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3 years ago

Factor f(x)= 3x³+5x²-47x+15 into linear factors given that -5 is a zero of f(x)

1 answer:

7 0

If -5 is a zero then f(x) is divisible by (x + 5)

the quotient when F*x) is divided by x + 5 is :-
3x^2 - 10x + 3
this factors to
(3x - 1)(x - 3)

so the answer is (x + 5)(3x - 1)(x - 3)

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Answer:

The area of the rectangle TOUR is 80.00 unit².

Step-by-step explanation:

The area of a rectangle is computed using the formula:

$Area\ of\ a\ Rectangle=length\times width$

Since the dimensions of the rectangle are not provided we can compute the dimensions using the distance formula for two points.

The distance formula using the two point is:

$distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Considering the rectangle TOUR the area formula will be:

Area of Rectangle TOUR = TO × OU

The co-ordinates of the four vertices of a triangle are:

T = (-8, 0), O = (4, 4), U = (6, -2) and R = (-6, -6)

Compute the distance between the vertices T and O as:

$TO=\sqrt{(4-(-8))^{2}+(4-0)^{2}}\\=\sqrt{12^{2}+4^{2}} \\=\sqrt{160} \\=4\sqrt{10}$

Compute the distance between the vertices O and U as:

$OU=\sqrt{(6-4)^{2}+(-2-4)^{2}}\\=\sqrt{2^{2}+6^{2}} \\=\sqrt{40} \\=2\sqrt{10}$

Compute the area of rectangle TOUR as follows:

$Area\ of\ TOUR=TO\times OU\\=4\sqrt{10}\times 2\sqrt{10}\\=80\\\approx80.00 unit^{2}$

Thus, the area of the rectangle TOUR is 80.00 unit².

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