 - 1)**4*(i + 6)/3
Let a = 47555/28639 + 409/2203. Factor 2/13*m**2 + 72/13 + a*m.
2*(m + 6)**2/13
Let q(i) be the second derivative of -2*i**6/15 - 39*i**5/5 + 124*i**4/3 - 56*i**3 - 532*i + 3. Factor q(v).
-4*v*(v - 2)*(v - 1)*(v + 42)
Determine a, given that 3*a**5 + 7344/5*a + 864/5 + 302/5*a**4 + 6768/5*a**2 + 440*a**3 = 0.
-6, -2, -2/15
Let a = 759/124 - 182/31. Let d(y) be the third derivative of -5*y**2 + 3/40*y**5 - 1/40*y**6 - a*y**3 + 0*y**4 + 0 + 0*y. Suppose d(k) = 0. Calculate k.
-1/2, 1
Let f be 10/(-3)*36/(-20). Solve -41*o**2 + 6 - 29*o - f*o**5 + 9*o**4 + 20*o + 26*o**2 + 15*o**3 = 0.
-1, 1/2, 1, 2
Let u(h) be the second derivative of 25*h + 0*h**2 - 1/6*h**6 + 2*h**5 - 65/12*h**4 + 2 + 5*h**3. What is a in u(a) = 0?
0, 1, 6
Let u(v) be the third derivative of -v**5/15 - 50*v**4 - 598*v**3/3 - v**2 - 54*v + 1. Suppose u(a) = 0. What is a?
-299, -1
Let c(z) be the third derivative of z**8/252 - 4*z**7/315 - 2*z**6/45 + 8*z**5/45 - z**2 - 365. Determine a, given that c(a) = 0.
-2, 0, 2
Let z(n) be the first derivative of n**4 - 200*n**3/3 + 1400*n**2 - 12000*n - 105. Find p such that z(p) = 0.
10, 30
Let z(c) be the third derivative of c**6/540 - 4*c**5/135 + 19*c**4/108 - 4*c**3/9 - 1099*c**2. Let z(f) = 0. Calculate f.
1, 3, 4
Let f(t) be the first derivative of -108/7*t - 18/7*t**2 - 3/35*t**5 + 11/7*t**3 + 82 + 3/14*t**4. Factor f(g).
-3*(g - 3)**2*(g + 2)**2/7
Solve 4*i**4 - 993*i**2 + 1821*i**5 + 989*i**2 - 1822*i**5 + 3*i - 2*i**3 = 0.
-1, 0, 1, 3
Suppose 14*o = 30 - 2. What is g in -15*g**o - 9133*g + 45 + 9003*g + 0 = 0?
-9, 1/3
Let i(x) be the second derivative of -2*x - 16*x**3 - 23 + 1/3*x**4 - 50*x**2. What is s in i(s) = 0?
-1, 25
Factor -65098*m + 146*m**2 + 187627*m + 5*m**3 + 5049*m**2 + 1076889*m + 152577*m + 1346805.
5*(m + 1)*(m + 519)**2
Let k(n) be the first derivative of 0*n + 10/7*n**4 + 40 - 4/7*n**3 - 2/7*n**2. Solve k(s) = 0 for s.
-1/5, 0, 1/2
Suppose 103684 + 163801*i**2 + 297347*i**5 + 312340*i - 81795*i**2 + 232914*i**2 + 107560*i**3 - 297343*i**5 + 1300*i**4 = 0. What is i?
-161, -1
Let c(o) be the second derivative of -o - 3/28*o**4 + 0*o**2 - 1/30*o**6 + 1/42*o**3 + 3/28*o**5 + 13. Factor c(f).
-f*(f - 1)**2*(7*f - 1)/7
Suppose 32*b - 208/3 + 160/3*b**2 - 1/3*b**5 - 20/3*b**3 - 9*b**4 = 0. What is b?
-26, -2, 1, 2
Let h = -105801/4 - -26457. Find w such that -21/4*w**4 + 2*w**5 - 1/4*w**3 - 7/4*w + h*w**2 - 3/2 = 0.
-1, -3/8, 1, 2
Let u = 492 + -247. Factor -70*r**2 - u*r + 5*r**3 + 7*r**3 - 17*r**3.
-5*r*(r + 7)**2
Suppose -68*n + 3612 + 20020 = 4660. Suppose -2*s - 2*s + 20 = 0. Find z such that -z**2 + s*z + n - 289 - 5*z**3 + 11*z**2 = 0.
-1, 1, 2
Let l = 27 - 24. Suppose 2*q = l + 7. Factor q*p**2 - 9*p + 0 + 0 - 5*p**3 + 19*p.
