
Let h = 108 + -105. Let n be -1 + (-3 + 0)*-1. Determine l, given that -11*l**2 + 7*l**3 + 12*l + 59*l**2 - n*l**h + 23*l**3 - 8 = 0.
-1, 2/7
Suppose 58/3 - 2/3*s**2 + 56/3*s = 0. What is s?
-1, 29
Let i(l) be the third derivative of 1/280*l**6 - 13/14*l**3 + 13/140*l**5 - 8 - l**2 + 0*l - 1/56*l**4. Factor i(s).
3*(s - 1)*(s + 1)*(s + 13)/7
Let i(l) = -12*l**2 - 13*l + 14. Let t(g) = -g**2 - g + 1. Let n(f) = -2*i(f) + 22*t(f). Let x be n(2). Solve -x*d**2 + 4*d + 4*d + 5*d**2 + 7*d = 0 for d.
0, 3
Factor 24 - 1/6*b**3 + 70/3*b + 16/3*b**2.
-(b - 36)*(b + 2)**2/6
Let v = 749 + -741. Let m be -4 + 49/14 - (-10)/v. Determine i, given that -m*i + 3/4*i**2 - 9/2 = 0.
-2, 3
Let s(u) = -68*u - 578. Let y(o) be the first derivative of -o**3/3 + 68*o**2 + 1156*o - 5. Let m(d) = 5*s(d) + 2*y(d). Suppose m(n) = 0. What is n?
-17
Let n(x) be the second derivative of -1147/35*x**5 - 29/3*x**6 - 332/21*x**3 - 1387/42*x**4 - 4*x**2 - 97*x + 4/3*x**7 + 0. Let n(k) = 0. What is k?
-1, -2/7, -1/4, 7
Let a = -18/2035 - -28796/34595. Factor -48/17*j**2 - 20/17 + 54/17*j + a*j**3.
2*(j - 1)**2*(7*j - 10)/17
Factor -1/4*l**2 + 89 - 44*l.
-(l - 2)*(l + 178)/4
Factor 31/5 - 32/5*f + 1/5*f**2.
(f - 31)*(f - 1)/5
Let a(s) be the third derivative of s**5/40 + 67*s**4/3 - 179*s**3/3 - 1475*s**2. Suppose a(g) = 0. What is g?
-358, 2/3
Let g(o) be the first derivative of o**4/10 - 172*o**3/15 - 449*o**2/5 - 1092*o/5 + 480. Factor g(n).
2*(n - 91)*(n + 2)*(n + 3)/5
Determine m so that -1/2*m**4 + 84 + 62*m - 19/2*m**3 - 31*m**2 = 0.
-14, -6, -1, 2
Suppose -1530/7*k**2 + 878/7*k**3 + 918/7*k - 218/7*k**4 + 20/7*k**5 + 108/7 = 0. Calculate k.
-1/10, 2, 3
Let s(c) = 13*c**2 - 50*c - 5. Let b(n) = 51*n - 106*n**2 + 212*n**2 + 6 - 121*n**2. Let k(j) = 5*b(j) + 6*s(j). Factor k(w).
3*w*(w - 15)
Let h(l) = l**3 + 2*l**2 - 1. Let a(r) = 5*r**3 - 72*r**2 + 286*r - 213. Let o(k) = -a(k) + 3*h(k). Suppose o(c) = 0. What is c?
1, 3, 35
Solve 402 - 21*k**2 + 8*k**2 - 3*k**2 + 606*k - 326 = 0.
-1/8, 38
Let d(n) = -3*n**3 - 28*n**2 + 188*n - 316. Let a(p) = -5*p**3 - 56*p**2 + 373*p - 633. Let b(u) = 8*a(u) - 14*d(u). Factor b(r).
2*(r - 20)*(r - 4)**2
Suppose -3*t - k - 82 = -99, 0 = 4*t - 2*k - 6. Find h, given that -2/5*h**t + 2/5*h**2 + h**5 - h**3 + 0*h + 0 = 0.
-1, 0, 2/5, 1
Suppose 4*o + 5*r = 2*r + 86, 102 = 4*o - 5*r. Let u = -2 - -4. Find a, given that -7*a - 3 + o*a - 2*a**u - 10*a - a**2 = 0.
1
Let p(f) be the first derivative of f**4/4 + 22*f**3/3 - 26*f + 151. Let j(b) = 2*b**3 + 34*b**2 - 40. Let t(x) = -5*j(x) + 8*p(x). Factor t(d).
-2*(d - 2)**2*(d + 1)
What is n in 3210578/3 + 2/3*n**2 - 5068/3*n = 0?
1267
Let r = 12377/828 - -1408/207. Suppose -r*d + 24*d**3 - 3/2 + 75/2*d**2 = 0. Calculate d.
