show 2x^2+3x+1 is a factor of 2x^4-5x^3-5x^2+5x+3
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if 2x²+3x+1 is factor then it will equal to 0
2x²+2x+x+1=0
2x(x+1)+1(x+1)=0
x=-1/2nd -1
putting the value in 2x⁴-5x³-5x²+5x+3,we get
when x=-1
2+5-5-5+3=0
when x=-1/2
2×1/16+5×1/8-5×1/4+3
1/8+5/8-5/4+3
20/8=5/4
it divides p(x) completely so it is factor of p(x)
2x²+2x+x+1=0
2x(x+1)+1(x+1)=0
x=-1/2nd -1
putting the value in 2x⁴-5x³-5x²+5x+3,we get
when x=-1
2+5-5-5+3=0
when x=-1/2
2×1/16+5×1/8-5×1/4+3
1/8+5/8-5/4+3
20/8=5/4
it divides p(x) completely so it is factor of p(x)
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