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3 years ago

15. Multiply the following: a. (3x − 2)(2x +1)

Mathematics

2 answers:

Stolb23 [73]3 years ago

8 0

Answer:

6x^2 Plus x - 2

Doss [256]3 years ago

7 0

Answer:

Step-by-step explanation:multiply 3x first with (2x+1)

=6x²+3x

then multiply -2 with (2x+1)

= -4x-2

then add both equations

answer =6x²-x-2

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4 years ago

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3 years ago

Find the polynomial of minimum degree, with real coefficients, zeros at x=4±2⋅i and x=−8, and y-intercept at −480. Write your an

valkas [14]

Answer:

The polynomial of minimum degree is $p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$ .

Step-by-step explanation:

According to the statement, we appreciate that polynomial pass through the following points:

(i) $(4 + 2\,i,0)$ , (ii) $(4 - 2\,i, 0)$ , (iii) $(-8, 0)$ , (iv) $(0, -480)$

From Algebra we know that any n-th grade polynomial can be constructed by knowing n+1 different points. Hence, the polynomial of minimum degree is a quartic function. The polynomial has the following form:

$p(x) = (x-4-2\,i)\cdot (x-4+2\,i)\cdot (x+8)\cdot (x-r_{1})$

We proceed to expand the expression until standard form is obtained:

$p(x) = (x^{2}-4\cdot x-2\,i\cdot x-4\cdot x +16+8\,i+2\,i\cdot x-8\,i+4)\cdot (x+8)\cdot (x-r_{1})$

$p(x) = (x^{2}-8\cdot x+20)\cdot (x+8)\cdot (x-r_{1})$

$p(x) = (x^{3}-8\cdot x^{2}+20\cdot x +8\cdot x^{2}-64\cdot x+160)\cdot (x-r_{1})$

$p(x) = (x^{3}-44\cdot x +160)\cdot (x-r_{1})$

If we know that $p (0) = -480$ , then:

$-480=160\cdot (-r_{1})$

$-160\cdot r_{1} = -480$

$r_{1} = 3$

Then, the polynomial is:

$p(x) = (x^{3}-44\cdot x +160)\cdot (x-3)$

$p(x) = x^{4}-44\cdot x^{2}+160\cdot x-3\cdot x^{3}+132\cdot x -480$

$p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$

The polynomial of minimum degree is $p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$ .

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3 years ago

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mixas84 [53]

Answer:7,560cm

Step-by-step explanation: Area is found by multiplying each side by each other. 7 x 6 x 12 x 15=7560

7 x 6=42

12 x 15=180

180 x 42=7560

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3 years ago

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The research group asked the following question of individuals who earned in excess of $100,000 per year and those who earned l

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3 years ago