Factorise[math: x2−8x−20]
ormalsize x^2 - 8\, x - 20

Question

Factorise[math: x2−8x−20] 
ormalsize x^2 - 8\, x - 20

BlackTom AI · Accepted Answer

We start by understanding the task: factorising the quadratic x^2 - 8x - 20.

Option a: (x+2)(x-10). Expanding gives x^2 - 10x + 2x - 20 = x^2 - 8x - 20, which matches the original expression. This option is consistent with the standard factoring method: find two numbers that multiply to -20 and sum to -8, namely 2 and -10.

Option b: (x+10)(x-2). Expanding yields x^2 - 2x + 10x - 20 = x^2 + 8x - 20. This does not match the middle term, which should be -8x, so this option is incorrect.

Option c: (x-8)(x-20). Expanding yields x^2 - 28x + 160, which is far from the target expression. The product and sum conditions are not satisfied here, making this invalid.

Option d: (x+8)(x-20). Expansion gives x^2 - 20x + 8x - 160 = x^2 - 12x - 160. The middle coefficient and constant term do not align with x^2 - 8x - 20, so this is incorrect.

Option e: (x-2)(x-2). This is x^2 - 4x + 4, which has a different linear coefficient and constant term, so it cannot be the factorisation of x^2 - 8x - 20.

In summary, the only option that yields the exact original quadratic upon expansion is option a, as it uses the pair of numbers that multiply to -20 and sum to -8 (2 and -10). The other choices fail to meet either the sum or the product condition required for correct factorisation.

MUF0091 Mathematics Unit 1 - Semester 1, 2025 Quiz - 3 Expansion and factorisation questions

Factorise[math: x2−8x−20] \normalsize x^2 - 8\, x - 20

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