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oksano4ka [1.4K]
3 years ago
15

Without actual division, prove that 2x^4 - 5x^3 + 2x^2 - x + 2 is divisible by x^2 + 3x + 2.

Mathematics
2 answers:
adell [148]3 years ago
7 0

Answer:

Thinking Process

(i) Firstly, determine the factors of quadratic polynomial by splitting middle term.

(ii) The two different values of zeroes put in bioquadratic polynomial.

(iii) In both the case if remainder is zero, then bioquadratic polynomial is divisible by

quadratic polynomial.

Art [367]3 years ago
7 0

Answer:

2x⁴ - 5x³ + 2x² - x + 2=

2x²(x²-3x+2) +x³-2x² -x +2=

2x²(x²-3x+2) + x(x²-3x+2) +x² -3x +2=

(x²-3x+2)(2x²+x+1)

since x²-3x+2 is the factor of the given polynomial, we can state the polynomial is divisible by x²-3x+2

-------------

<em>note: x²+3x+2 is not the factor of the given polynomial </em>

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