Question

Shauna says that 2x2 + x - 12 is the same as (x+4)(x-3). Is

she correct? Are the two expressions equal? Explain your
answer.

Answer 1

1. No she's wrong
2. Two equations are unequal.
3. Explained below

Explanation:

`\sf \rightarrowtail \: (x + 4)(x - 3) \\ \sf \rightarrowtail \: x(x - 3) + 4(x - 3) \\ \sf \rightarrowtail \: {x}^(2) - 3x + 4x - 12 \\ \sf \rightarrowtail \: {x}^(2) + x - 12 \cancel{ = } {2x}^(2) + x - 12`

Answer 2

Shauna is incorrect, because (x + 4)(x - 3) is NOT equivalent to 2x² + x - 12

Explanation:

Check if she is correct by expanding (x + 4)(x - 3), with FOIL:

(x + 4)(x - 3)

x² - 3x + 4x - 12

x² + x - 12

So, Shauna is incorrect, because the two expressions are not equal.

(x + 4)(x - 3) is equivalent to x² + x - 12, NOT 2x² + x - 12.