
-(i + 1)*(i + 22)/3
Factor 1/4*n**2 - 99 - 49*n.
(n - 198)*(n + 2)/4
Let k be 1/(-5)*(0 + -2). Let g be (-17618)/(-766) - (-1 + 22). Let 0 - k*r**g + 6/5*r = 0. What is r?
0, 3
Factor -32*s + 2/3*s**3 + 104/3 + 6*s**2.
2*(s - 2)**2*(s + 13)/3
Factor 32*g - 8*g**3 + 0*g**2 + 117 + 37*g + 7*g**3 - 3*g**2 + 10*g**2.
-(g - 13)*(g + 3)**2
Let r be (-1)/(-4) - (-45)/12. Let s(h) = 3 - r + 0 - h**2. Let w(f) = -f**3 + 2*f**2 - f + 4. Let d(p) = 4*s(p) + w(p). What is k in d(k) = 0?
-1, 0
Suppose -3*o - 84 = -4*w, -42 = -2*w + 2*o - 3*o. Suppose -33*v = -w - 45. Find a such that 1/2*a - 1/2*a**v + 0 = 0.
0, 1
Let x(a) = -24*a + 72. Let u be x(3). Let l be (-30)/12*(2 - 4) - u. Factor -8/11*b**4 + 10/11*b**3 - 4/11*b**2 + 2/11*b**l + 0*b + 0.
2*b**2*(b - 2)*(b - 1)**2/11
Find m, given that 168/5 + 2/5*m**2 - 8*m = 0.
6, 14
Find l, given that 12/5*l**4 - 18/5*l**3 - 2/5*l**5 + 0 + 24/5*l - 8/5*l**2 = 0.
-1, 0, 2, 3
Let w(f) be the second derivative of 1/36*f**4 - 1/180*f**5 + 5*f - 1/270*f**6 + 1/9*f**2 + 1 + 5/54*f**3. Factor w(a).
-(a - 2)*(a + 1)**3/9
Suppose -4*s - 77 = -52 - 37. Let l(n) be the first derivative of 0*n - 1/12*n**4 + 1/18*n**s - 3 - 1/30*n**5 + 1/6*n**2. Factor l(g).
-g*(g - 1)*(g + 1)*(g + 2)/6
Suppose -208/3*i - 68*i**3 + 2/3*i**4 - 138*i**2 + 0 = 0. Calculate i.
-1, 0, 104
Let g(w) = -11*w - 106. Let q be g(-10). Factor 9*h**q + 8*h**3 + 0*h**3 - 28*h - 56*h**3 - 20*h + 9 + 78*h**2.
3*(h - 3)*(h - 1)**2*(3*h - 1)
Determine b so that 4/5*b**2 + 716/5 + 144*b = 0.
-179, -1
Let w(k) be the first derivative of 5*k**3 - 1371*k**2/2 + 546*k - 1362. Suppose w(i) = 0. Calculate i.
2/5, 91
Let n(k) = -9*k**2 - 1913*k - 1922. Let a(g) = 160*g**2 + 32520*g + 32675. Let l(i) = -2*a(i) - 35*n(i). Factor l(c).
-5*(c - 384)*(c + 1)
Let j(r) = -2*r**2 - 9*r - 6. Let v be j(-3). What is l in 8640 + 0*l**v - 5*l**3 - 817*l + 180*l**2 - 1343*l = 0?
12
Let s = -23676 - -23681. Let d(n) be the first derivative of 20/3*n**3 - 8/3*n**6 - 32/5*n**s + 0*n - 41 - 4*n**2 + 3*n**4. Determine q, given that d(q) = 0.
-2, -1, 0, 1/2
Let l = 1285 - 605. Factor -l*k**3 - k**5 + 0*k**4 + 686*k**3 + 0*k**5 + k**4.
-k**3*(k - 3)*(k + 2)
Let w = -278178/7 - -39740. Factor -2/7*x + 0 + 2/7*x**3 - w*x**2 + 2/7*x**4.
2*x*(x - 1)*(x + 1)**2/7
Let h(k) be the first derivative of -228 - 52*k**3 + 256*k - 5/2*k**4 - 288*k**2. Factor h(w).
-2*(w + 8)**2*(5*w - 2)
Let d = 4103/9 + -28577/63. Solve d - 6/7*v**2 + 46/7*v = 0.
-1/3, 8
Let m be (6/8)/((-2)/(-8)). Suppose 0 = -954*r + 2726*r + 1349*r. Let -2/3*t**2 + r*t - t**4 - 7/3*t**m + 0 = 0. What is t?
-2, -1/3, 0
Let f = 5/4718 - -4535/17980298. Let g = f - -487733/57165. Factor g + 2/15*x**2 - 32/15*x.
