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3 years ago

Which binomial is a factor of the polynomial? x2 - 6x + 9 A) (x - 9) B) (x + 3) C) (x + 9) D) (x - 3)

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

8 0

$x^2-6x+9=x^2-3x-3x+9=x(x-3)-3(x-3)=(x-3)(x-3)\\\\Answer:\ \boxed{D)\ (x-3)}$

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2 years ago

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50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle

aalyn [17]

Answer:

$EF=4\sqrt{3}$

Step-by-step explanation:

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

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We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

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$\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2$

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$\displaystyle 12=\frac{1}{2}(DE)(DF)$

Since DE = DF:

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Thus:

$DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE$

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

$(DE)^2+(DF)^2=(EF)^2$

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Add:

$EF^2=48$

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3 years ago

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Consider the roots of a cubic equation with integral coefficients: −1, −4, and 3. Which choice is a factor of the cubic equation

mash [69]

Answer:

Step-by-step explanation:

Lets go case by case.

Given the roots, a factor will be part of the equation if for some of the roots the factor becomes null, i.e., equal to 0.

Is there any root that makes (x+3)=0? No, as it only becomes 0 for x = - 3 and -3 is not a root. So A NO!

Is there a root that makes (x-1)=0? No, as it only becomes 0 for x=1 and 1 is not a root. So B NO!

(x-4)=0 only for x=4, and as 4 is not a root, C NO!

The last, (x-3)=0 if x=3. As 3 is one of the roots, (x-3) is a factor of our equation!

D is the only correct option!

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