$(x^2 - 14x + 49)(x^2 + 6x + 9)$
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.
Similar Questions
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Important Questions from Polynomials
If (x + y) 3+ 8 (x - y) 3= (3x + Ay) (3x 2+ Bxy + Cy 2), then the value of A + B + C is:
Given that x 8- 34x 4+ 1 = 0, x > 0. What is the value of (x 3+ x -3 )?
If \(x - \frac 3 x = 6,\; x \ne 0,\) then the value of \(\frac {x^4 - \frac {27}{x^2}}{x^2 - 3x - 3}\) is:
If \(x\left(3 - \frac 2 x\right) = \frac 3 x,\) then the value of \(x^3 - \frac 1 {x^3}\) is equal to:
The coefficient of x in (x – 3y) 3is:
