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Margarita [4]
3 years ago
7

Factorise (2t-7)²-(5t-4)² with working pls​

Mathematics
1 answer:
sertanlavr [38]3 years ago
5 0

Answer:

33+12t−21t^2

Step-by-step explanation:

(2t-7)²-(5t-4)²

Use binomial theorem (a−b)^2 = a^2−2ab+b^2 to expand (2t-7)².

4t^2−28t+49−(5t-4)²

Use binomial theorem (a−b)^2 = a^2−2ab+b^2 to expand (5t-4)².

4t^2−28t+49−(25t^2−40t+16)

To find the opposite of 25t^2

−40t+16, find the opposite of each term.

4t^2−28t+49−25t^2−40t+16

Combine 4t^2  and −25t^2  to get −21t^2.

−21t^2−28t+49+40t−16

Combine −28t and 40t to get 12t.

−21t^2+12t+49−16

Subtract 16 from 49 to get 33.

−21t^2+12t+33

Swap terms to the left side.

33+12t−21t^2

I hope this helped!

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Rewrite the following quadratic functions in intercept or factored form. Show your work.
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Answer:

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Step-by-step explanation:

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2. Factor f(x) = x4 + x3 – 8x2 + 6x + 36 completely.
k0ka [10]
Take the leading coefficient and the last coefficient, and list all their factors. In this case, the leading coefficient is 1 because it is the number in front of the highest order term. 36 is the last coefficient.

a_n = 1: 1
a_0 = 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 

Next we will find all the possible rational roots. To do so, divide each of the a_0 factors by each of the a_n factors. For each result there is a positive and negative root. In this case 1 is the only a_n factor. Since anything divided by 1 is itself, the possible rational roots are the same as the factors of 36 (except now we have positive and negative numbers).

So the possible roots are -1, 1, -2, 2, -3, 3, -4, 4, -6, 6.... etc.

Now use synthetic division to test each of the possible roots. If the answer does not have a remainder, then it is a root. After one possible root works, use the result of the division to continue finding other roots. Let me know if you need help with this step and I will upload a picture. Otherwise, division is pretty straight forward.

After dividing the polynomial by each possible rational root, we find -2 and -3 as roots. We can express these roots as the factors (x+2) and (x+3). So after wee factor them out, we get:

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Hope this helps! Rational Root Theorem is a lot of work, but it is easy once you understand it!


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