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solong [7]
3 years ago
15

each week, Alfonso earned $85 for every shift he works at the theater and $15 for every dog-walking job. He uses the expression

85x + 15 y to keep track of his earnings. How many terms are in the expression, what are they, and how do you know?
Mathematics
1 answer:
In-s [12.5K]3 years ago
4 0

In Algebra a term is either a single number or variable, or numbers and variables multiplied together. There are two terms in this expression, and i know this because terms are separated by a + or - sign.

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A level maths factor theorem <br>help in part (b) please​
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Given polynomial f(x)=4 x^{3}-12 x^{2}+2 x-6.

(a) To show that (x – 3) is a factor of f(x).

Factor theorem:

<em>A polynomial f(x) has a factor of (x – a), if and only if f(a) = 0.</em>

f(x)=4 x^{3}-12 x^{2}+2 x-6

f(3)=4 (3)^{3}-12 (3)^{2}+2 (3)-6

       =4(27)-12(9)+6-6

       =108-108

       = 0

f(3) = 0

Hence (x – 3) is a factor of f(x).

(b) f(x)=0

4 x^{3}-12 x^{2}+2 x-6=0

Here 4x^2 is common in first 2 terms and 2 is common in next 2 terms.

4x^2(x-3 )+2 (x-3)=0

Now, (x – 3) is common in both terms.

(x-3)(4x^2+2)=0

(x-3)=0 and (4x^2+2)=0

x = 3 and 4x^2+2=0

3 is the real root.

using quadratic formula solve 4x^2+2=0 and find the other roots.

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

$x=\frac{-0 \pm \sqrt{0^{2}-4 (4) (2)}}{2 (4)}

$x=\pm\frac{\sqrt{-32}}{8}

$x=\pm\frac{4\sqrt{2}i}{8}

$x=\pm\frac{\sqrt{2}i}{2}

These are complex roots.

Hence 3 is the only real root of the equation f(x) = 0.

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Step-by-step explanation:


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