ppose 68/3*t - 22/3*t**2 + 2/3*t**3 - 16 = 0. Calculate t.
1, 4, 6
Suppose -6 + 0 = 3*l. Let k(s) = -60*s + 0*s**2 + 10*s - 15 + 23*s**2 - 3*s**2. Let v(x) = -3*x**2 + 7*x + 2. Let f(u) = l*k(u) - 15*v(u). Factor f(n).
5*n*(n - 1)
Let z be 641/(-6) + 14/(-21). Let w = z - -2799/26. Find a, given that -w*a**2 + 0 - 6/13*a = 0.
-3, 0
Let q(i) = -2*i**2 - 10*i - 12. Let c(d) = -5*d - 10*d**2 + 7*d**2 - 13 - 4*d + d**2. Let h(p) = -2*c(p) + 3*q(p). What is o in h(o) = 0?
-5, -1
Let t(i) be the second derivative of -i**4/72 - 2387*i**3/18 - 5697769*i**2/12 - 4321*i. Factor t(s).
-(s + 2387)**2/6
Let w(l) be the third derivative of -l**8/560 + 7*l**7/50 - 741*l**6/200 + 3339*l**5/100 - 1323*l**4/20 + 2616*l**2. What is a in w(a) = 0?
0, 1, 6, 21
Let i = -288 - -297. Determine x so that -9*x**2 + x**2 + 8*x**2 - 3*x**3 - 6 + i*x = 0.
-2, 1
Let y be 0 + (-6 + -2 + 8)/(-4) + 4. Let l(i) be the second derivative of 0 + 65/4*i**y + 35*i + 6*i**2 + 15/2*i**5 + 14*i**3. Factor l(v).
3*(2*v + 1)*(5*v + 2)**2
Let l be 0 - 0 - 14/(-7). Suppose -a = 5, 0 = l*c - 0*a + 4*a - 290. Solve -3*m - 3*m**2 + c - 155 = 0.
-1, 0
Let h(j) be the second derivative of -2*j + 1/294*j**7 - 1/7*j**3 - 3/140*j**5 - 11/84*j**4 + 0*j**2 + 1 + 1/70*j**6. Factor h(g).
g*(g - 2)*(g + 1)**2*(g + 3)/7
Suppose 5*q + 88 = -u - 17, 0 = 2*q + 5*u + 19. Let p be ((-8)/(-6))/(-3 + q/(-6)). Factor -7*l**p + 6*l + 0*l + 5*l**2 + l**2.
-l*(l - 6)
Let m(c) = -3*c**2 + 23*c - 10. Let u be m(7). Factor 312*l**2 + 3*l**5 + 144 + 31*l**4 - 16*l**u + 695*l - 359*l + 18*l**4 + 144*l**3.
3*(l + 2)**4*(l + 3)
Let g be (9 + 382*(-8)/336)*(-34629)/204. Factor -g*c**2 + 16*c + 1/6.
-(c - 1)*(97*c + 1)/6
Let q be (-5 - -8)*(-4)/(-3). Factor q*o**2 + 31 - 15 + 16*o - 4.
4*(o + 1)*(o + 3)
Let r(h) be the first derivative of 2/9*h**2 + 29 + 4/45*h**5 + 1/3*h**4 + 0*h + 4/9*h**3. Factor r(o).
4*o*(o + 1)**3/9
Let l be (155/(-135))/((-60)/585). Let p = l - 43/4. Suppose 10/9*x**3 + 0 - 2*x**2 + 2*x**4 + p*x - 14/9*x**5 = 0. Calculate x.
-1, 0, 2/7, 1
Let f(d) = 57*d + 3729. Let o be f(-65). Let h(y) be the third derivative of 1/96*y**4 + 0 + 0*y - o*y**2 + 1/12*y**3 - 1/240*y**5. Factor h(b).
-(b - 2)*(b + 1)/4
Factor 0 + 1/3*p**4 - 61/3*p**2 - 6*p**3 - 14*p.
p*(p - 21)*(p + 1)*(p + 2)/3
Let n(t) be the first derivative of 0*t + 0*t**3 + 1/660*t**6 + 21 - 11/2*t**2 + 0*t**4 - 2/165*t**5. Let j(y) be the second derivative of n(y). Factor j(i).
2*i**2*(i - 4)/11
Solve 63/5*k**3 + 1021/5*k**2 + 837/5*k - 1922/5 + 1/5*k**4 = 0.
-31, -2, 1
Let h = 25/12 - 139/84. Let l = -229 + 231. Suppose -3/7*w**l - h + 6/7*w = 0. What is w?
1
Let d = 34464/13 + -34452/13. Factor d*c + 2/13*c**2 + 16/13.
