Hint
Use the stated units and precision. Use the HCF and the smallest variable exponents, dividing every original term by the complete common factor.
Worked solution
(a)
The numerical HCF is 6. The common variable factor is \(x^{2}y\). Dividing both terms by their product gives \(2 x + 3 y\).
Answer: \(6 x^{2} y \left(2 x + 3 y\right)\)
(b)
Use the HCF and the smallest variable exponents, dividing every original term by the complete common factor.
\(2\)
Answer: \(2\)
(c)
Use the HCF and the smallest variable exponents, dividing every original term by the complete common factor.
\(3\)
Answer: \(3\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 3 marks
- 1 mark: Extract the greatest common numerical and variable factor.
- 1 mark: Divide each original term by that factor and check that the bracket has no further common factor.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Use the HCF and the smallest variable exponents, dividing every original term by the complete common factor.
- 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: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Use the HCF and the smallest variable exponents, dividing every original term by the complete common factor.
- 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: Keep intermediate values exact until the final step.
Total: 7 marks.