 1
Let y(o) be the first derivative of -o**5/135 + o**4/27 + 2*o**3/9 + o**2/2 - 99*o + 63. Let i(d) be the second derivative of y(d). Suppose i(l) = 0. What is l?
-1, 3
Let s = -572239/11 + 52025. What is l in -6/11*l + s - 6/11*l**2 = 0?
-3, 2
Factor -4*j**3 - 13*j**5 + 24*j**4 - 42*j + 42*j - 24*j**2 + 17*j**5.
4*j**2*(j - 1)*(j + 1)*(j + 6)
Let b = 68147 - 68145. Factor -1/3*s**b + 1/3*s**3 + 0 + 1/9*s - 1/9*s**4.
-s*(s - 1)**3/9
Suppose -30 - 796 = -4*b - 2*l, -b - 4*l = -196. Let a = -1036/5 + b. Suppose -2/5 - 2/5*v**5 - a*v**3 - 4/5*v**2 + 6/5*v**4 + 6/5*v = 0. What is v?
-1, 1
Suppose 0 = 5*l, 3*t + 4*l - 320 = -2*t. Factor -50*k**3 + 13*k**3 + 402*k**4 - 407*k**4 + 32 - 54*k**2 + t*k.
-(k - 1)*(k + 4)**2*(5*k + 2)
Let y(c) = -c**2 + 11. Let j(i) = -5*i**3 + 289*i**2 - 280*i - 44. Let q(r) = -j(r) - 4*y(r). Let q(g) = 0. What is g?
0, 1, 56
Let l(q) = 5*q**2 - q**2 + 7996 + 13*q - 7995. Let y(n) = -4*n**2 - 3*n - 7*n - 4*n. Let f(k) = 4*l(k) + 3*y(k). Determine r so that f(r) = 0.
-2, -1/2
Let b = -351 + 1182. Let s = -1653/2 + b. Factor 3*q - s - 1/2*q**2.
-(q - 3)**2/2
Suppose 132 = -317*a + 641*a - 280*a. Let b(f) be the first derivative of -1/4*f - 1/4*f**a + 3/8*f**2 + 28 + 1/16*f**4. Factor b(x).
(x - 1)**3/4
Let m = 31694 - 31691. Solve -2 + 1/3*z**4 - 11/3*z - z**2 + z**m = 0 for z.
-3, -1, 2
Suppose 0 = 23*k - 35*k. Suppose -73*n + 56*n + 34 = k. Solve -4/15*r**4 + 28/5*r**3 - 88/15*r**n - 14/15*r**5 + 2/3*r + 4/5 = 0 for r.
-3, -2/7, 1
Let y(k) be the third derivative of k**8/4032 + 11*k**7/315 + 17*k**6/72 + 7*k**5/15 + 539*k**2. Factor y(h).
h**2*(h + 2)**2*(h + 84)/12
Suppose -1318*a = -1376*a. Factor -16*j**3 + 0 + 6*j**4 + 32/3*j**2 - 2/3*j**5 + a*j.
-2*j**2*(j - 4)**2*(j - 1)/3
Let g(x) = 17*x**2 + 3973*x + 788105. Let u(a) = -4*a**2 - a - 20. Let o(r) = g(r) + 3*u(r). Factor o(f).
5*(f + 397)**2
Let i = 2/375021 - -1125049/2625147. Determine k so that -36/7 + i*k + 3/7*k**2 = 0.
-4, 3
Let u = -1314299/300 + 4381. Let o(d) be the third derivative of 30*d**2 + u*d**5 - 1/1050*d**7 + 0*d**3 + 0*d + 0 + 0*d**6 + 0*d**4. Factor o(w).
-w**2*(w - 1)*(w + 1)/5
Let g be (-328)/(-41) + (-8)/2. Factor 11*u**3 - 8*u + 12*u**g - 57*u**5 - 7*u**3 - 12*u**2 + 61*u**5.
4*u*(u - 1)*(u + 1)**2*(u + 2)
Suppose z - 12 - 3 = 0. Suppose 47 = z*q + 47. Factor -2/13*u**3 + 0*u + 4/13*u**4 - 2/13*u**5 + q + 0*u**2.
-2*u**3*(u - 1)**2/13
Let g be (-2 - -15) + ((-8)/10)/((-516)/(-7482)). Factor g*a - 1/5*a**4 + 9/5*a**3 + 0 - 3*a**2.
-a*(a - 7)*(a - 1)**2/5
Let k be (5/4)/(((-750)/(-135))/10). Let 3/4*y**2 + 3/2 + k*y = 0. Calculate y.
-2, -1
Let u = -11161 - -11181. Let p(o) be the second derivative of 1/5*o**5 + u*o + 0 - 1/2*o**4 - 1/33*o**6 - 4/11*o**2 + 20/33*o**3. Let p(t) = 0. Calculate t.
