Question

Paul creates the diagram to help him factor 4x2 + x – 5 by using double grouping. His diagram is incomplete.

A 2-column table with 2 rows. The labels for the columns and rows are blank. First column entries are 4 x squared, M Subscript 2 Baseline. Second column entries are M Subscript 1 Baseline, negative 5.
Which terms should Paul write in squares M1 and M2?

5x and −4x
–5x and 4x
–2x and 10x
2x and −10x

Answer 1

5x and −4x.

Reason: you need two terms that sum to 1x and have product 4·(−5) = −20. 5x + (−4x) = x and 5x·(−4x) = −20x^2, so split as 4x^2 + 5x − 4x − 5 = (4x+5)(x−1).