Answer: (2x – 7) (3x^3 – 2x – 5)
SOLVINGS
Given the polynomial f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case,
The Leading Coefficient is 6
The Trailing Constant is -35.
Factors of the Leading Coefficient are 1, 2, 3 and 6
Factors of the Trailing Constant are 1, 5, 7, and 35
Testing for the rational roots,
If P= 7 and Q = 2
P/Q = 3.5
F (P/Q) = 0.00
Using the Factor Theorem; which states that if P/Q is root of a polynomial then this polynomial can be divided by Q.x – PTherefore, the polynomial 6x^4 – 21x^3 – 4x^2 + 24x – 35 is divisible by 2x –
7
Factorizing 2x – 7
Divide the polynomial into two groups (6x^4 – 21x^3 and – 4x^2 + 24x – 35)
Factorizing Group 1
6x^4 – 21x^3 divided by 2x – 7 = 3x^3
∴ 6x^4 – 21x^3 = 3x^3 (2x – 7) ….. (Group 1)
Factorizing Group 2
– 4x^2 + 24x – 35 divided by 2x – 7 = -2x+5
∴ 4x^2 + 24x – 35 = (-2x+5)(2x – 7) ….. (Group 2)
Bringing together Groups 1 and 2
6x^4 – 21x^3 – 4x^2 + 24x – 35 = (2x – 7) (3x^3 – 2x – 5)
Answer: k - 8
Step-by-step explanation:
Answer:
The length is 22.5 and the width is 19.5
Step-by-step explanation:
2L + 2W = P
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2L + 2W = 84
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W + 3 + W + 3 + W + W= 84
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4W + 6 = 84
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4W = 78
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W = 19.5 L = 19.5 + 3 = 22.5
I hope this helps, have a nice day! :D
Answer:
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