2/5, 1, 2
Factor 80*i - 2000*i**2 - i**3 + 2124*i**2 - 324*i.
-i*(i - 122)*(i - 2)
Let s(r) = -r**3 - r**2 - 6*r - 1. Let a(y) = y**4 + 13*y**3 + 8*y**2 - 2*y - 23. Let j(p) = a(p) + 5*s(p). Find b, given that j(b) = 0.
-7, -2, -1, 2
Let f(y) = 29*y**2 - 2147*y + 249. Let d be f(74). Determine t, given that -d*t**2 - 147*t**3 - 4/3 - 88/3*t = 0.
-1, -2/21
Let u(b) be the first derivative of b**3/4 - 2619*b**2 + 9145548*b + 5864. Factor u(m).
3*(m - 3492)**2/4
Let p = 569 - 566. Find g, given that 31163 - p*g**4 - 48836 - 49152*g - 192*g**3 - 178935 - 4608*g**2 = 0.
-16
Let i = -284592 - -284595. Let -13/6*x**4 - 8/3 + 4*x**2 + 1/2*x**5 - 8/3*x + 4/3*x**i = 0. What is x?
-1, -2/3, 2
Let d(q) = q**2 + 23*q + 31*q - 53*q + 1. Let z(n) = -4*n**2 - 10*n - 3. Let f(g) = 3*d(g) + z(g). Solve f(x) = 0 for x.
-7, 0
Let d(u) = -u**2 + 5*u - 25. Let x(v) = 0 + 3 + v - 3 + 2. Let o(b) = -3*d(b) - 21*x(b). Factor o(l).
3*(l - 11)*(l - 1)
Let g = -186477 + 373109/2. Let g*u**2 - 5/4*u**5 + 65*u - 305/4*u**3 + 20*u**4 - 110 = 0. What is u?
-1, 2, 11
Let m(l) be the third derivative of -l**5/270 - 10*l**4/27 - 175*l**3/27 - l**2 - 133. Solve m(o) = 0.
-35, -5
Find a, given that 18*a - 3/2*a**3 + 3/4*a**4 - 69/4*a**2 + 108 = 0.
-3, 4
Let g = -93 - -97. Let -7*t**2 - 5*t**4 + 0*t**4 + 23*t**2 + 16*t**3 + 18*t**g - 9*t**4 = 0. Calculate t.
-2, 0
Let f(u) = u**3 - 16*u**2 + 51*u - 6. Let a be f(11). Let s be ((-10)/(-55))/(a/(-220)). Determine c so that 1/10*c**3 + 1/5*c - 1/2*c**2 + s = 0.
-1, 2, 4
Let i(r) be the second derivative of r**4/9 + 868*r**3/9 - 3937*r. Suppose i(o) = 0. Calculate o.
-434, 0
Let a = 13693 + -13691. Factor -4*k - 8/5 - 4/5*k**3 - 16/5*k**a.
-4*(k + 1)**2*(k + 2)/5
Suppose -47*y = -43*y - 260. Suppose -y*m**3 + 17*m**2 - 32*m - 6*m**2 + 64*m**3 + 28 = 0. What is m?
2, 7
Suppose -55 = 15*o - 4*o. Let d be ((-66)/(-44))/(o/(-2)). Factor -27/5*c - d*c**2 - 24/5.
-3*(c + 1)*(c + 8)/5
Find y such that -2/13*y**2 + 298/13*y - 876/13 = 0.
3, 146
Let f(x) = -11*x**3 - 38*x**2 + 136*x. Let a(u) = -14*u**3 - 40*u**2 + 134*u. Let g(w) = 4*a(w) - 5*f(w). Find d such that g(d) = 0.
0, 6, 24
Suppose -1 - 4 = 70*v - 5. Let d(u) be the third derivative of 0*u + 1/105*u**7 - 1/15*u**6 + v*u**3 + 1/3*u**4 - 1/30*u**5 + 16*u**2 + 0. Factor d(q).
2*q*(q - 4)*(q - 1)*(q + 1)
Let s(z) be the second derivative of -z**5/70 + 47*z**4/42 - 13*z**3/3 + 45*z**2/7 + 1470*z. Factor s(d).
-2*(d - 45)*(d - 1)**2/7
Let p(k) be the third derivative of 5/8*k**4 + 0*k - 7/12*k**5 + 0*k**3 + 0 + 29*k**2. Suppose p(j) = 0. Calculate j.
0, 3/7
Let h be (-5 - 1 - -11) + -3. Determine y, given that 2*y**h + 0*y**3 - y**3 + 79*y - 80*y = 0.
