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Mandarinka [93]
3 years ago
15

Double digit subtraction with regrouping

Mathematics
1 answer:
goblinko [34]3 years ago
8 0
Here is an example... ( look at the attachment bellow ) :

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When a polynomial f(x) is divided by 2x-3,the quotient is x^2-x+2 and the remainder is -1. Find the f(x)​
joja [24]

Answer:

f(x) = 2x³ - 5x² + 7x - 7

Step-by-step explanation:

In the division statement: m ÷ n = q + \frac{r}{n}

  • m is the dividend
  • n is the divisor
  • q is the quotient
  • r is the remainder
  • m = q × n + r

Let us use the fact above to solve the question

∵ f(x) is divided by (2x - 3), the quotient is x² - x + 2 and the remainder is -1

∴ f(x) is the dividend ⇒ m

∴ (2x - 3) is the divisor ⇒ n

∴ (x² - x + 2) is the quotient ⇒ q

∴ -1 is the remainder ⇒ r

→ Use the rule above to find f(x)

∵ f(x) = (x² - x + 2) × (2x - 3) + -1

∴ f(x) = (x² - x + 2)(2x - 3) - 1

→ Multiply the 2 brackets at first

∵ (x² - x + 2)(2x - 3) = x²(2x) + x²(-3) + -x(2x) + -x(-3) + 2(2x) + 2(-3)

∴ (x² - x + 2)(2x - 3) = 2x³ - 3x² - 2x² + 3x + 4x - 6

→ Add the like terms

∴ (x² - x + 2)(2x - 3) = 2x³ + (-3x² - 2x²) + (3x + 4x) - 6

∴ (x² - x + 2)(2x - 3) = 2x³ + (-5x²) + 7x - 6

∴ (x² - x + 2)(2x - 3) = 2x³ - 5x² + 7x - 6

→ Substitute it in f(x)

∴ f(x) = 2x³ - 5x² + 7x - 6 - 1

→ Add the like term

∵ f(x) = 2x³ - 5x² + 7x + (- 6 - 1)

∴ f(x) = 2x³ - 5x² + 7x + (-7)

∴ f(x) = 2x³ - 5x² + 7x - 7

3 0
3 years ago
Let the random variable X denote the number of network blackouts in a day. The
faltersainse [42]
E(X) = 0(0.7) + 1(0.2) + 2(0.1) = 0.2 + 0.2 = 0.4
The expected daily loss due to blackouts = 0.4 * $500 = $200

Var(X) = 0(0.7 - 0.4)^2 + 1(0.2 - 0.4)^2 + 2(0.1 - 0.4)^2 = 0.04 + 0.18 = 0.22
The expected daily variance due to blackouts = 0.22 * $500 = $110
6 0
3 years ago
PLSS I NEED HELL ASAP!!!
zheka24 [161]

Your question is so blur i cant see

plzz send a nice pics

7 0
3 years ago
Help pls and thank you :)
klio [65]

Answer:

The one on the bottom right

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The length of a rectangle is x² + 6x + 3 and the width is 3x² + 4x - 2. Which expression represents the are of the rectangle
miss Akunina [59]

Answer:

Step-by-step explanation:

area of rectangle=length×width

=(x²+6x+3)×(3x²+4x-2)

=3x^4+(4+18)x³+(-2+24+9)x²+(-12+12)x-6

=3x^4+22x³+31x²-6

7 0
3 years ago
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