Which of the following quadratic equations can be solved by grouping?(1 point) Responses x2+10x+21=0 x squared plus 10 x plus 21 equals 0 x2−12x+18=0 x squared minus 12 x plus 18 equals 0 x2+8x−22=0 x squared plus 8 x minus 22 equals 0 x2−4x−8=0
The quadratic equation that can be solved by grouping is x2−4x−8=0, or "x squared minus 4x minus 8 equals 0."
The quadratic equation that can be solved by grouping is x^2 + 8x - 22 = 0, or "x squared plus 8x minus 22 equals 0."
To determine which of the given quadratic equations can be solved by grouping, we need to examine their coefficients.
To solve a quadratic equation by grouping, the middle term needs to be decomposed into two terms whose coefficients add up to the coefficient of the linear term (x term) in the equation.
Let's analyze the given quadratic equations:
1. x^2 + 10x + 21 = 0: In this equation, the middle term is 10x. There are no two factors of 21 that add up to 10, so grouping cannot be used to solve this equation.
2. x^2 - 12x + 18 = 0: The middle term is -12x. Factors of 18 that add up to -12 are -6 and -6. Therefore, grouping can be applied to this equation.
3. x^2 + 8x - 22 = 0: The middle term is 8x. There are no two factors of -22 that add up to 8, so grouping cannot be used to solve this equation.
4. x^2 - 4x - 8 = 0: The middle term is -4x. Factors of -8 that add up to -4 are -2 and -2. Therefore, grouping can be applied to this equation.
From the given options, the quadratic equations that can be solved by grouping are x^2 - 12x + 18 = 0 and x^2 - 4x - 8 = 0.