-5*p*(p - 2)*(p + 1)
Let g(h) be the first derivative of -16/3*h + 0*h**2 - 14 + 4/9*h**3. Suppose g(m) = 0. Calculate m.
-2, 2
Factor 1/7*p**2 + 14400/7 + 240/7*p.
(p + 120)**2/7
Let m = -26 - -36. Suppose -m*c = -9*c - 5*f - 13, 0 = f + 2. Factor -45*w**2 - 24*w**3 + 8 + c*w + 7 + 47*w + 4*w**3.
-5*(w - 1)*(w + 3)*(4*w + 1)
Let k(j) be the first derivative of 5*j**4/4 - 8375*j**3/3 + 3511215*j**2/2 - 3502845*j - 10070. Factor k(n).
5*(n - 837)**2*(n - 1)
Let q(t) = 2137*t + 252168. Let j be q(-118). Factor 2/19*c**j - 14/19*c - 60/19.
2*(c - 10)*(c + 3)/19
Let q(p) = 152*p**3 + 4*p**2 - 7*p + 4. Let g be q(1). Suppose 7*y + 132 = g. Factor -1/4*v**y - 3/4*v**2 - 3/4*v - 1/4.
-(v + 1)**3/4
Determine l, given that 748 - 748*l**2 - l**3 - 451233*l - 3*l**3 + 451237*l = 0.
-187, -1, 1
Let n(g) = -5*g**3 + 28*g**2 - 64*g. Let r(v) = 7*v**3 - 29*v**2 + 65*v. Let y(t) = 5*n(t) + 4*r(t). Suppose y(o) = 0. Calculate o.
-10, 0, 2
Suppose -3*n = 3*q - 15, 5*q + 0 + 5 = 5*n. Determine j so that 543 + 32*j**2 + 8*j**3 - 559 - 4*j**5 - n*j - j - 16*j**4 = 0.
-4, -1, 1
Suppose 0 = 5*d - 4*x - 100, -3*d + 15 = 4*x - 45. Let j(t) = 2*t**2 - 39*t - 20. Let o be j(d). Let -5/4*q**3 + 5*q**2 + o + 0*q = 0. What is q?
0, 4
Let m(v) be the first derivative of 2*v**3/15 - 217*v**2/5 + 3344*v/5 - 2896. Find f, given that m(f) = 0.
8, 209
Let d(m) be the first derivative of -m**5 - 35/2*m**2 - 55 + 0*m + 35/4*m**4 + 5/3*m**3. Factor d(a).
-5*a*(a - 7)*(a - 1)*(a + 1)
Let n = 354 - 97. Let x = n - 2311/9. Find i, given that 0*i + 0 - x*i**3 + 0*i**2 = 0.
0
Let l(k) be the second derivative of -k**5/180 - 37*k**4/54 + 77*k**3/54 + 25*k**2/3 - 1944*k. Factor l(w).
-(w - 2)*(w + 1)*(w + 75)/9
Let r(n) = -53*n - 2912. Let q be r(-55). Suppose -96/7 - 634/7*a**q - 108/7*a**4 - 568/7*a + 2*a**5 - 984/7*a**2 = 0. What is a?
-2, -1, -2/7, 12
Let i(u) = u + 19. Let x(j) = -j**2 - 17*j + 8. Let g be x(-18). Let k be i(g). Determine m so that -24 - 18*m**2 + 7*m**3 + 5*m**3 - k*m**3 + 36*m = 0.
2
Let s be 4/12 - (-58)/6. Let z = 206 + -203. Factor 36*d**2 - 3*d**5 + 18*d**4 + z*d**3 - 42*d**3 + 0*d**3 - s*d - 2*d.
-3*d*(d - 2)**2*(d - 1)**2
Let w be (-2)/((-32)/116) - 2 - (298 - 294). Factor 0 + 5/4*x**2 - w*x.
5*x*(x - 1)/4
Factor 25 + 81/2*p**2 + 347/6*p - 1/6*p**4 + 15/2*p**3.
-(p - 50)*(p + 1)**2*(p + 3)/6
Let f(z) be the second derivative of 2/25*z**5 + 2/15*z**4 + 0*z**2 - 1/75*z**6 + 0 + 0*z**3 - 1/105*z**7 - 15*z. Determine g, given that f(g) = 0.
-2, -1, 0, 2
Let a = 5066 - 15325/3. Let z = 45 + a. Find o, given that -1/3*o**3 + 4/3 - z*o + 5/3*o**2 = 0.
1, 2
Let j(t) be the third derivative of 0 + 1/180*t**6 + 15*t**2 + 0*t + 0*t**3 + 0*t**5 + 1/630*t**7 + 0*t**4. Find r, given that j(r) = 0.
