swransidhu1
Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

(a) What must be added to 1 - 2x + 3x² to obtain 3 + 5x - 7x2?
(b) What must be subtracted from -4m2 + 5m - 3 to obtain m2 – 3m?
(c) From the sum of 4b2 + 5bc, -2b2 - 2bc – 2z2 and 2bc + 4c?, subtract the sum of 5b²-c²and -3b²+2bc+c
solve step by step ​

Sagot :

facundo3141592

Answer:

When we sum polynomials, like:

p(x) = a*x^2 + b*x + c

q(x) = k*x^3 + n*x^2 + m*x + ñ

The sum grups terms with the same power of x, where we just take the x part as a common factor, so we can write, in this case:

p(x) + q(x) = k*x^3 + (a + n)*x^2 + (b + m)*x + (c + ñ)

This is just an example, let's see how we can apply this to the given problems.

a) We start with:

3*x^2 - 2*x + 1

and we want to add something to get: 3 + 5*x - 7*x^2

Then we need to add a quadratic polynomial a*x^2 + b*x + c

(we know this because the end polynomial is also a quadratic one, the same as the first one)

Then we get

(3*x^2 - 2*x + 1) + (a*x^2 + b*x + c) = -7*x^2 + 5*x + 3

(3 + a)*x^2 + (-2 + b)*x + (1 + c) =  -7*x^2 + 5*x + 3

Is easy to see that we must have:

3 + a = -7

-2 + b = 5

1 + c = 3

Solving these 3 equations, we get:

a = -7 - 3 = -10

b = 5 + 2 = 7

c = 3 - 1 = 2

Then the polynomial that we must add is:

-10*x^2 + 7*x + 2

b)

Here we start with:

(-4*m^2 + 5*m - 3)

and want to subtract something to get: m^2 - 3*m

Then let's subtract a polynomial like:

a*m^2 + b*m + c

And let's do the same than in the case "a"

(-4*m^2 + 5*m - 3) - (a*m^2 + b*m + c) = m^2 - 3*m + 0

(-4 - a)*m^2 + (5 - b)*m + (-3 - c) = m^2 - 3*m + 0

Then we must have:

-4 -a = 1

5 - b = -3

-3 - c = 0

Solving the above equations, we get:

a = -4 - 1 = -5

b = 5 + 3 = 8

c = -3

Then the polynomial that we must subtract is:

-5*m^2 + 8*m - 3

c)

Here we have a lot of variables, so remember to take the correct common factors, take your time:

we start with:

(4*b^2 + 5*b*c) + (-2*b^2 - 2*b*c - 2*z^2) + (2*b*c - 4*c)

We want to subtract the sum:

(5*b^2 - c^2) + (-3*b^2 + 2*b*c + c)

First let's simplify both of these sums, we can rewrite the first one as:

(4 - 2)*b^2 + (5 - 2 + 2)*b*c - 2*z^2 - 4*c

= 2*b^2 + 5*b*c - 2*z^2 - 4*c

Now, for the other sum we can simplify as:

(5 - 3)*b^2 - c^2 + 2*b*c + c

= 2*b^2 - c^2 + 2*b*c + c

Finally, we can calculate the difference between these two as:

( 2*b^2 + 5*b*c - 2*z^2 - 4*c) - (2*b^2 - c^2 + 2*b*c + c)

This is equal to:

(2 - 2)*b^2 + (5 - 2)*b*c - 2*z^2 + (-4 - 1)*c - c^2

3*b*c - 2*z^2 - 5*c + c^2

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.