Pregunta
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( 4x^2 + x - 33 = (4x - 11)(x + 3) \)
Solución
1. The expression is
\[
4x^2 + x - 33.
\]
2. First, identify the coefficients in the quadratic \( ax^2 + bx + c \):
\[
a = 4,\quad b = 1,\quad c = -33.
\]
3. Compute the product \( a \cdot c \):
\[
4 \times (-33) = -132.
\]
4. We need two numbers that multiply to \(-132\) and add up to \(1\) (the coefficient \( b \)).
Testing factor pairs of \(-132\), we find that \(12\) and \(-11\) satisfy:
\[
12 \times (-11) = -132 \quad \text{and} \quad 12 + (-11) = 1.
\]
5. Rewrite the middle term \( x \) using \( 12x \) and \(-11x \):
\[
4x^2 + 12x - 11x - 33.
\]
6. Group the terms:
\[
(4x^2 + 12x) + (-11x - 33).
\]
7. Factor each group:
- In the first group, factor out \( 4x \):
\[
4x(x + 3).
\]
- In the second group, factor out \(-11\):
\[
-11(x + 3).
\]
8. Since both groups contain the common factor \((x+3)\), factor it out:
\[
(4x - 11)(x + 3).
\]
Thus, the factorization of \( 4x^2 + x - 33 \) is
\[
(4x-11)(x+3).
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Bonus Knowledge
Let’s break it down! To find the roots of the quadratic equation \( 4x^{2}+x-33 = 0 \), you can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 4 \), \( b = 1 \), and \( c = -33 \). Plugging in these values will give you two possible solutions for \( x \). Now, for an extra twist: did you know that quadratics aren’t just numbers and letters? They have real-world applications everywhere! From projectile motion to optimizing areas in business, this equation could help solve problems in physics or economics, showing how math truly reflects our daily lives!
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
