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smc

algebra senior

Problem

The expression

x^{2} - y^{2} - z^{2} + 2 y z + x + y - z

has:

(A)

no linear factor with integer coefficients and integer exponents

(B)

the factor - x + y + z

(C)

the factor x - y - z + 1

(D)

the factor x + y - z + 1

(E)

the factor x - y + z + 1

Solution

Factor the perfect square trinomial.

x^{2} - (y - z)^{2} + x + y - z

Factor the difference of squares.

(x + y - z) (x - y + z) + x + y - z

Factor by grouping.

(x + y - z) (x - y + z + 1)

The answer is

the factor x - y + z + 1

.

Final answer

E