What are the values of b and c for the trinomial x2 + x − 12, and what are the two integers r and s that…

Question

What are the values of b and c for the trinomial x2 + x − 12, and what are the two integers r and s that satisfy the conditions for factoring?

ScanSolve AI Tutor · Accepted Answer

Step 1: Determine the values of b and c for x² + x − 12. The general form of a trinomial is ax² + bx + c. Comparing x² + x − 12 to ax² + bx + c: a = 1; b = 1; c = −12 a) The value of b is 1. b) The value of c is −12. Step 2: Complete the table for finding integers r and s for x² + x − 12. We need two integers r and s such that their product r × s = c = −12 and their sum r + s = b = 1. Factors of −12 — Product of the two factors — Sum of the two factors — Result1 and −12 — 1 × (−12) = −12 — 1 + (−12) = −11 — Not 1; −1 and 12 — −1 × 12 = −12 — −1 + 12 = 11 — Not 1; 2 and −6 — 2 × (−6) = −12 — 2 + (−6) = −4 — Not 1; −2 and 6 — −2 × 6 = −12 — −2 + 6 = 4 — Not 1; 3 and −4 — 3 × (−4) = −12 — 3 + (−4) = −1 — Not 1; −3 and 4 — −3 × 4 = −12 — −3 + 4 = 1 — Is 1 The two integers are −3 and 4. Step 3: Show the mathematical steps for factoring x² + x − 12. | Explanation | Mathematical steps

Factors of -12	Product of the two factors	Sum of the two factors	Result
1 and $-12$	$1 \times (-12) = -12$	$1 + (-12) = -11$	Not 1
$-1$ and 12	$-1 \times 12 = -12$	$-1 + 12 = 11$	Not 1
2 and $-6$	$2 \times (-6) = -12$	$2 + (-6) = -4$	Not 1
$-2$ and 6	$-2 \times 6 = -12$	$-2 + 6 = 4$	Not 1
3 and $-4$	$3 \times (-4) = -12$	$3 + (-4) = -1$	Not 1
$-3$ and 4	$-3 \times 4 = -12$	$-3 + 4 = 1$	Is 1

What are the values of b and c for the trinomial x2 + x - 12, and what are the two integers r and s that satisfy the conditions for factoring?

Answer

Step-by-step solution

Part a

Part b· 2 steps
$-3 \text{ and } 4$

Complete the table for finding integers $r$ and $s$ for $x^2 + x - 12$ .

Show the mathematical steps for factoring $x^2 + x - 12$ .

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