Outside the middle school program / Equations 9 exercises (100% corrected)

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1. Factor by (ax+b) E.827 Let the expression be : E =(5 x − 2) 2 − ( x − 7)(5 x − 2) 1 Expand and reduce E . 2 Calculate the numerical value of E for x = − 1 . 3 Factorize E 4 Solve equation : (5 x − 2)(4 x +5)=0 E.828 Consider the expression : C =(2 x +5) 2 − ( x +3)(2 x +5) 1 Expand and simplify C . 2 Factor C . 3 Solve the equation : (2 x +5)( x +2)=0 . 4 Calculate the expression C for x = − 2 5 (Express the result as an irreducible fraction) E.840 1 Expand and reduce : A =(2 x − 1) 2 − 4(2 − x ) 2 Factor: B =( x − 1) 2 +(3 x +5)( x − 1) 3 Solve the equation : ( x − 1)(4 x +4)=0 E.816 Consider the expression E : E =(2 x + 1) 2 − 4 1 Expand and simplify the expression E . 2 Factor the expression E into a product of linear factors. 3 Solve the equation : (2 x +3)(2 x − 1)=0 . 4 Calculate E when x equals − 3 2 , and then when x equals 0. E.838 1 Consider the expression : E =( x − 3) 2 − ( x − 1)( x − 2) a Expand and simplify E . b How can we determine, without a calculator, the result of : 99 997 2 − 99 999 × 99 998 2 a Factor the expression : F = (4 x + 1) 2 − (4 x + 1)(7 x − 6) b Solve the equation : (4 x +1)(7 − 3 x )=0 2. Factoring by (ax+b) and the square root E.839 Let the expression be : D =(2 x − 3)(3 x − 1)+(2 x − 3) 2 1 Expand and reduce D . 2 Factorize D . 3 Calculate D for x = 2 , write the answer as a − b c ( a , b and c integers) . 4 Solve equation : (2 x − 3)(5 x − 4)=0 E.830 1 Consider the following expression D : D = (2 x − 3) 2 + (2 x − 3)(5 x + 1) a Expand and reduce the expression D . b Factorize D . 2 Solve the equation : (2 x − 3)(7 x − 2)=0 3 We pose : E =14 x 2 − 25 x +6 . Calculate E for x = 45 and give the result as a + b 5 , where a and b denote relative integers. E.833 Let be the expression A = 9 x 2 − 49+(3 x +7)(2 x +3) 1 Expand the expression A . 2 Factorize 9 x 2 − 49 ; then the expression A . 3 Calculate A for x = 2 . The result will be given as a + b 2 4 Solve equation : (3 x +7)(5 x − 4)=0 E.815 Solve the following equations (results will be given in simplified form) : a 4 x + 2 − (5 x + 1) = 3 − 3(2 x + 1) b 3 x + 1 4 − 2 x − 4 3 = 1 + x + x + 1 6 c 3 2 × x + 6 = 9 2 × x − 5 6 https://chingmath.fr chapExoCorrec/827 sacados/827 chapExoCorrec/828 sacados/828 Groupe Est - Juin 2003 - 5,5 points chapExoCorrec/840 sacados/840 chapExoCorrec/816 sacados/816 chapExoCorrec/838 sacados/838 chapExoCorrec/839 sacados/839 chapExoCorrec/830 sacados/830 chapExoCorrec/833 sacados/833 chapExoCorrec/815 sacados/815