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# 4 questions on polynomials

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1. Find the product $(x - 3)(2x^2 + 5x - 7).$

2. Find the coefficient of $z$ in the product$(-3z^2 - 7z + 4)(6z^2 - z + 6).$

3. Let $f(x) = x^4-3x^2 + 2$ and $g(x) = 2x^4 - 6x^2 + 2x -1$. Let $b$ be a constant. What is the smallest possible degree of the polynomial $f(x) + b\cdot g(x)$?

4. Let $f(x) = x^4-3x^2 + 2$ and $g(x) = 2x^4 - 6x^2 + 2x -1$. What is the degree of $f(x) \cdot g(x)$?

Feb 21, 2021

#1
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1. $$(x-3)(2x^2 + 5x - 7) = (2x^3 + 5x^2 - 7x) -(6x^2 - 15x + 21)$$

$$\boxed{2x^3 - x^2 + 8x - 21}$$

2. $$(-3z^2 - 7z + 4)(6z^2 - z + 6) = -18z^4 - 39z^3 + 13z^2 -\boxed{ 46z} + 24$$

The coefficient of z is -46.

Feb 22, 2021
#3
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Thanks

Randompersonlol  Feb 22, 2021
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3. f(x) has degree 4 and g(x) has degree 4. Because b is a constant, the maximum degree of $$f(x) + b\cdot g(x)$$ can only be 4.

4. f(x) has degree 4 and g(x) has degree 4. By multiplying, you are adding the degrees, so the degree of f(x) * g(x) is 8.

Feb 22, 2021
#4
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Thanks

Randompersonlol  Feb 22, 2021
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Hi Cubey,

Welcome to the Web2.0 forum!

I know you are very active here and I like your enthusiasm

but

Hints and partial answers (for which you know the full answer) are much better.

This is especially true when it is clear the asker is just looking for quick answers.

I am sure you do not want this forum to be a place where people come with the sole intention of cheating.

Feb 22, 2021
#6
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I will keep that in mind, thank you!

CubeyThePenguin  Feb 22, 2021