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Which of the following quadratic equations can be solved by grouping?(1 point)%0D%0AResponses%0D%0A%0D%0Ax2−4x−8=0%0D%0Ax squared minus 4 x minus 8 equals 0%0D%0A%0D%0Ax2+8x−22=0%0D%0Ax squared plus 8 x minus 22 equals 0%0D%0A%0D%0Ax2−12x+18=0%0D%0Ax squared minus 12 x plus 18 equals 0%0D%0A%0D%0Ax2+10x+21=0

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To determine which of the given quadratic equations can be solved by grouping, we typically look for an expression that can be factored into two binomials. Grouping is a technique often used when the quadratic can be rearranged into two pairs that can be grouped together.

Let's analyze each equation one by one:

  1. \(x^2 - 4x - 8 = 0\):

    • Factoring group: Not easily factorable with integers.
    • Not suitable for grouping.

  2. \(x^2 + 8x - 22 = 0\):

    • Factoring group: The quadratic can be rearranged, but does not lend itself to easy splitting.
    • Not suitable for grouping.

  3. \(x^2 - 12x + 18 = 0\):

    • This can be factorable by finding factors of 18 that add up to -12.
    • Factors are not integers.
    • Not suitable for grouping.

  4. \(x^2 + 10x + 21 = 0\):

    • This can be factored easily as \((x + 3)(x + 7) = 0\).
    • Can be grouped into pairs leading to a solution.
    • Suitable for grouping.

After examining all options, the quadratic equation that can be solved by grouping is \(x^2 + 10x + 21 = 0\).