Simplify: StartFraction x cubed plus 5 x squared minus 20 over x plus 3 EndFraction
Move values to the blanks to complete the equation.
Response area with 4 blank spaces
Blank space 1 empty
Blank space 5 empty
Blank space 7 empty
Blank space 8 empty
Answer options with 7 options.
StartFraction x cubed plus 5 x squared minus 20 over x plus 3 EndFraction = x(x squared + 5x - 20) / (x + 3)
To simplify the expression, we need to factor the numerator:
Numerator: x^3 + 5x^2 - 20
First, we can factor out the greatest common factor (GCF), which is x:
Numerator: x(x^2 + 5x - 20)
Next, we can factor the quadratic expression inside the parentheses using the product-sum method or by applying the quadratic formula. The factored form is:
Numerator: x(x + 10)(x - 2)
Therefore, the simplified expression is:
StartFraction x(x + 10)(x - 2) over x + 3 EndFraction
To simplify the given expression, we need to factor the numerator and then cancel out the common factors.
The numerator of the expression is x^3 + 5x^2 - 20. Let's factor it:
x^3 + 5x^2 - 20 = x^2(x + 5) - 4(x + 5) = (x^2 - 4)(x + 5)
Now we can rewrite the expression as:
StartFraction (x^2 - 4)(x + 5) over x + 3 EndFraction
To move values to the blanks and complete the equation, we can rewrite the expression as:
StartFraction x^2 - 4 over x + 3 EndFraction * {Blank Space}
To simplify further, we can factor x^2 - 4 as a difference of squares:
x^2 - 4 = (x - 2)(x + 2)
Now the expression becomes:
StartFraction (x - 2)(x + 2) over x + 3 EndFraction * {Blank Space}
At this point, it seems that there might be a mistake in the question as there are extra blank spaces and answer options provided. Without further information, it is not possible to determine the intended completion of the equation or the available answer options.