$(x^2 - 14x + 49)(x^2 + 6x + 9)$
Factoring the Algebraic Expression
The expression provided is: $(x^2 - 14x + 49)(x^2 + 6x + 9)$
To find its square root, we first factor each quadratic part.
- The first quadratic, $x^2 - 14x + 49$, is a perfect square trinomial. It factors as $(x - 7)^2$.
- The second quadratic, $x^2 + 6x + 9$, is also a perfect square trinomial. It factors as $(x + 3)^2$.
Substituting these factors back, the expression becomes:
$(x - 7)^2 (x + 3)^2$Calculating the Square Root
Now, we calculate the square root of this factored expression:
$\sqrt{(x - 7)^2 (x + 3)^2}$Using the property $\sqrt{a^2 b^2} = \sqrt{a^2}\sqrt{b^2} = |a||b|$, we get:
$|x - 7| \times |x + 3|$In algebraic contexts like this multiple-choice question, the principal square root is typically considered, simplifying to:
$(x - 7)(x + 3)$This result matches Option B.
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Solve the following.
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- If $x=2$ is one of the zeros of the polynomial $x^3 - 6x^2 + 11x - 6$, which are the other two zeros?
- Find the sum of zeroes for the quadratic polynomial $3x^2 + 5x - 2$
- Find the zeros of the following quadratic polynomial $x^2 - 2x - 15$
