If <em>x</em> + 1 is a factor of <em>p(x)</em> = <em>x</em>³ + <em>k</em> <em>x</em>² + <em>x</em> + 6, then by the remainder theorem, we have
<em>p</em> (-1) = (-1)³ + <em>k</em> (-1)² + (-1) + 6 = 0 → <em>k</em> = -4
So we have
<em>p(x)</em> = <em>x</em>³ - 4<em>x</em>² + <em>x</em> + 6
Dividing <em>p(x)</em> by <em>x</em> + 1 (using whatever method you prefer) gives
<em>p(x)</em> / (<em>x</em> + 1) = <em>x</em>² - 5<em>x</em> + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
<em>x</em>² - 5<em>x</em> + 6 = (<em>x</em> - 3) (<em>x</em> - 2)
so that, in addition to <em>x</em> = -1, the other two zeros of <em>p(x)</em> are <em>x</em> = 3 and <em>x</em> = 2
If your salving for n it would be n=0.75
If your salving by factoring it is 3/4
Answer:
In mathematics, a coefficient is a factor linked to a monomium. Given a monomium divider, the coefficient is the ratio of the monomium by the divider. Thus the monomium is the product of the coefficient and the divider. The different coefficients will depend on the factorization of the monomium. This is usually next to the letter that accompanies the algebraic fraction. A numeric coefficient is a constant factor of a specific object. For example, in the expression 9x2, the coefficient of x2 is 9. In elemental algebra, numeric coefficients of similar terms are grouped together to simplify algebraic expressions.
Step-by-step explanation:
Answer:
g(7) = 16
Step-by-step explanation:
The domain definitions in this piecewise function tell you that the third (bottom) piece applies when x=7.
g(7) = (7+1)(7-5) = (8)(2)
g(7) = 16