Question

Rewrite cx = x^2 + 5x + 2x - 3 in the form y = qx + r(x)b(x) where r has degree less than b.

a) y = x(x + 7) - 3
b) y = x^2 + 7x - 3
c) y = x(x + 7) + 6
d) y = x^2 + 7x + 6

Answer 1

To rewrite the expression cx = x^2 + 5x + 2x - 3, you combine like terms to get x^2 + 7x - 3, which then matches option (a) y = x(x + 7) - 3.

Step-by-step explanation:

To rewrite the given expression cx = x^2 + 5x + 2x - 3 in the form y = qx + r(x)b(x), where r has a degree less than b, we must first combine like terms. The expression simplifies to cx = x^2 + 7x - 3. This can be rearranged to y = x(x + 7) - 3, matching option (a), where q = x, r(x) = -3, and b(x) = x + 7, with the degree of r being zero, which is less than the degree of b, which is one.