2*(c + 2)*(c + 4)/13
Let h(v) be the third derivative of 1/4*v**5 + 0*v**3 + 3 + 1/10*v**7 - 11/40*v**6 - 1/112*v**8 + 13*v**2 + 0*v + 0*v**4. Solve h(q) = 0 for q.
0, 1, 5
Let -132*y**4 - 301*y**3 - 28*y**5 - 322*y**3 + 663*y**3 = 0. What is y?
-5, 0, 2/7
Let q = 1195 - 1182. Suppose -4*u = -4*k - 0*u - 4, u - q = -5*k. Factor -32/9 - 16/3*j - 4/9*j**3 - 8/3*j**k.
-4*(j + 2)**3/9
Let g(l) be the third derivative of 0*l**4 + 0*l**3 + 0*l - 1/120*l**5 + 1/420*l**7 + 1 + 10*l**2 + 0*l**6. Factor g(q).
q**2*(q - 1)*(q + 1)/2
Let p(n) be the third derivative of -n**7/70 + 4*n**6/5 + 67*n**5/20 + 17*n**4/4 - 5*n**2 - 366. Factor p(c).
-3*c*(c - 34)*(c + 1)**2
Let u be 2/4*(-55 - -61). Factor -u*g**2 - 30*g + 42 - 5*g + 9*g + 11*g.
-3*(g - 2)*(g + 7)
Let t(h) be the first derivative of -h**8/6720 - h**7/3360 + h**6/240 + 36*h**3 + 22. Let l(y) be the third derivative of t(y). Factor l(a).
-a**2*(a - 2)*(a + 3)/4
Let j(d) be the first derivative of d**4/102 + d**3/51 - 6*d**2/17 - 25*d - 3. Let m(x) be the first derivative of j(x). Factor m(h).
2*(h - 2)*(h + 3)/17
Let o(b) = 64*b**3 + 195*b**2 + 7*b - 4. Let x be o(-3). Suppose -80 - 16*s - 4/5*s**x = 0. What is s?
-10
Let z(g) be the first derivative of -1/6*g**3 - 1/30*g**5 - 1/6*g**4 + 2/3*g + 1 + 1/3*g**2. Factor z(l).
-(l - 1)*(l + 1)*(l + 2)**2/6
Let n(u) = -5*u**3 + 347*u**2 - 1056*u + 698. Let a(z) = -28*z**3 + 1735*z**2 - 5284*z + 3489. Let v(d) = 6*a(d) - 33*n(d). Let v(o) = 0. What is o?
-350, 1, 2
Factor -108*x - 2*x**3 + x**3 - 13*x**2 - 27 + 69*x + 0.
-(x + 1)*(x + 3)*(x + 9)
Let q(r) be the second derivative of -r + 4/13*r**3 + 0*r**2 - 1/130*r**5 - 10 - 11/78*r**4. Factor q(c).
-2*c*(c - 1)*(c + 12)/13
Let 18*n**2 + 218 + 148*n + 254 + 132*n - 14*n**2 - 196 = 0. What is n?
-69, -1
Let m = 321733/3 + -107244. Factor 8*s - m*s**2 - 23/3.
-(s - 23)*(s - 1)/3
Let h(m) be the second derivative of 1/240*m**5 + 54*m + 1/36*m**4 + 1/24*m**3 + 0*m**2 + 0. Factor h(f).
f*(f + 1)*(f + 3)/12
Let p = -503 - -498. Let g be (p/6)/(34/(-204)). Factor 0*n + 4*n**3 + 6*n**4 + 0 + 8/3*n**g + 2/3*n**2.
2*n**2*(n + 1)**2*(4*n + 1)/3
Suppose 71*z = -342*z - 203*z. Determine j, given that 0*j + z*j**3 - 1/7*j**2 + 0 + 1/7*j**4 = 0.
-1, 0, 1
Suppose -2020 = -16*p + 6*p. Find v such that 109*v**2 - 325*v + 30*v**4 + 82*v**2 + p*v**3 + 20 + 459*v + 177*v**2 - 82*v**2 = 0.
-5, -1, -2/5, -1/3
Let p(x) = 2*x**4 + 242*x**3 + 1404*x**2 + 2776*x + 2092. Let t(m) = 18. Let u(h) = p(h) - 14*t(h). Determine l, given that u(l) = 0.
-115, -2
Let h(m) = -m**2 - 70*m - 1054. Let z be h(-48). Factor 4/9*f**z - 8/3 - 4/9*f.
4*(f - 3)*(f + 2)/9
Suppose -24*z + 68 = -20*z - 4*b, 0 = -2*b + 2. Let o be 11 + (11 - z - 1). Factor 0 + 3/10*i**o + 1/5*i**2 + 1/10*i**4 + 0*i.
i**2*(i + 1)*(i + 2)/10
Let n(r) be the second derivative of 7/15*r**5 + 1/45*r**6 + 8/3*r**4 + 18 - 49/3*r**2 - 14/9*r**3 + r. Determine h, given that n(h) = 0.
