by \(x + 3\) gives \(x^{3} - 9 x^{2} - 25 x + 33\).
Answer: \(x^{3} - 9 x^{2} - 25 x + 33\)
(b)
Collect all degree-one products.
\(x^{3} - 9 x^{2} - 25 x + 33\)
Answer: \(-25\)
(c)
Multiply the three constant terms.
\(33\)
Answer: \(33\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternatives and consequential reasoning; an unexplained final answer does not earn a method mark.
(a) · 2 marks
- 1 mark: Multiply the factors and collect each power of x.
- 1 mark: Give all results requested in this part, with the correct signs, exact values, units, branch and boundary inclusion where applicable.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Do not multiply only matching powers.
(b) · 2 marks
- 1 mark: Collect all degree-one products.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: A polynomial identity is stronger than one equation at one x.
(c) · 2 marks
- 1 mark: Multiply the three constant terms.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Do not multiply only matching powers.
Total: 6 marks.