-2, 0
Let 22/5*s - 57/5*s**5 + 629/5*s**2 - 629/5*s**4 + 0 + 7*s**3 = 0. What is s?
-11, -1, -2/57, 0, 1
Let j = 94 + -90. Factor -169 + 87 + 6*o - 6*o**3 - 3*o**j + 85.
-3*(o - 1)*(o + 1)**3
Suppose -8 = 11*p - 294. Let -j**2 + p*j - 95 - 47 - 27 = 0. What is j?
13
Let r(a) be the first derivative of 4*a**2 - 18 + 0*a + 40*a**3 - 99/2*a**4. Determine i so that r(i) = 0.
-2/33, 0, 2/3
Let v be (-1 - 120/(-126))*(-5 - 1). Let -4/21 + 2/21*x**4 + 2/21*x**2 - 2/7*x + v*x**3 = 0. Calculate x.
-2, -1, 1
Let u(w) be the third derivative of w**6/24 + 77*w**5/12 - 65*w**4/4 + 2756*w**2. Suppose u(i) = 0. What is i?
-78, 0, 1
Let v(s) be the third derivative of s**6/80 - 29*s**5/40 + 7*s**4/4 + 11*s**2 - 60. Solve v(c) = 0 for c.
0, 1, 28
Let w = 366 + -316. Determine v, given that -4*v**2 + w*v - 6*v**2 + 8*v**2 + 52 = 0.
-1, 26
Let f(t) = t**3 - 20*t**2 + 41*t - 22. Let w be 30/(-40)*(-12)/(-9). Let d(k) = -k**2 + 1. Let l(v) = w*f(v) + 4*d(v). Factor l(x).
-(x - 13)*(x - 2)*(x - 1)
Suppose 6 - 1/4*w**5 - 13/2*w**4 + 49/4*w - 12*w**3 + 1/2*w**2 = 0. What is w?
-24, -1, 1
Suppose -74*h**3 + 16 + 252*h**2 + 68*h**4 + 104*h + 330*h**2 - 650*h**2 - 14*h**5 = 0. Calculate h.
-1, -1/7, 2
Let k be (1162/(-84) - -6) + 3 + 5. Let r(l) be the second derivative of 0*l**2 - l**3 - k*l**4 - 24*l + 0. Suppose r(g) = 0. Calculate g.
-3, 0
Let m(c) be the second derivative of 3*c**5/100 - 11*c**4/2 + 212*c**3/5 + 1182*c. Determine p, given that m(p) = 0.
0, 4, 106
Suppose 19*i = -5*i + 24. Factor -5 + 3 - i + g**2 + 2.
(g - 1)*(g + 1)
Let k(j) = 11*j**2 - 27*j + 45. Let h = -167 - -163. Let o(l) = -5*l**2 + 13*l - 22. Let d(x) = h*k(x) - 9*o(x). Factor d(w).
(w - 6)*(w - 3)
Factor 674*a**3 + 3*a**5 - 1421*a**3 + 12*a**4 + 699*a**3 - 3*a**4 + 36*a**2.
3*a**2*(a - 2)*(a - 1)*(a + 6)
Factor -2/15*l**3 - 552/5*l**2 - 1652/15 - 1102/5*l.
-2*(l + 1)**2*(l + 826)/15
Let f = 336 - 877. Let l = f + 3803/7. Factor 16/7*o**3 + 1/7*o**5 + o**4 - l - 16/7*o + 8/7*o**2.
(o - 1)*(o + 2)**4/7
Factor -46/3*b - 56 - 1/3*b**2.
-(b + 4)*(b + 42)/3
Suppose -72 = -4*g - 108. Let l(o) = -o**2 + 27*o + 328. Let i be l(g). Determine c so that 4/7*c**2 - 4/7*c + 0 - 4/7*c**i + 4/7*c**3 = 0.
-1, 0, 1
Let w(v) be the third derivative of -3*v**6/10 + 416*v**5/5 - 175525*v**4/24 + 170569*v**3/6 - 7241*v**2. Let w(k) = 0. What is k?
1, 413/6
Let z be (-9)/(-90)*(-9 - (-1400)/152). Let x(n) be the first derivative of z*n**5 + 0*n**2 + 6 + 1/57*n**6 - 1/19*n**4 + 0*n**3 + 0*n. Factor x(m).
2*m**3*(m - 1)*(m + 2)/19
Let x(s) be the second derivative of -7*s**6/150 + 3*s**5/4 + 41*s**4/30 + 43*s + 11. Factor x(l).
-l**2*(l + 1)*(7*l - 82)/5
Let q = 82 + -74. Let z be 5 - q - 10/(-2). Factor -43*g + 192 + 3*g**z + 13*g - 18*g.
3*(g - 8)**2
Let c be (-14*(