Andrew Keir Potw
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The document contains three equations: x+x-1=3, x2+x-2=a, and x3+x-3=b. It asks to find the numerical value of a+b by solving these simultaneous equations for a and b.
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This problem asks us to factor the expression x^2 - 4x + 5 and use it to find the coefficients a and b in the polynomial ax^3 + bx^2 + 25, whose factors include x^2 - 4x + 5. We are asked to compute and report the sum of a + b.
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To solve a quadratic equation by completing the square, rewrite the left side in the form of x^2 + bx, add (b/2)^2 to both sides to create a perfect square on the left, then take the square root of both sides. To solve by the quadratic formula, identify the coefficients a, b, and c and plug them into the formula x = (-b ± √(b^2 - 4ac)) / 2a to find the solutions.
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Brittany's POTW
This problem asks us to factor the expression x^2 - 4x + 5 and use it to find the coefficients a and b in the polynomial ax^3 + bx^2 + 25, whose factors include x^2 - 4x + 5. We are asked to compute and report the sum of a + b.
How to test
To solve a quadratic equation by completing the square, rewrite the left side in the form of x^2 + bx, add (b/2)^2 to both sides to create a perfect square on the left, then take the square root of both sides. To solve by the quadratic formula, identify the coefficients a, b, and c and plug them into the formula x = (-b ± √(b^2 - 4ac)) / 2a to find the solutions.
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This document provides methods for solving quadratic equations including factoring, using the difference of squares, completing the square, and using the quadratic formula. Examples are given for solving quadratic equations by factoring, taking square roots, completing the square, and using the quadratic formula to graph the equation and find the x-intercept(s).
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The document provides steps to factor the expression (3y - 5)(y + 1). It first writes out the expression, then multiplies the terms using distribution. It groups like terms and factors the resulting expression into (y + 1)(3y - 5).
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