0, 1
Factor 5/7*h**2 + 152/7 + 194/7*h.
(h + 38)*(5*h + 4)/7
Let c(l) be the second derivative of -l**4/60 - 149*l**3/6 - 372*l**2/5 - 8*l + 244. What is j in c(j) = 0?
-744, -1
Let u(o) = -8*o**3 - 3037*o**2 + 12301*o - 9235. Let s(n) = -3*n**3 - 1012*n**2 + 4101*n - 3080. Let t(i) = -7*s(i) + 2*u(i). Factor t(z).
5*(z - 3)*(z - 1)*(z + 206)
Let f(h) = -36 + h**2 - 31*h + 4*h + 3*h. Let m be f(26). Solve 210*i**2 + 76*i**3 + 9*i**4 - 78*i**2 + i**4 + 84*i + m + 2*i**4 = 0.
-4, -1, -1/3
Determine n, given that -77/4*n**2 + 75/4*n + 1/4*n**4 + 19 - 75/4*n**3 = 0.
-1, 1, 76
Let v(k) be the second derivative of -k**5/600 + k**4/24 + 11*k**3/60 - 8*k**2 + 82*k. Let z(q) be the first derivative of v(q). Determine f so that z(f) = 0.
-1, 11
Let j(s) be the third derivative of -s**6/720 + s**5/30 - 5*s**4/36 - 1009*s**2. Factor j(l).
-l*(l - 10)*(l - 2)/6
Suppose -65*g**3 - 3*g**5 - 3*g + 98*g**3 + 27*g**2 - 51*g - 3*g**4 = 0. What is g?
-3, -2, 0, 1, 3
Factor 18*g**2 - 1920/7*g - 2048/7 - 2/7*g**3.
-2*(g - 32)**2*(g + 1)/7
Let m(x) be the first derivative of 7/15*x**3 + 0*x - 2/5*x**4 + 3/5*x**2 - 1/5*x**5 - 56. Suppose m(u) = 0. What is u?
-2, -3/5, 0, 1
Let u(j) = j**2 - 147*j + 276. Let h(t) = 3*t**2 - 299*t + 551. Let b(d) = 2*h(d) - 5*u(d). Find a such that b(a) = 0.
-139, 2
Let a(n) be the first derivative of 192/5*n + 12/25*n**5 + 4*n**4 + 176/5*n**2 + 736/45*n**3 + 1/45*n**6 + 65. Factor a(r).
2*(r + 2)**3*(r + 6)**2/15
Let j be 2/2 - (-17 + 59 + -43). Let b(s) be the first derivative of -12/5*s - 8/15*s**3 + 11/5*s**j - 1/10*s**4 - 16. Factor b(q).
-2*(q - 1)**2*(q + 6)/5
Let x = -7/10459 + -5156189/146426. Let o = -236/7 - x. Determine b so that 0*b + 0 + 0*b**2 + 0*b**4 - 3/2*b**3 + o*b**5 = 0.
-1, 0, 1
Let c(g) be the third derivative of -g**5/300 + 109*g**4/24 + 547*g**3/15 - 1906*g**2 + 1. What is h in c(h) = 0?
-2, 547
Let y(d) = -6*d**3 - 473*d**2 - 1848*d - 1810. Let g(v) = -2*v**3 - 158*v**2 - 616*v - 604. Let b(w) = 7*g(w) - 2*y(w). Factor b(i).
-2*(i + 2)**2*(i + 76)
Let x(i) be the second derivative of -i**5/10 - 101*i**4/6 - 100*i**3/3 - 2*i + 75. Factor x(w).
-2*w*(w + 1)*(w + 100)
Let r(g) = -5*g**3 + 53*g**2 + 205*g + 163. Let s(d) = -6*d**3 + 54*d**2 + 204*d + 164. Let y(i) = 5*r(i) - 4*s(i). Determine w so that y(w) = 0.
-3, -1, 53
Let g be (-10540)/(-9765) - 4/18. Let r(w) be the first derivative of -9/14*w**2 - 1/7*w**3 - 3/35*w**5 - 6 + g*w + 9/28*w**4. Find h such that r(h) = 0.
-1, 1, 2
Let z(p) be the first derivative of p**3/2 + 321*p**2/2 + 639*p/2 + 5178. Factor z(h).
3*(h + 1)*(h + 213)/2
Factor 2/5*a**3 + 1072/5*a + 146/5*a**2 + 416.
2*(a + 4)**2*(a + 65)/5
Let s(q) = -q**3 + 3*q**2 + 58*q - 171. Let m be s(3). Let y = 16 + -14. Find c such that 9*c**m + 234*c + 6*c**4 - 6 + 3*c**y - 3*c**4 - 243*c = 0.
-2, -1, 1
