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Algebra
Pregunta

(1) What are the \( x \) -intercepts of the graph ...

(1) What are the \( x \) -intercepts of the graph of \( y = ( 3 x + 8 ) ( 5 x - 3 ) ( x - 1 ) \) ? 

Solve the polynomials by factoring. Please enter the list the solutions from smallest to largest and separate solutions by commas. 

(2) \( x ^ { 4 } - 37 x ^ { 2 } + 36 = 0 \) 

(3) \( x ^ { 3 } + 3 x ^ { 2 } - 9 x = 27 \) 

     \( 2 x ^ { 3 } + 6 x ^ { 2 } - 36 = 0 \) 

(4)  \( 3 x ^ { 4 } + 11 x ^ { 3 } = 4 x ^ { 2 }\) 

Answer

1. When y=0, \(x= -\frac{8}{3},\frac{3}{5},1\)

 

2. 

\(x^4- 37x^2+ 36= 0\\\Rightarrow (x^2- 1)(x^2- 36)= 0\\\Rightarrow (x+ 1)(x- 1)(x+ 6)(x- 6)= 0\\\Rightarrow x= -6,- 1,1,6\)

 

3. 

\(x^3+ 3x^2- 9x= 27\\\Rightarrow x^3+ 3x^2- 9x- 27= 0\\\Rightarrow (x^2- 9)(x+ 3)= 0\\\Rightarrow (x+ 3)^2(x- 3)= 0\\\Rightarrow x= -3,3\\\Rightarrow 2x^3+ 6x^2- 36\ne0\)

So, the system has no solution.

 

4.

\(3x^4+ 11x^3= 4x^2\\\Rightarrow 3x^4+ 11x^3- 4x^2= 0\\\Rightarrow x^2(3x^2+ 11x- 4)= 0\\\Rightarrow x^2(x+ 4)(3x- 1)= 0\\\Rightarrow x= -4,0,\frac{1}{3}\)

Solución
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