j - 2)/7
Let v = -50/417 - -63/139. Let a(c) be the first derivative of -2/9*c**3 - v*c**4 + 16 + 2*c + 4/3*c**2. Factor a(m).
-2*(m + 1)**2*(2*m - 3)/3
Suppose 10*i = 32 - 2. Let 8*q**2 - 6*q**3 - 3*q**4 + 12*q**5 - 13*q**4 - q**3 - 13*q**i = 0. Calculate q.
-1, 0, 1/3, 2
Suppose 20*n - 16*n + 16 = 0, -3*s + 170921 = -2*n. Factor 12*r**3 + 5*r**4 - 25*r**4 - s*r**2 + 16*r + 57019*r**2.
-4*r*(r - 2)*(r + 1)*(5*r + 2)
Let v(d) = d**2 + 144*d - 1869. Let f be v(12). Solve -1/2*h**f + 3 - 2*h**2 - 1/2*h = 0.
-3, -2, 1
Let l(o) = o**3 - 11*o**2 + 24*o. Let t be -4*(-10)/40 - (-8 + 1). Let d be l(t). Find u such that -1/2*u**5 + 0*u + 0 + 1/2*u**3 + d*u**4 + 0*u**2 = 0.
-1, 0, 1
Let m(g) be the first derivative of 16/5*g**2 + 12/25*g**5 - 35 + 1/10*g**4 + 1/15*g**6 + 0*g - 16/5*g**3. Solve m(d) = 0 for d.
-4, 0, 1
Let f = -6/2227 + 4580/46767. Let y(s) be the first derivative of 0*s + 0*s**2 - 1/14*s**4 - 11 + 2/7*s**5 - f*s**3 - 1/7*s**6. Factor y(a).
-2*a**2*(a - 1)**2*(3*a + 1)/7
Let a(i) be the first derivative of 65/2*i**2 - 192 + 180*i + 5/3*i**3. Factor a(j).
5*(j + 4)*(j + 9)
Suppose 48 = -3*n + 7*n. Suppose 3*z - n = 4*d, -2*z + 10 - 2 = -4*d. Find x such that -7*x**3 + 37*x**3 - 10*x + 5*x**2 + 0*x - 15*x**3 - 5*x**5 - 5*x**z = 0.
-2, -1, 0, 1
Find c such that 978/11 + 332/11*c + 2/11*c**2 = 0.
-163, -3
Let r(j) be the second derivative of 1/30*j**4 + 12/5*j**3 + 0 + 159*j - 37/5*j**2. Factor r(d).
2*(d - 1)*(d + 37)/5
Factor 0 - 2/21*g**2 + 124/21*g.
-2*g*(g - 62)/21
Factor 25*t**2 - 2232*t - 4826809 - 142*t**2 + t**3 - 102*t**2 - 288*t**2 + 87915*t.
(t - 169)**3
Let c be 1 - (0 + 24 - -4). Let m be 0*((-6)/c + 76/(-180)). Determine j, given that 5/3*j**2 + m - 10/3*j = 0.
0, 2
Let w(a) = -a**3 + 6*a**2 + 4*a - 5. Let r be w(6). Suppose u + 14 = r. Determine x so that 38*x**2 + u*x - 9*x**2 - 15*x**2 - 13*x**2 = 0.
-5, 0
Let b(v) be the second derivative of 89*v + 0 + 0*v**2 - 25/24*v**4 - 5/2*v**3 + 1/8*v**5. Determine q so that b(q) = 0.
-1, 0, 6
Let n(r) = -r + 1. Let b be -1*147/35 + 4/20. Let c(v) = v**3 - 8*v**2 + 4*v + 3. Let l(t) = b*c(t) + 36*n(t). Determine j, given that l(j) = 0.
1, 6
Suppose -68*g + 71*g - 663 = 0. Let h be 1*1/(-5) - g/(-85). Find x, given that -2/5*x**2 - 18/5 + h*x = 0.
3
Let l(j) be the first derivative of -42/5*j**2 - 18/5*j**3 + 3/5*j**5 + 21/20*j**4 - 24/5*j - 5. Solve l(t) = 0.
-2, -1, -2/5, 2
Let u(g) be the third derivative of g**5/150 - 37*g**4/10 - 904*g**3/15 + 5*g**2 + 77. Factor u(y).
2*(y - 226)*(y + 4)/5
Let p(q) be the second derivative of -q**7/315 - 143*q**6/225 - 1128*q**5/25 - 1152*q**4 + 12288*q**3/5 - 214*q + 2. Factor p(w).
-2*w*(w - 1)*(w + 48)**3/15
Let q(v) be the first derivative of -5*v**3/6 - 120*v**2 - 475*v/2 - 2069. Factor q(o).
