The complete equation of the polynomial is 2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2
<h3>How to complete the blanks?</h3>
The equation is given as:
_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2
Complete the blanks using alphabets
ax(x^2 - bx) + cx^3 = dx(ex^2 + fx) - x^2
Open the brackets
ax^3 - abx^2 + cx^3 = dex^3 + dfx^2- x^2
Factorize the expression
(a + c)x^3 - abx^2 = dex^3 + (df - 1)x^2
By comparison, we have:
a + c = de
-ab = df - 1
Rewrite the second equation as:
ab + df = 1
So, we have:
a + c = de
ab + df = 1
Set a = 2 and c = 10.
So, we have:
a + c = de ⇒ de = 2 + 10 ⇒ de = 12
ab + df = 1 ⇒2b + df = 1
Express 12 as 3 * 4 in de = 12
de = 3 * 4
By comparison, we have:
d = 3 and e = 4
So, we have:
2b + df = 1
This gives
2b + 3f = 1
Set b = 11.
So, we have:
2 * 11 + 3f = 1
This gives
22 + 3f = 1
Subtract 22 from both sides
3f = -21
Divide by 3
f = -7
Hence, the complete equation is:
2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2
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Answer:
Step-by-step explanation:
<u>Given</u>
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<u>Step 1: Combine Like Terms on LHS</u>
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<u>Step 2: Subtract 11 on both sides</u>
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<u>Step 3: Divide both sides by -4 to isolate the x-variable</u>
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<u>Final Answer</u>
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C . the graph will shift upwards because it is increasing on a graph
Answer:
(11b^2 + 7) (11b^2 - 7)
Explanation:
Since both terms are perfect squares, factor using the difference of squares formula, a^2 - b^2 = (a + b) (a - b) where a = 121b^4 and b = 49