Answer:
(d) x = 3 or x = 4
Explanation:
The zero product property can be used to find the solutions to a polynomial equation when it is written in factored form.
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Your polynomial can be put in factored form like this:
x² +12 = 7x . . . . . given
x² -7x +12 = 0 . . . . . standard form
(x -3)(x -4) = 0 . . . . . factored form*
x = 3 or x = 4 . . . . . . values of x that make the factors zero
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* The constants in the binomial factors must have a sum of -7 and a product of +12. It is often convenient to find them by listing factor pairs of 12:
12 = (-1)(-12) = (-2)(-6) = (-3)(-4)
Negative factors are used because we know the sum must be negative. Both have the same sign so their product is positive. The sums of the pairs shown are -13, -8, -7. The last pair is what we're looking for.