Match List-I with List-II.
| List-I (Expression) | List-II (Factors) | ||
|---|---|---|---|
| (A) | \(x^2-5x+6\) | (I) | \((x+2)(x+3)\) |
| (B) | \(x^2+x-6\) | (II) | \((x-3)(x+2)\) |
| (C) | \(x^2-x-6\) | (III) | \((x-2)(x-3)\) |
| (D) | \(x^2+5x+6\) | (IV) | \((x+3)(x-2)\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
Multiply out each pair of factors: \((x+p)(x+q)=x^2+(p+q)x+pq\). The sum \(p+q\) gives the middle term and the product \(pq\) gives the last term.
(I) \((x+2)(x+3)\): sum \(5\), product \(6\) → \(x^2+5x+6\), which is (D)
(II) \((x-3)(x+2)\): sum \(-1\), product \(-6\) → \(x^2-x-6\), which is (C)
(III) \((x-2)(x-3)\): sum \(-5\), product \(6\) → \(x^2-5x+6\), which is (A)
(IV) \((x+3)(x-2)\): sum \(1\), product \(-6\) → \(x^2+x-6\), which is (B)
So the matching is (A)-(III), (B)-(IV), (C)-(II), (D)-(I).