2*(x - 8)**2/15
Let p(t) = t**3 + 3*t**2 - 2*t - 6. Let i = 247 + -250. Let k be p(i). Factor 0*v**2 + k*v + 3/4*v**5 + 0*v**3 + 3/2*v**4 + 0.
3*v**4*(v + 2)/4
Let a(l) = 2529*l + 17705. Let y be a(-7). Determine c so that 0 + 0*c**y + 1/3*c**5 + 1/3*c - 2/3*c**3 + 0*c**4 = 0.
-1, 0, 1
Factor -598/9 + 49/9*b - 1/9*b**2.
-(b - 26)*(b - 23)/9
Let z be 13/6 - (5 + 984/(-144)). Factor 0 + 8/7*l**2 + 24/7*l + 2/7*l**z - 2*l**3.
2*l*(l - 6)*(l - 2)*(l + 1)/7
Suppose 4*h + 1680 = 432. Let j be (-9)/h*12 - (-14)/91. Let 0*m**3 + 0 - j*m**4 + m + 3/2*m**2 = 0. Calculate m.
-1, 0, 2
Factor -1045*d**2 - 1057*d**2 - 33*d**3 - 3*d**4 + 2057*d**2 + 81*d.
-3*d*(d - 1)*(d + 3)*(d + 9)
Let t be -3 + (-4)/(12/(-15)). Determine k so that -159*k**t - 62*k**3 + 8*k - 76*k**4 + 175*k**2 + 6*k**4 = 0.
-1, -2/7, 0, 2/5
Let b(y) be the third derivative of 0*y - 24/25*y**5 + 289/30*y**3 + 0 - 1/1050*y**7 + 17/60*y**4 + 92*y**2 - 17/300*y**6. Factor b(p).
-(p - 1)*(p + 1)*(p + 17)**2/5
Let j(r) be the second derivative of r**4/4 - 1493*r**3/10 - 897*r**2/5 + 5024*r + 2. Determine f so that j(f) = 0.
-2/5, 299
Let g(t) be the first derivative of -t**5/20 - t**4/3 - t**3/2 + 43*t - 44. Let y(d) be the first derivative of g(d). What is j in y(j) = 0?
-3, -1, 0
Let p(x) = x**3 + 4*x**2 - 7*x + 5. Let c be p(4). Suppose -c = -0*w - w + 5*z, -5*w = -2*z - 433. Factor -g**2 - 79*g - 3*g**3 + 4*g**2 + w*g.
-3*g*(g - 2)*(g + 1)
Let z(y) be the first derivative of 3*y**4/16 + 5*y**3/4 - 4223. Factor z(r).
3*r**2*(r + 5)/4
Let c(f) be the second derivative of 5*f**4/16 + 57*f**3/8 + 105*f**2/4 - 2300*f. Factor c(s).
3*(s + 10)*(5*s + 7)/4
Suppose -159/5*d**2 + 0 - 3/5*d**3 + 0*d = 0. Calculate d.
-53, 0
Let c(w) be the second derivative of -4*w + 10/51*w**3 + 29/102*w**4 + 7 + 0*w**2 - 1/357*w**7 + 27/170*w**5 + 7/255*w**6. Factor c(v).
-2*v*(v - 10)*(v + 1)**3/17
Let l(v) = -4*v + 1 + 3*v**2 - 2*v**2 + v**3 + 2*v + 4. Let f be l(-2). Factor -3 - f - 4*u + 5*u**2 + 5 + 2*u**3.
(u - 1)*(u + 3)*(2*u + 1)
Suppose 2*f + 4*z = 12, -8 = -2*f + 4*z - 12. Factor 30*j + 486 - 453 - 4*j**2 + j**f.
-3*(j - 11)*(j + 1)
Let i(d) be the third derivative of d**6/60 - 2*d**5/5 - 13*d**4/12 - d**2 - 2002*d. Factor i(o).
2*o*(o - 13)*(o + 1)
Suppose 0 = 2*b + 6, -5*b + 152 = 5*f - 28. Let d = f - 35. Solve 2 + 0 - 17*x**4 - 16*x**4 - 4*x**2 + 35*x**d = 0.
-1, 1
Let x(c) be the third derivative of -c**7/1260 + c**6/12 + c**5/120 - 89*c**4/72 - 10*c**3/3 - c**2 - 656*c. Find h such that x(h) = 0.
-1, 2, 60
Solve -64*w**3 + 62/3*w**4 - 2/3*w**5 - 712/3*w**2 + 1600/3*w + 1152 = 0.
-2, 4, 27
Factor 832 - 240*d**3 - 227*d**3 + 964*d**3 - 2932*d**2 - 233*d**3 - 236*d**3 + 2072*d.
4*(d - 104)*(d - 1)*(7*d + 2)
Suppose 157*a - 624 = 41*a - 92*a. Factor -1/5*k**a - 9/5*k**2 + 1/5*k + 9/5.
