Factor the quadratic trinomial x2 + x − 12 by finding two integers whose product is −12 and sum is 1.

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Step 1: Identify b and c in the trinomial x² + x − 12. The general form of a quadratic trinomial is ax² + bx + c. Comparing x² + x − 12 with ax² + bx + c: a = 1; b = 1; c = −12; b = 1; c = −12 Step 2: Determine the two integers, r and s, whose product is −12 and sum is 1. We need two numbers that multiply to c = −12 and add up to b = 1. Let's list factors of −12: 1 × (−12) = −12, Sum: 1 + (−12) = −11; −1 × 12 = −12, Sum: −1 + 12 = 11; 2 × (−6) = −12, Sum: 2 + (−6) = −4; −2 × 6 = −12, Sum: −2 + 6 = 4; 3 × (−4) = −12, Sum: 3 + (−4) = −1; −3 × 4 = −12, Sum: −3 + 4 = 1 The two integers are −3 and 4. Factors of −12 — Product of the two factors — Sum of the two factors — Result1, −12 — −12 — −11 −1, 12 — −12 — 11 2, −6 — −12 — −4 −2, 6 — −12 — 4 3, −4 — −12 — −1 −3, 4 — −12 — 1 — ✓ Step 3: Complete the table for factorizing x² + x − 12. Using the integers 4 and −3 from Step 2, we rewrite the middle term x as 4x − 3x. Mathematical steps — Explanationx² + 4x − 3x − 12 — Rewrite the middle term of the trinomial using the values from the chart above. (x² + 4x) + (−3x − 12) — Group pairs of terms. x(x + 4) — Factor out the HCF of the first group. −3(x + 4) — Factor out the HCF of the second group. (x + 4)(x − 3) — Factor out HCF of the two terms. (x + 4)(x − 3) — The final factorized answer.

Factors of -12	Product of the two factors	Sum of the two factors	Result
1, -12	-12	-11
-1, 12	-12	11
2, -6	-12	-4
-2, 6	-12	4
3, -4	-12	-1
-3, 4	-12	1	✓

Factor the quadratic trinomial x2 + x - 12 by finding two integers whose product is -12 and sum is 1.

Answer

Step-by-step solution

Identify $b$ and $c$ in the trinomial $x^2 + x - 12$ .

Determine the two integers, $r$ and $s$ , whose product is $-12$ and sum is 1.

Complete the table for factorizing $x^2 + x - 12$ .

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