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GarryVolchara [31]
2 years ago
11

Please help, I have attached a picture of the question! Thank you!

Mathematics
1 answer:
tigry1 [53]2 years ago
6 0

Answer:

Factors:

A. x+3

B. 4x+3

C. x-5

Step-by-step explanation:

Given polynomial:

4x^4-21x^3-46x^2+219x+180

Rewrite it as follows:

4x^4-21x^3-46x^2+219x+180\\ \\=4x^4+12x^3-33x^3-99x^2+53x^2+159x+60x+180\\ \\=4x^3(x+3)-33x^2(x+3)+53x(x+3)+60(x+3)\\ \\=(x+3)(4x^3-33x^2+53x+60)

Now factor polynomial 4x^3-33x^2+53x+60:

4x^3-33x^2+53x+60\\ \\=4x^3-16x^2-17x^2+68x-15x+60\\ \\=4x^2(x-4)-17x(x-4)-15(x-4)\\ \\=(x-4)(4x^2-17x-15)

Now factor polynomial 4x^2-17x-15:

4x^2-17x-15\\ \\=4x^2-20x+3x-15\\ \\=4x(x-5)+3(x-5)\\ \\=(x-5)(4x+3)

Hence,

4x^4-21x^3-46x^2+219x+180=(x+3)(x-4)(x-5)(4x+3)

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