-(k - 1)*(k + 1)*(k + 9)/5
Let v(w) be the first derivative of 67 + 64/27*w**3 + 20/9*w**2 - 2/3*w. Solve v(l) = 0.
-3/4, 1/8
Let z = 2971/2480 - -1/496. Let s(g) be the second derivative of 4/5*g**3 + 8*g + 0 - 1/4*g**4 - z*g**2 + 3/100*g**5. Let s(f) = 0. Calculate f.
1, 2
Let g(x) = 50*x - 13*x**2 - x**3 + 1 - 30*x - 33*x. Let s be g(-12). Suppose -44*m**2 + 20*m**3 + 16*m + 10*m**4 + s*m**4 - 15*m**4 = 0. Calculate m.
-4, 0, 1/2, 1
Factor 0*j**2 + 6545*j - 5669*j - 95922 - j**2 - j**2.
-2*(j - 219)**2
Let r be (-122 + 1)*((-130)/(-60) + -3). Let a(y) be the third derivative of 0 + 55/12*y**4 + r*y**3 - 7*y**2 + 1/12*y**5 + 0*y. Factor a(k).
5*(k + 11)**2
Let x(k) be the first derivative of 5*k**6/12 - 22*k**5/5 + 39*k**4/40 + 1084*k**3/15 - 85*k**2 + 168*k/5 - 2451. Solve x(r) = 0 for r.
-3, 2/5, 4, 7
Suppose -27 - 112 = -97*q + 96 + 56. Factor 24/5*c**2 + 9*c + 0 + 3/5*c**q.
3*c*(c + 3)*(c + 5)/5
Suppose 0 = 21*a - 24*a - 5*l + 21, 0 = -2*l. Let m be 7/(a - 0) - -1. Factor -2*z**3 - 26/3*z**m - 32/3*z - 8/3.
-2*(z + 2)**2*(3*z + 1)/3
Let 1477/3*j - 1/6*j**2 - 2181529/6 = 0. Calculate j.
1477
Suppose 2*o - 3*t = 28, 33*o + 44 = 38*o - t. Let g be (-1 + -1)/o + 234/520. Factor 6/5 + g*b**3 + 1/5*b - 4/5*b**2.
(b - 3)*(b - 2)*(b + 1)/5
Let a(m) be the second derivative of 4/3*m**3 - 1/30*m**6 - 6*m + 2*m**2 + 1/4*m**4 - 1/10*m**5 + 2. Find c such that a(c) = 0.
-2, -1, 2
Let f(g) be the third derivative of g**5/30 + 47*g**4/4 + 278*g**3/3 + 10*g**2 - 127*g. Factor f(y).
2*(y + 2)*(y + 139)
Let i(y) be the first derivative of -4*y**3/21 + 356*y**2/7 - 4128*y/7 + 9460. Factor i(t).
-4*(t - 172)*(t - 6)/7
Find o such that -2*o**2 + 7/2 + 1/4*o**3 + 5/4*o = 0.
-1, 2, 7
Let t = 1063 + -439. Factor 10 + 2*q**3 + t*q**2 - 599*q**2 - 11*q**3 + q**4 - 27*q.
(q - 5)*(q - 2)*(q - 1)**2
Let y(c) be the third derivative of -c**6/600 - 2407*c**5/100 - 5793649*c**4/40 - 13945313143*c**3/30 - c**2 - 159*c - 2. Determine f so that y(f) = 0.
-2407
Let y(s) be the first derivative of s**8/1848 - s**7/1155 - s**6/660 + s**5/330 - 51*s**2 - 110. Let a(n) be the second derivative of y(n). Solve a(p) = 0.
-1, 0, 1
Let j(b) = 74*b**3 - 10*b**2 - 68*b + 10. Let d(n) = 222*n**3 - 29*n**2 - 205*n + 29. Let y = -697 - -691. Let v(z) = y*d(z) + 17*j(z). Factor v(u).
-2*(u - 1)*(u + 1)*(37*u - 2)
Let l be (-56)/(-539) - ((-18)/(-22) + (-7 - -6)). Factor -l*n**2 + 64/7 + 62/7*n.
-2*(n - 32)*(n + 1)/7
Solve 285*k - 1/5*k**3 + 9/5*k**2 + 16967/5 = 0 for k.
-19, 47
Let g = 882 - 880. Suppose 12513*x - 12491*x + x**g + 48 + x**2 = 0. Calculate x.
-8, -3
Let x = -14091 - -957927/68. Let a = 78/17 + x. Factor 3/8 + 3/8*f**2 + a*f.
3*(f + 1)**2/8
Suppose -2*z + 22 = 12. Find r such that -85 - z*r + 3*r**3 - 20*r**2 + 64 + 41 + 2*r**3 