-7, -1, 1
Let c(f) = 26*f**2 + 73*f - 521. Let w(i) = -9*i**2 - 24*i + 174. Let h(g) = 6*c(g) + 17*w(g). Factor h(z).
3*(z - 4)*(z + 14)
Let h = 965289 - 965285. Factor -6/7*x**3 + 6/7*x**h + 0*x - 12/7*x**2 + 0.
6*x**2*(x - 2)*(x + 1)/7
Suppose 2*j + 82 = 3*u, u - 1 = -j - 37. Let q = j - -648/17. Factor 0 + 0*c**4 - 2/17*c + 0*c**2 + 4/17*c**3 - q*c**5.
-2*c*(c - 1)**2*(c + 1)**2/17
Let y = 52427/146 + -25958/73. Let 12 - 19*m - 141/2*m**2 - 36*m**3 + y*m**4 = 0. What is m?
-1, 2/7, 12
Let d(i) be the first derivative of -3*i**4/20 + 26*i**3/5 - 138*i**2/5 + 264*i/5 + 575. What is m in d(m) = 0?
2, 22
Let q(a) = 3*a + 48. Let b be q(-15). Solve 43*l + 26*l + b*l**3 - 2 - 4*l**2 + 44 + 34*l**2 = 0.
-7, -2, -1
Let s(r) be the third derivative of 5*r**4 - 3 + 0*r + 10/9*r**5 + 9*r**3 + 12*r**2. Factor s(g).
2*(10*g + 9)**2/3
Let g = 127 + -234. Let k = g + 215/2. Solve -2*s**2 - k*s**3 + 0 - 2*s = 0 for s.
-2, 0
Solve 34668*m**2 + 53136*m + 313*m**4 - 15552 + 2597*m**3 + 14*m**5 + 3766*m**3 - 2*m**5 + 152*m**4 = 0.
-12, -3, 1/4
Let b = -302 + 307. Find c such that 6*c**2 + 5*c**5 - 2*c**5 - 3*c**3 + 0*c**4 + 0*c**b - 6*c**4 = 0.
-1, 0, 1, 2
Suppose 6*r = 186 - 168. What is m in 60 + 137*m + 70*m**2 - 40*m + 5*m**r - 8*m + 36*m = 0?
-12, -1
Let -10/13*c**2 + 2/13*c**5 + 80/13 + 2/13*c**4 + 116/13*c - 46/13*c**3 = 0. Calculate c.
-5, -1, 2, 4
Factor -76/3 + 77/3*m - 1/3*m**2.
-(m - 76)*(m - 1)/3
Factor 26*v + 179*v**2 + 20*v**3 + 413*v + 161*v + 33*v**2 + 288.
4*(v + 4)*(v + 6)*(5*v + 3)
Let d(q) = -12*q**3 - 44*q**2 + 416*q + 440. Let h(c) = -94*c**3 - 351*c**2 + 3327*c + 3522. Let w(m) = 31*d(m) - 4*h(m). Let w(n) = 0. What is n?
-16, -1, 7
Let c = 65 - 87. Let t(u) = -u**3. Let y(b) = -57*b**3 - 2*b**2 + 4*b**4 + 22*b**2 - 10*b**4 - 4*b**4. Let f(w) = c*t(w) + 2*y(w). Factor f(p).
-4*p**2*(p + 5)*(5*p - 2)
Suppose -5 = -5*p, -5*b + 8 = p + 497. Let n be (-147)/b*4/33. Factor 2/11*i**2 + 0 - n*i.
2*i*(i - 1)/11
Let r = 2182 + -1453. Let 729 - 58*i - 60*i**2 - r - 2*i**3 = 0. Calculate i.
-29, -1, 0
Let w(a) = a**4 - a**3 - a**2 - 5*a. Let s(i) = 12*i**4 - 215*i**3 - 1259*i**2 - 2567*i - 1680. Let h(o) = s(o) - 11*w(o). Factor h(m).
(m - 210)*(m + 2)**3
Let h(k) be the first derivative of 4*k**5/5 + 786*k**4 + 614644*k**3/3 - 619368*k**2 + 620944*k - 4808. Factor h(w).
4*(w - 1)**2*(w + 394)**2
Let j(t) be the third derivative of t**5/240 - 41*t**4/48 + 1368*t**2. What is x in j(x) = 0?
0, 82
Let v(w) be the first derivative of -2*w**5/5 + 11*w**4/2 - 16*w**3 - 4*w**2 + 64*w + 41. Factor v(l).
-2*(l - 8)*(l - 2)**2*(l + 1)
Suppose 14*s - 50 = -22. Let 2*i**3 + 1 - 3 + s + i**2 + i**4