-5*(o + 1)*(o + 95)/2
Suppose 5*n - 50 = -5*v, n - 4 - 1 = 0. Suppose v*j = -5*a + 50 - 25, -a = 4*j - 5. Factor 2/5*q**a - 6/5*q**3 + 0 + 0*q + 4/5*q**2 + 0*q**4.
2*q**2*(q - 1)**2*(q + 2)/5
Let f = -1012868/9 - -112541. What is x in 1/9*x**3 - 1/9*x**4 + 0 + f*x**2 - 1/9*x = 0?
-1, 0, 1
Let w be 1*(4 + -5) - 89/(-1). Determine s, given that 39 + 41*s**3 - s**3 + 11 + w*s**2 + 58 + 216*s + 56*s**2 + 4*s**4 = 0.
-3, -1
Let z = -26/339 + 295/2373. Let u(t) be the second derivative of 0*t**2 + 4/21*t**3 - 18*t + 0 - z*t**4. Factor u(x).
-4*x*(x - 2)/7
Let s(w) be the first derivative of -36*w**5/5 + 52*w**4 + 208*w**3 + 64*w**2 + 1446. Find h such that s(h) = 0.
-2, -2/9, 0, 8
Factor 2/5*c**4 - 4/5*c**2 + 0*c**3 + 0*c + 2/5.
2*(c - 1)**2*(c + 1)**2/5
Factor 9/5*w - 319/10 + 1/10*w**2.
(w - 11)*(w + 29)/10
Let 10*f - 4/5*f**4 + 151/5*f**2 + 0 - 197/5*f**3 = 0. Calculate f.
-50, -1/4, 0, 1
Suppose 2/5 + 23/5*h**3 - 2/5*h**2 - 23/5*h = 0. Calculate h.
-1, 2/23, 1
Let -1936/7*b + 481/7*b**2 + 1/7*b**3 + 1940/7 = 0. Calculate b.
-485, 2
Let k be 1/(-4) - 13/((-780)/13815). Find n such that 52*n**3 - 2*n**4 + n**4 + 26*n**2 + 368*n + 5*n**4 + k + 190*n**2 - 6 = 0.
-7, -2
Suppose 30 = -4*h - 2. Let k be ((-6)/h)/(2/8). Let 23 + u**3 + 3*u**5 + 17*u**k + 3*u**2 - 21*u - 9*u**2 + 15*u**4 - 32 = 0. What is u?
-3, -1, 1
Let u(l) be the first derivative of -32 - 1/4*l**4 - 33*l + 5/2*l**3 - 6*l**2. Let x(j) be the first derivative of u(j). Suppose x(n) = 0. Calculate n.
1, 4
Let u(k) be the third derivative of -k**5/60 + 15*k**4 + 6211*k**2. Factor u(i).
-i*(i - 360)
Let i = -4805/3 - -1602. Let a(o) be the first derivative of i*o**3 + 9 + 2/5*o + 7/10*o**2. Determine p so that a(p) = 0.
-1, -2/5
Let z be (19 - 1904/49) + 714/34. Factor -z*j + 2/7*j**3 + 0 + 0*j**2.
2*j*(j - 2)*(j + 2)/7
Let z(o) = -o**4 - 3*o**3 + 130*o**2 - 6*o + 12. Let b(g) = g**4 + 4*g**3 - 130*g**2 + 7*g - 14. Let w(p) = 6*b(p) + 7*z(p). Find i such that w(i) = 0.
-10, 0, 13
Let n be (-5)/15 + 7 + (-40)/6. Let o(s) be the second derivative of 11*s + 0*s**3 + 0*s**4 + n + 0*s**5 + 0*s**2 - 1/105*s**6. Factor o(t).
-2*t**4/7
Suppose 8*u + 159 = 263. Let t(s) be the second derivative of -1/42*s**7 - 2/15*s**3 + 11/75*s**6 + 1/3*s**4 - u*s - 33/100*s**5 + 0 + 0*s**2. Solve t(v) = 0.
0, 2/5, 1, 2
Solve 244*a**3 + 3099515*a**2 - 3101375*a**2 + 4*a**4 - 1360 - 609*a + 3581*a = 0.
-68, 1, 5
Solve 84*j + 3*j**5 - 6*j**5 - 27*j**4 + 12*j**4 + 159*j**2 + 184*j**3 - 121*j**3 = 0 for j.
-7, -1, 0, 4
Let f(q) = 2*q**3 + 4*q. Suppose -4*z = 9*z - 39. Let k(y) = 3*y**3 + y**2 + 7*y - 1. Let o(v) = z*k(v) - 5*f(v). Factor o(a).
-(a - 3)*(a - 1)*(a + 1)
Let -5*m**5 + 113*m + 4*m**2 + m**2 - 17*m**4 + 7*m**4 + 5*m**2 - 153*m + 45*m**3 = 0. What is m?
-4, -1, 0, 1, 2
Let a be 12/10*(-200)/(-24). Factor 13 - 49*x - 3 - 123*x**2 - a - 57*x**3 + 3*x**4 - 14*x.
