Problem

Classify \(x^{2}-18\) as a difference of squares over the integers.

Answer choices

Choose your path.

Preview only

operation=difference; first term square=x²; second term perfect integer square=no because18 is not k² for integer k; difference-of-squares over integers=no; note=over reals it factors as(x−3√2)(x+3√2)

operation=sum; square status=x² and18; difference-of-squares over integers=no because operation is addition; integer factorization=none; field note=none

operation=difference; square terms=x² and(√18)²; difference-of-squares over integers=yes; integer factorization=(x−√18)(x+√18); field note=√18 is an integer

operation=difference; square terms=x² and(3√2)²; difference-of-squares over integers=yes; integer factorization=(x−3√2)(x+3√2); field note=all coefficients are integers

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Classify \(x^{2}-18\) as a difference of squares over the integers.

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.