2x2 - 13x − 14

Question

2x2 - 13x − 14

ScanSolve AI Tutor · Accepted Answer

The expression shown is 2h² − 13x − 14. This contains two different variables, h and x. To apply the "splitting the middle term" method, the expression must be a quadratic in a single variable. Assuming the first term's variable was intended to be x, making the expression 2x² − 13x − 14, we proceed as follows: Step 1: Identify the coefficients and find two numbers that multiply to a × c and add to b. For 2x² − 13x − 14, we have a=2, b=−13, c=−14. We need two numbers that multiply to a × c = 2 × (−14) = −28 and add up to b = −13. Step 2: List integer pairs that multiply to −28 and check their sums. The integer pairs that multiply to −28 are (1, −28), (−1, 28), (2, −14), (−2, 14), (4, −7), and (−4, 7). Their respective sums are 1 + (−28) = −27, −1 + 28 = 27, 2 + (−14) = −12, −2 + 14 = 12, 4 + (−7) = −3, and −4 + 7 = 3. Step 3: Conclude based on the sums. Since none of these pairs sum to −13, the quadratic expression 2x² − 13x − 14 cannot be factored into linear factors with integer coefficients using the splitting the middle term method. Not factorable over integers

2x2 - 13x - 14

Answer

Step-by-step solution

Identify the coefficients and find two numbers that multiply to $a \times c$ and add to $b$ .

List integer pairs that multiply to $-28$ and check their sums.

Conclude based on the sums.

Try one yourself

Still stuck on this one?

More Mathematics Questions