Answer:
d) p(4) = 0.
Step-by-step explanation:
p(4) = 0:-
p(4) = 4^2 + 8(4) - 48
= 16 + 32 - 48
= 0.
This is an application of the Factor Theorem ( a special case of The Remainder Theorem)
The Factor theorem states that if (x - a) is a factor of P(x) then P(a) = 0.
Answer:
a = 8 2/3.
Step-by-step explanation:
The y coordinate of the point is 5, andthe x coordinate is a so substituting for these in the given equation:
3a - 4(5) = 6
3a - 20 = 6
3a = 26
a = 26/3
= 8 2/3
Step-by-step explanation:
<em>How do you factor a polynomial?
</em>
<em>follow these steps:
</em>
<em>1.Check for the GCF first. ...
</em>
<em>2.Multiply the quadratic term and the constant term. ...
</em>
<em>3.Write down all the factors of the result, in pairs. ...
</em>
<em>4.From this list, find the pair that adds to produce the coefficient of the linear term.</em>
Step-by-step explanation:
I'll do the first one as an example.
"What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5,1) that partitions the segment into a ratio of 3 to 2?"
Let's call the point we're trying to find P. Ratio of 3 to 2 means that the distance from K to P divided by the distance from P to L is 3/2.
KP / PL = 3 / 2
Which also means the horizontal distances and vertical distances between the points have a ratio of 3:2.
KxPx / PxLx = 3 / 2
KyPy / PyLy = 3 / 2
First, let's use the x coordinates:
(x − (-5)) / (5 − x) = 3 / 2
(x + 5) / (5 − x) = 3 / 2
2 (x + 5) = 3 (5 − x)
2x + 10 = 15 − 3x
5x = 5
x = 1
And now with the y coordinates:
(y − (-4)) / (1 − y) = 3 / 2
(y + 4) / (1 − y) = 3 / 2
2 (y + 4) = 3 (1 − y)
2y + 8 = 3 − 3y
5y = -5
y = -1
So the point P is at (1,-1).
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