Solve x2 − 7x = −12. (6 points) x = 6 and x = −2 x = 4 and x = 3 x = 2 and x = 6 x = −4 and x = −3

Work Shown:

x^2 - 7x = -12

x^2 - 7x + 12 = 0

(x - 3)(x - 4) = 0 ... see note below

x - 3 = 0 or x - 4 = 0

x = 3 or x = 4

Note: we're looking for two numbers that multiply to 12 and add to -7. Those two numbers are -3 and -4, so that's where the factorization (x-3)(x-4) comes in. After this step, you set each factor equal to zero and solve for x.

x=3  x=4

Step-by-step explanation:

x^2 − 7x = −12

Add 12 to each side

x^2 - 7x +12 =0

Factor

What 2 numbers multiply to 12 and add to -7

-3*-4 = 12

-3+-4 = -7

(x-3)(x-4) =0

Using the zero product property

x-3 =0   x-4 =0

x=3  x=4

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step-by-step explanation:

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(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3