Property 3
The Equality of Two-Polynomials
For two polynomials to be equal to each other their factors of similar degree terms should be equal.
1.
\(P(x)=(5a-1)x^2+(b+1)x\)
\(Q(x)=9x^2+4x\)
\(P(x)=Q(x)\)
\(\Rightarrow a+b=?\)
2.
\(P(x)=(a+2)x^2+4x-c\)
\(Q(x)=3x^2-(b+1)x+3\)
\(P(x)=Q(x)\)
\(\Rightarrow a\cdot b\cdot c=?\)
3.
\((a-1)x^2+3x-2=(b-3)x^3+x^2+3x-c\)
\(\Rightarrow a+b+c=?\)
4.
\((x+2)(x-3)=ax^2+bx+c\)
\(\Rightarrow a+b+c=?\)
5.
\((x-1)(2x+1)=ax^2+bx+c\)
\(\Rightarrow a+b+c=?\)
6.
\((a-1)x^2+3x+1=x^2+(b-1)x+1\)
\(\Rightarrow a+2b=?\)
7.
\(\samefrac{5x+4}{x^2+x-2}=\samefrac{A}{x-1}+\samefrac{B}{x+2}\)
\(\Rightarrow A\cdot B=?\)
8.
\(\samefrac{3x+3}{x^2-9}=\samefrac{A}{x-3}+\samefrac{B}{x+3}\)
\(\Rightarrow A\cdot B=?\)
9.
\(\samefrac{3x+7}{x^2+5x+6}=\samefrac{A}{x+2}+\samefrac{B}{x+3}\)
\(\Rightarrow A\cdot B=?\)
10.
\(P(x)=(a-1)x^3+2x^2+c-1\)
\(Q(x)=(b+1)x^2+6\)
\(P(x)=Q(x)\)
\(\Rightarrow a\cdot b\cdot c=?\)
11.
\(x(x-1)+2x=ax^2+bx+c\)
\(\Rightarrow a\cdot b\cdot c=?\)
12.
\(x(x^2+2)=(a-1)x^3+(b+1)x^2+cx\)
\(\Rightarrow a+b+c=?\)
13.
\(3x-3=a(x+1)+b(x-2)\)
\(\Rightarrow a\cdot b=?\)
14.
\(5x-2=a(x-1)+b(x+2)\)
\(\Rightarrow 2a+b=?\)
15.
\(P(x)=x^2-2\)
\(Q(x)=ax^2+bx+c\)
\(P(x+1)=Q(x)\)
\(\Rightarrow a+b+c=?\)