The factors of x²+5x+4 : (x + 4) (x + 1) Further explanation Factoring A Quadratic Equation means finding a factor of an equation that if multiplied produces a quadratic equation We can solve the quadratic equation with the formula or we can do it by finding the common factor as below (x + a) (x + b) = x² + (a + b) x + ab From the x² + 5x + 4 equation, we can determine a, b and c from the general quadratic equation namely ax² + bx + c:
a = 1, b = 5, c = 4 First, find two numbers that multiply to give a x c and add to give b. From the equation above: axc=1x 4 = 4, and b = 5 we look for a factor of 4 which when added together gets the number 5 a factor of 4: 1,2,4 of these factors which can be added to 5 are 1 and 4 So the form of the equation becomes:
So the form of the equation becomes: x+5x+4 x² + x + 4x + 4 x (x + 1) +4 (x + 1) (x + 1) -> common to both terms We use the principle of distributive property of addition ax (b + c) = axb + axc -> a = x + 1 so the factors: (x + 4) (x + 1)
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The factors of x²+5x+4 : (x + 4) (x + 1) Further explanation Factoring A Quadratic Equation means finding a factor of an equation that if multiplied produces a quadratic equation We can solve the quadratic equation with the formula or we can do it by finding the common factor as below (x + a) (x + b) = x² + (a + b) x + ab From the x² + 5x + 4 equation, we can determine a, b and c from the general quadratic equation namely ax² + bx + c:
a = 1, b = 5, c = 4 First, find two numbers that multiply to give a x c and add to give b. From the equation above: axc=1x 4 = 4, and b = 5 we look for a factor of 4 which when added together gets the number 5 a factor of 4: 1,2,4 of these factors which can be added to 5 are 1 and 4 So the form of the equation becomes:
So the form of the equation becomes: x+5x+4 x² + x + 4x + 4 x (x + 1) +4 (x + 1) (x + 1) -> common to both terms We use the principle of distributive property of addition ax (b + c) = axb + axc -> a = x + 1 so the factors: (x + 4) (x + 1)