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BabaBlast [244]

3 years ago

12

Help me Please..

1 answer:

Fittoniya [83]3 years ago

7 0

Just general definitons:

a TRInomial has 3 terms (tri means three)
a BInomial has 2 terms (bi means two)
a MONOmial has 1 term (mono means one)

the degree is the highest exponent found in the algebraic expression

so they should be pretty easy to solve with that information, but just in case:

1. trinomial, degree of 4
2. binomial, degree of 3
3. monomial, degree of 2

for the final question, all you have to do is plug in 2 for x, so

(2)^2 - 2(2) + 1

4 - 4 + 1

so the answer is 1

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Divide.<br> (18x² + 45x+29) = (3x+5)<br> Your answer should give the quotient and the remainder.

MrRa [10]

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3 years ago

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F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2)<br><br> I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

<u>Given function</u>:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find <em>a</em>, compare the coefficients of x³:

$\implies a=3$

To find <em>b</em>, substitute the found value of <em>a</em> into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

$\implies b=-8$

To find <em>c</em>, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

<u>Zero Product Property</u>

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

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1 year ago

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Write and solve an equa

adell [148]

Answer:

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Step-by-step explanation:

Given -

Temperature at 6:00 PM = -20 degree Celsius

Let the temperature at midnight be X degree Celsius

From midnight to 6:00 am, the temperature rose by 8 degree Celsius

X - (-20) = 8

X = 8-20

X = -12 degree Celsius.

The temperature at midnight is -12 degree Celsius.

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3 years ago