Question

8. The area of a rectangular painting is given by the trinomial x2 + 4x – 21. What are the possible dimensions of the painting? Use factoring. (1 point)

Answer 1

First, you have to think of two binomials that when multiplied together yields the polynomial x2 + 4x - 21. Question would be: what are the two number that when multiplied with each other equals -21 and when added together sums up to 4?

That would be +7 and -3. Because 7 × -3 = -21 and 7 + -3 = +4

Thus, the factor would be
(x + 7)(x - 3) = 0
By zero product property,
(x + 7) = 0 and (x-3)=0
x = -7 and x = 3

Notice that even if 7 has a negative sign, when substituted to the polynomial, you take its square so it would still be positive. Thus, the absolute value is taken.

Thus, the possible dimensions of the rectangle are 7 and 3 units.