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UNO [17]
2 years ago
8

The polynomial f(x) = x³-x²+px+q, where p and q are constants, has remainder 8 when divided by (x-1). If (x+1) is factor of f(x)

, find the values of p and q​
Mathematics
2 answers:
quester [9]2 years ago
7 0

Answer:p=-1 and q=1

Step-by-step explanation:

valentina_108 [34]2 years ago
3 0

Answer:

p=3, q=5

Step-by-step explanation:

f(x) = x³-x²+px+q

factor: x+1 = 0   x = -1

(-1)³ - (-1)² + p*(-1) + q = 0

-2 - p + q = 0

p = q-2

(x-1) is factor of f(x) - 8, root x = 1 : f(x) = x³-x²+(q-2)x+q-8

(1)³ - (1)² + (q-2)(1) + q - 8 = 0

q - 2 + q - 8 = 0

2q = 10     q = 5

p = q-2 = 3

check: x³-x²+3x+5 = <u>(x+1)</u>(x²-2x+5)

x³-x²+3x+5 = (x²+3)(x-1) + <u>8</u>

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Aneli [31]

Point (2, 4) was reflected over the x axis to give (2, -4). It was then dilated by a scale factor of 2 to get (4, -8). Hence (2, 4) ⇒ (4, -8)

<h3>What is a transformation?</h3>

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Point (2, 4) was reflected over the x axis to give (2, -4). It was then dilated by a scale factor of 2 to get (4, -8). Hence (2, 4) ⇒ (4, -8)

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6 0
2 years ago
Mitchell took a math exam today. If he got 63 out of 84 questions correct, what percentage did Mitchell get wrong? (answer using
Mars2501 [29]

Answer:

75%


Step-by-step explanation:

If Mitchell took a math exam and got 63 out of 84 questions correct, that would turn into the fraction: 63/84

In order to convert this to a decimal, you divide 84 by 63 (since every fraction is a division problem), and get 0.75.

When you change decimals into percents, you move the decimal point two times to the right. So, that would be 75.

Then you add the percent symbol and you're done!

I hope that helped :)

7 0
2 years ago
Read 2 more answers
Car A travels at 45 miles per hour and Car B travels at a greater speed of x miles per hour. Write and simplify an expression th
jonny [76]

farther = 2 \times (x - 45) = 2x - 90

3 0
3 years ago
Need help fast due today thanks
cricket20 [7]

1

Move everything to the left by subtracting 25 from both sides:

81x^2-25=0

Both terms are squares: 81x^2 is the square of 9x, while 25 is the square of 5. So, we can apply the factoring

a^2-b^2=(a+b)(a-b)

To factor the expression as

(9x+5)(9x-5)=0

A multiplication is zero if and only if one of the factors is zero, so we have

(9x+5)(9x-5)=0 \iff 9x+5=0 \lor 9x-5=0 \iff x=-\dfrac{5}{9} \lor x=\dfrac{5}{9}

2

The discriminant of the quadratic expression ax^2+bx+c is defined as

\Delta = b^2-4ac

So, you have

\Delta = 0^2-4\cdot(-1)\cdot(-25) = -100

3

Similarly, we have

\Delta = 7^2-4\cdot(-3)\cdot 6 = 49+72=121

8 0
3 years ago
In the following number, which place value does the 3 hold? 993,140 hundreds thousands ten thousands hundred thousands
Agata [3.3K]
It's in the thousand place value
4 0
3 years ago
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