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2X 2 6X 4. X2 −3x + 2 = 0 find the factors of 2 which add up to 3. The x values should be selected around the vertex.
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Let's do the arithmetic of the polynomial. 2(x2 + 3x+2) = 0 2 ( x 2 + 3 x + 2) = 0 factor. Rearrange to ax2 + bx+ c = 0 −2x2 = 2x −4 ⇒ 2x2 +2x− 4 = 0. Step 1 :equation at the end of step 1 : Notice that all the coefficients are even. The x values should be selected around the vertex. ⇒ −2(x + 1)(x +2) = 0. Each factor could be equal to. The factors of + 2 which sum to + 3 are +1 and + 2. Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
We can therefore divide by 2 to simplify matters. If we express 2x2 +6x+ 11 in the form a(x− h)2 +k, then what is h? Polynomials can have constants, variables and exponents, but never division by a variable. Factor the polynomial by factoring out the greatest common factor,. Notice that all the coefficients are even. Step 3 :pulling out like terms : Therefore, the turning points can be picked up such that x = − 3 2,y = − 1 2 therefore coordinates: (2x2 + 6x) + 4 = 0 step 2 : Web 2x^{2}+6x+4=0 all equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction. The factors of + 2 which sum to + 3 are +1 and + 2.