-2, -1/16, 1/2
Let q(v) be the second derivative of -7/80*v**5 + 1/120*v**6 + 0*v**2 + 0 + 1/168*v**7 - 1/4*v**3 - 13/48*v**4 + 35*v. Factor q(y).
y*(y - 3)*(y + 1)**2*(y + 2)/4
Suppose -5*o - v - 2*v + 25 = 0, 3*v = 4*o + 7. Solve -65 - c**o + 49*c + 6*c**2 - 107*c - 2*c = 0.
-1, 13
Suppose 122*z - 3 = 121*z. Let v be 27/z - 7/1. Factor -2/3*a**v - 4/3*a - 2/3.
-2*(a + 1)**2/3
Determine w, given that -1310*w - 4*w**2 + 2371*w + 2*w**2 - 1215*w + 316 = 0.
-79, 2
Let d(s) = -2*s**2 - 1. Let l be (3 - (-4 - -7)) + -21 + 3. Let u(f) = 11*f**2 + 177*f - 41. Let n(t) = l*d(t) - 2*u(t). Factor n(a).
2*(a - 25)*(7*a - 2)
Suppose -s = 3*s + 3*p - 300, -150 = -2*s - 4*p. Let k = s - 70. Suppose -10*i**3 - 16*i - 4*i**3 + 7*i - 16*i**2 + 0 - i**k - 6*i**4 - 2 = 0. Calculate i.
-2, -1
Let u be 127510/(-27368) + (69/(-33) - -2) - -5. Factor -5/4*l - u - l**2.
-(l + 1)*(4*l + 1)/4
Suppose -711*t - 61*t + 15840 = 284*t. Factor -t - 13/2*u - 1/2*u**2.
-(u + 3)*(u + 10)/2
Suppose -q - 3435 + 79 = -5*p, -4*q + 3376 = 5*p. Let b be p/(-40) + 6 - -11. Factor -m + b*m**2 - 6/5.
(m - 6)*(m + 1)/5
Let o(f) = -15*f + 32. Let t be o(2). Suppose p - 10 = -t*h, p + 2*p - 5*h = -14. Factor 1/2*c + 0 - c**p - 5/8*c**3.
-c*(c + 2)*(5*c - 2)/8
Suppose 0 = -5*k + 4*d + 113, 4*k + 2*d = 4*d + 88. Let -35*t**3 - 25*t + 39*t**2 + 16*t**2 - 16*t**4 + k*t**4 = 0. Calculate t.
0, 1, 5
Let z = -17276/43 + 402. Let c = 2014/215 + z. Factor -2/5*x**4 - 64/5*x - 32/5 - c*x**2 - 16/5*x**3.
-2*(x + 2)**4/5
Suppose -15*i + 180 = 30. Suppose -1077*x - i*x**2 - 3*x**3 - 44*x**2 - 1084*x + 2110*x = 0. What is x?
-17, -1, 0
Let f be ((-104)/36 - -4)*30/300. Let g be 22/(-45) - 36/(-60). Suppose g*t**3 + 2/9 - 2/9*t**2 - f*t = 0. What is t?
-1, 1, 2
Let f = -66 - -75. Suppose 0 = -f*n + 23 + 4. Solve u**n - 26*u**2 - 4 - 5*u + 27*u**2 + u = 0.
-2, -1, 2
Let s(y) be the third derivative of -2*y**7/105 - 13*y**6/60 - 2*y**5/15 + 13*y**4/12 + 2*y**3 + 9*y**2 - 18. Solve s(p) = 0.
-6, -1, -1/2, 1
Suppose -136*y + 51*y = 0. Let n(v) = v**2 - 12*v + 14. Let f be n(11). Solve y - 2/3*r**4 - 2/3*r**f + 0*r + 4*r**2 = 0 for r.
-3, 0, 2
Let h(g) be the second derivative of -g + 1/42*g**7 + 0*g**2 + 783/20*g**5 - 28/15*g**6 - 392/3*g**3 + 14/3*g**4 - 98. Let h(u) = 0. Calculate u.
-1, 0, 1, 28
Let r be 944/240 + (-4)/(-60). Suppose -228*t**5 - 4*t**3 + 226*t**5 + 2*t**r + 8*t**3 = 0. What is t?
-1, 0, 2
Suppose -o = 39 - 339. Suppose 3*x = -2*x + o. Factor q**5 - 32*q**3 + 4*q**5 + 40 - x*q + 0 + 87*q**3 - 30*q**4 - 10*q**2.
5*(q - 2)**3*(q - 1)*(q + 1)
Let c(b) = -48*b - 323. Let a be c(-8). Suppose -a = -24*o - 61. Factor -2*u**2 + o - 2/3*u - 2*u**3 - 2/3*u**4.
-2*u*(u + 1)**3/3
What is y in -12*y**3 + 100/3*y**2 - 4/3*y**4 + 44*y + 0 = 0?