3*x*(x - 21)*(x + 1)**2
Let g(q) = 5*q**3 + 426*q**2 + 10*q - 2. Let w(v) = -15*v**3 - 1276*v**2 - 35*v + 7. Let f(b) = 7*g(b) + 2*w(b). Factor f(m).
5*m**2*(m + 86)
Solve 11 - 7*k**2 + k**3 + 13 - 16 - 4*k + 3*k**3 - k**2 = 0.
-1, 1, 2
Solve -8070 + 2393*y - 15*y**3 - 8483*y**2 + 3498*y**2 + 8985*y**2 + 7052*y = 0.
-3, 2/3, 269
Suppose 3*v = l - 16, -8*v + 9*v = -3*l + 8. Find x such that 0*x**3 + 0*x**2 + 3/7*x**l + 0*x - 1/7*x**5 + 0 = 0.
0, 3
Suppose 4*c = -r + 25, -5*c - 2 = 2*r - 10*c. Suppose 171 = 10*h + r*h. Factor -9/4*z**2 + h*z - 15/4*z**3 - 3.
-3*(z - 1)*(z + 2)*(5*z - 2)/4
Let s(a) = 38195*a**2 + 12590*a - 195. Let p(g) = -4243*g**2 - 1399*g + 22. Let j(k) = 35*p(k) + 4*s(k). Factor j(f).
5*(3*f + 1)*(285*f - 2)
Let k(f) be the second derivative of -f**4/36 - 89*f**3/18 - 15*f + 2. Solve k(z) = 0.
-89, 0
Let x = 11355 - 11352. Let j be 23/(-4) + -5 + 11. Determine m, given that -3/2 - 9/4*m**x - 19/4*m - j*m**4 - 21/4*m**2 = 0.
-6, -1
Suppose 28*m - 26*m = 0. Factor 24*q**3 + 3*q**5 + m*q**2 + 72 - 18*q**4 + 6*q**2 - 60 - 27*q.
3*(q - 4)*(q - 1)**3*(q + 1)
Let u(t) be the second derivative of t**6/10 - 51*t**5/20 - 21*t**4 + 8*t + 13. Let u(s) = 0. Calculate s.
-4, 0, 21
Let w(g) = -9*g**3 - g**2 + 2*g + 2. Let i be w(-1). Suppose -3*p = p - i*p. Factor 1/7*n**5 + 0*n**4 - 2/7*n**2 + 0 + p*n - 3/7*n**3.
n**2*(n - 2)*(n + 1)**2/7
Let t be 43272/132 - (-6)/33. Let m = 332 - t. Factor 0*y**3 + 3/5*y**m + 3/5 + 0*y - 6/5*y**2.
3*(y - 1)**2*(y + 1)**2/5
Factor -2/5*p + 8/5 - p**2 - 1/5*p**3.
-(p - 1)*(p + 2)*(p + 4)/5
Let y(f) be the third derivative of 8 - 4*f**3 + 1/5*f**5 - 4*f**2 + 0*f - 5/12*f**4 - 1/60*f**6. Solve y(l) = 0 for l.
-1, 3, 4
Let g(b) = b**3 + b**2 + b. Let t(c) = -11*c**2 - 7*c**3 - 55*c + 114*c**2 - 13*c**2 + 15 - 3*c**3. Let l(s) = 10*g(s) - t(s). Determine d so that l(d) = 0.
1/2, 3
Let o be (60/25)/(1134/945). Factor -6/11*g**3 + 0*g + 4/11*g**o + 2/11*g**5 + 0*g**4 + 0.
2*g**2*(g - 1)**2*(g + 2)/11
Suppose 138 = 4*y + 5*w, 3*w = -2*y - 0 + 70. Suppose y = 2*f - 24. Factor 8*v**2 - 5*v**3 + f*v**2 + 19*v**2.
-5*v**2*(v - 11)
Let w be 480/280 + (-2)/(-7). Factor -u**3 - 13357 + u**w + 2*u + 13357.
-u*(u - 2)*(u + 1)
Suppose 1078*s - 10 = 7 - 17. Factor 6/5*i**4 + s + 6/5*i**3 + 0*i + 2/5*i**2 + 2/5*i**5.
2*i**2*(i + 1)**3/5
Let r(w) be the second derivative of -w**6/15 - 6*w**5 + 31*w**4/3 + 20*w**3 - 61*w**2 + 4340*w. Factor r(y).
-2*(y - 1)**2*(y + 1)*(y + 61)
Let o be (-6)/4*7112/(-2667). What is l in -5/3*l**2 + 1/3*l**o + 5/3*l**3 + 4/3 - 4/3*l - 1/3*l**5 = 0?
-2, -1, 1, 2
Determine l, given that 116*l**3 + 96*l**3 - 