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Sagot :
Answer:
1. X^2+1/2x = [tex]x(x+\frac{1}{2})[/tex]
2. X^2+2x-3 = [tex](x-1)(x+3)[/tex]
3. (2x-3)^2 = (2x-3)(2x-3)
4. X^3+2x^2-19x-20 = [tex](x+1)(x-4)(x+5)[/tex]
Step-by-step explanation:
Each expression can be written as a product of linear factors as follows
1. X^2+1/2x ⇒ [tex]x^{2} + \frac{1}{2}x[/tex]
[tex]x^{2} + \frac{1}{2}x[/tex] = [tex]x(x+\frac{1}{2})[/tex]
Hence, X^2+1/2x = [tex]x(x+\frac{1}{2})[/tex]
2. X^2+2x-3 ⇒ [tex]x^{2} +2x-3[/tex]
[tex]x^{2} +2x-3 = x^{2} +3x-x-3[/tex]
[tex]x^{2} +3x-x-3 = x(x+3) -1(x+3)[/tex]
[tex]x(x+3) -1(x+3) = (x-1)(x+3)[/tex]
Hence, X^2+2x-3 = [tex](x-1)(x+3)[/tex]
3. (2x-3)^2 ⇒[tex](2x-3)^{2}[/tex]
[tex](2x-3)^{2} = (2x-3)(2x-3)[/tex]
Hence, (2x-3)^2 = (2x-3)(2x-3)
4. X^3+2x^2-19x-20 ⇒ [tex]x^{3}+2x^{2} -19x -20[/tex]
[tex]x^{3}+2x^{2} -19x -20 = (x+1)(x^{2} +x-20)[/tex]
First,
[tex]x^{2} +x-20 = x^{2} +5x-4x-20\\x^{2} +5x-4x-20= x(x+5)-4(x+5)\\x(x+5)-4(x+5) = (x-4)(x+5)[/tex]
∴ [tex](x+1)(x^{2} +x-20) = (x+1)(x-4)(x+5)[/tex]
Hence, X^3+2x^2-19x-20 = [tex](x+1)(x-4)(x+5)[/tex]
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