-11, -1, 0, 3
Let l(j) be the third derivative of j**7/210 - 2*j**6/5 - 33*j**5/20 - 25*j**4/12 - 15*j**2 - 1. Determine y so that l(y) = 0.
-1, 0, 50
Find y such that 448*y**2 - 900 + 4*y**3 - 3*y**3 + y**3 - 23840*y + 23386*y = 0.
-225, -1, 2
Let m(x) be the second derivative of -1/180*x**6 + 25*x + 0*x**2 + 1/15*x**5 - 1/3*x**4 - 25/6*x**3 + 0. Let l(o) be the second derivative of m(o). Factor l(v).
-2*(v - 2)**2
Let y = 442305/358904 + -3/12818. Let f = y - 6/7. Factor -f*b**5 + 3/4*b**2 - 3/8 - 3/8*b**4 - 3/8*b + 3/4*b**3.
-3*(b - 1)**2*(b + 1)**3/8
Let t(m) = m**3 - m - 1. Let i(y) = y - 1. Let o be i(-2). Let v(u) = 2*u**3 - 796 - 36*u**2 - 935 + 47*u - 482*u. Let z(a) = o*t(a) + v(a). Factor z(g).
-(g + 12)**3
Let n be (-2)/4*(-140)/35. Factor 5*k + 5*k**4 - 5*k**n - 112*k**3 + 51*k**3 + 56*k**3.
5*k*(k - 1)**2*(k + 1)
Let l(i) be the first derivative of -i**3/3 - 845*i**2/8 - 211*i/4 - 1110. Factor l(j).
-(j + 211)*(4*j + 1)/4
Let x = 3120837/1783340 - -2/445835. Solve -14*w**2 - 1/8*w**5 + 0 + x*w**4 - 33/8*w**3 - 8*w = 0.
-1, 0, 8
Let t(v) be the second derivative of -v**6/40 - 33*v**5/80 - 17*v**4/8 - 3*v**3 + 3857*v + 1. Find h such that t(h) = 0.
-6, -4, -1, 0
Let c(y) be the third derivative of 0*y**3 + 1/360*y**6 - 4*y + 0 - 1/24*y**4 + 7*y**2 - 1/90*y**5. Factor c(j).
j*(j - 3)*(j + 1)/3
Factor 3/10*v**2 + 93/5 + 281/10*v.
(v + 93)*(3*v + 2)/10
Let t(w) be the third derivative of w**6/300 - 7*w**5/50 + 4*w**4/3 + 84*w**3/5 + 3190*w**2. What is r in t(r) = 0?
-2, 9, 14
Let r(b) be the second derivative of -3*b**5/100 - 41*b**4/4 + b**3/10 + 123*b**2/2 - 2*b + 5107. Factor r(s).
-3*(s - 1)*(s + 1)*(s + 205)/5
Let a(c) = -2*c + 10. Let w = 80 + -76. Let b be a(w). Factor -111*x**2 + 113*x**2 + b + 4*x + 0.
2*(x + 1)**2
Solve 15*h**2 - 1/3*h**3 + 64*h + 196/3 = 0.
-2, 49
Let i = -1015 + 8141/8. Let l(t) = -185*t - 10543. Let z be l(-57). Factor -3/4 + i*q - 15/8*q**z.
-3*(q - 1)*(5*q - 2)/8
Factor 2/11*l**3 - 800/11*l**2 - 796/11 + 1594/11*l.
2*(l - 398)*(l - 1)**2/11
Let l be (0/8)/((-7)/(-7)). Determine q, given that 0*q - 6*q**4 - 3/4*q**5 - 12*q**3 + 0 + l*q**2 = 0.
-4, 0
Let x be (5/(-6))/1*23/((-5980)/624). Solve -2*f - 7/3 + 1/3*f**x = 0.
-1, 7
Suppose 2/7*c**2 - 2924/7 + 2922/7*c = 0. Calculate c.
-1462, 1
Suppose -2*o + 4*d + 16 = -6, 19 = 2*o - 3*d. Suppose r + 21 = 4*w + 6*r, -o*w = 2*r - 22. Factor 2/7*a**w + 2/7*a - 4/7*a**3 + 2/7 - 4/7*a**2 + 2/7*a**5.
2*(a - 1)**2*(a + 1)**3/7
Let f be 24/(-28)*175/195*-1. What is l in -f*l**2 + 0 + 0*l - 2/13*l**3 = 0?
-5, 0
Let l(h) = -807*h - 2 - 2 + 806*h - h**2 + 6. Let d(c) = -5*c**2 + 5*c - 10. Let p(f) = 5*d(f) - 20*l(f). Let p(a) = 0. What is a?
3, 6
Let y(s) = -4*s**4 + 626*s**3 - 4294*s**2 + 9094*s - 5436. Let o(g) = 3*g*