what polynomial of least degree must be subtracted from the polynomial p(x) = 8x⁴+14x³-3x²+8x-12 so that 4x²-3x-2 is a factor of p(x) .
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Answer:
What must be subtracted or added to p(x) = 8x4+14x3-2x2+8x-12 so that4x2+3x-2 is the factor of p(x)
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teenababy Helping Hand
Therefore 15x-4 is to be added
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wifilethbridge Ambitious
Answer:
15x-14
Step-by-step explanation:
Dividend = 8x^4+14x^3-2x^2+8x-12
Divisor=4x^2+3x-2
Since we know that :
Dividend = (Divisor \times Quotient)+Remainder
So, 8x^4+14x^3-2x^2+8x-12 = (4x^2+3x-2 \times 2x^2)+(8x^3+2x^2+8x-12)
8x^4+14x^3-2x^2+8x-12 = (4x^2+3x-2 \times 2x^2+2x)+(-4x^2+12x-12)
8x^4+14x^3-2x^2+8x-12 = (4x^2+3x-2 \times 2x^2+2x-1)+(15x-14)
So, Remainder is 15x-14
So, 15x-14 should be subtracted form 8x^4+14x^3-2x^2+8x-12 so that 4x^2+3x-2 is the factor of p(x).
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