**Objective:** Factor to find all x-intercepts of the function. **Function:** \[ f(x) = 2x^2 + x - 6 \] **Explanation:** To find the x-intercepts of the function, we need to set \( f(x) = 0 \) and solve for \( x \). This can be done by factoring the quadratic expression. The x-intercepts are the values of \( x \) for which \( f(x) = 0 \). **Steps for Factoring:** 1. **Identify Coefficients:** - \( a = 2 \) - \( b = 1 \) - \( c = -6 \) 2. **Find Two Numbers that Multiply to \( a \times c \) (i.e., \( 2 \times -6 = -12 \)) and Add to \( b \) (i.e., 1).** 3. **Rewrite Middle Term** using the numbers identified in step 2 and factor by grouping. 4. **Solve for \( x \)** by setting each factor equal to zero. **Note:** The exact factoring method may require trial and error or the quadratic formula if factoring is not straightforward. Understanding x-intercepts is crucial for analyzing the graphical behavior of functions, particularly in determining where the function crosses the x-axis.

Q: Factor to find all x-intercepts of the function. 2 f(x) = x² - 2x + 1 −

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Q: Find the remaining zeros of each function and write in factored form. 13. f(x) = x + 3x³ - 29x² - 3x…

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Q: Find p(1) and p(-3) of each polynomial function. p(x) = x3-7x2-20x+60

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Q: Find p(1) and p (-3) of each polynomial. p(x) = 3x4 - 2x2+1 %3D

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Q: Factor to find all x-intercepts of the function. 4 x5 f(x) = x³ - 8x¹ + 16x³

A: The given function is .The aim is to find the all intercepts of the function.

Q: Find the domain and range of the function. f(x) = 7x² + 5

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Q: Determine the x- and y-intercepts for the given function. B(x)=5x+8

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Q: and g(x) = 1,, write the composite function (fog) (x). 12 4x+3 4x+6 4x+3 x+3 4x x 31 - 3

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Q: If the solutions of p(x) = 0 are -14 and 11, which function could be p?

A: Given,          The solutions of px=0 are -14 and 11.

Q: Find the degree of the polynomial function. f(x) = -4x + 7x5

A: Introduction: A polynomial's degree is the highest power of the variable in a polynomial expression.…