q) be the first derivative of -24*q**3 + 69*q**2/2 + 15*q + 75. Let s(k) = 2*d(k) + 5*r(k). Find b such that s(b) = 0.
-2/9, 5/4
Factor 41171 - 123484 - 9*r**2 + 42*r + 41180 + 41184.
-3*(r + 1)*(3*r - 17)
Suppose 21 = 17*i - 13. Factor -36*p**3 + 12*p**2 + 65*p**3 - 6*p**i - 32*p**3.
-3*p**2*(p - 2)
Factor 72/5 + 4/5*s**2 + 76/5*s.
4*(s + 1)*(s + 18)/5
Let w(n) be the third derivative of -n**7/105 + 29*n**6/15 + 119*n**5/30 - 39*n**4/2 + 2300*n**2. Let w(k) = 0. Calculate k.
-2, 0, 1, 117
Factor -3/4*r**4 - 1316928000*r - 2599200*r**2 - 2280*r**3 - 250216320000.
-3*(r + 760)**4/4
Find h, given that 17647*h - 2*h**2 + h**2 - 92 - 17620*h = 0.
4, 23
Factor 1299/8*y**2 + 3/8*y**3 + 17658*y + 17496.
3*(y + 1)*(y + 216)**2/8
Let h(z) be the third derivative of -z**6/360 - 9*z**5/5 - 213*z**4/8 - 159*z**3 + 6235*z**2. Factor h(t).
-(t + 3)**2*(t + 318)/3
Suppose 257 = 2*u - 5*f, -2*f = 7 - 1. Let m = 137 - u. Factor -11*o + 41*o - m + 12 + 13 + 9*o**2.
3*(o + 3)*(3*o + 1)
Let j = 247/5346 + 7/486. Let x(p) be the first derivative of -6/11*p + 2/11*p**2 + j*p**3 - 11. Factor x(m).
2*(m - 1)*(m + 3)/11
Let d(i) = 5*i - 2. Let a(y) = 5*y + 66. Let h be a(-13). Let n be d(h). Factor 3/4*l**2 + 0 + 0*l - 3/4*l**n.
-3*l**2*(l - 1)/4
Suppose -w - 2*r + 24 = -15, -4*r = w - 35. Let d = w + -40. Factor -d*n - 6*n**2 + 3*n**3 - 7 + 8 + 5.
3*(n - 2)*(n - 1)*(n + 1)
Let y(r) be the second derivative of 0 - 1/15*r**6 - 76*r + 7/10*r**5 + 18*r**2 - 13/6*r**4 - r**3. Determine l so that y(l) = 0.
-1, 2, 3
Suppose -5*m = -q - 22, 3*m - 500*q - 21 = -502*q. Factor -m*l**3 + 0*l**2 + 5/2*l**4 + 0*l + 0.
5*l**3*(l - 2)/2
Let h = 451 + -443. Suppose -6*d - m - 1 = -h*d, -5*d = -3*m - 3. Solve d*q + 1/4 - 1/4*q**2 = 0 for q.
-1, 1
Suppose -35*n - 29 + 17 + 12 = 0. Let v(x) be the second derivative of 3/70*x**5 + 0*x**3 + n*x**2 + 0 - 3/28*x**4 - 17*x + 1/70*x**6. Factor v(w).
3*w**2*(w - 1)*(w + 3)/7
Let d(x) be the third derivative of 7/180*x**5 - 2/27*x**3 + 1/108*x**6 + x**2 + 0*x**4 - 31 + 0*x. Factor d(a).
(a + 2)*(2*a + 1)*(5*a - 2)/9
Let k(v) be the third derivative of v**5/90 - 26*v**4/9 + 103*v**3/9 - 1357*v**2. What is t in k(t) = 0?
1, 103
Let k(x) be the first derivative of -2*x**5/85 - 45*x**4/34 - 856*x**3/51 + 1920*x**2/17 + 4608*x/17 + 350. Let k(t) = 0. What is t?
-24, -1, 4
Factor 0 + 232*k**2 + 20184*k + 2/3*k**3.
2*k*(k + 174)**2/3
Let y be 9/27 + 4/(12/11). Suppose -y*t - t**2 - 4*t**2 + 21 - 6 - 6*t = 0. What is t?
-3, 1
Let d(b) be the first derivative of 2/3*b**6 + 28/5*b**5 + 26*b**2 + 12*b + 88/3*b**3 + 18*b**4 - 2. Factor d(r).
4*(r + 1)**4*(r + 3)
Let h = -19289 + 38603/2. Solve -h*t**3 - 5/2 - 135/2*t**2 - 51/2*t = 0.
-5, -1/5
Let l(j) be the first derivative of -4*j**5/25 + 3*j**4/5 + 8*j**3/5 - 56*j**2/5 + 96*j/5 + 2228. Factor l(r).
-4*(r - 2)**3*(r + 3)/5
Solve 9243/2*g - 28477683/4*g**2 + 29246580441/8*g**3 - 1 = 0.
2/3081
Let r = 340975 + -340975. Factor -9/4*n**3 - 11/4*n + 1/4*n**4 + r - 21/4*n**2.
n*(n - 11)*(n + 1)**2/4
Let q be (-35)/(-28)*(0 + 8). Suppose -2*t + q = 4. Factor 4*f**2 + t*f**3 - 2*f - f**2 - 4*f + 3*f - 3*f**4.
-3*f*(f - 1)**2*(f + 1)
Let s(h) be the first derivative of 5*h**4/4 + 10*h**3/3 - 10*h**2 - 40*h - 3075. Suppose s(l) = 0. What is l?
-2, 2
Let r be 54*(-4)/(-36)*6. Suppose 28*c + 23*c**4 - 10 + 5*c**5 - r*c + 30*c**3 + 4*c**2 + 10 = 0. What is c?
-2, -1, 0, 2/5
Let v(t) be the third derivative of t**5/120 + 41*t**4/48 + 15*t**3 + 327*t**2. Factor v(k).
(k + 5)*(k + 36)/2
Suppose -4*m - 10 = -5*m. Suppose -10*g - 9*g = m*g. Find x, given that -3/8*x**4 + 3/8 + g*x**2 - 3/4*x + 3/4*x**3 = 0.
-1, 1
Let -44*h**3 + 861*h**2 - 12*h**4 + 56 - 16 - 889*h**2 + 44*h = 0. What is h?
-2, -5/3, -1, 1
Determine o, given that -88/17*o**2 + 2/17*o**3 + 326/17*o - 240/17 = 0.
1, 3, 40
What is t in 2/19*t**2 - 112/19 - 52/19*t = 0?
-2, 28
Let d(i) be the third derivative of i**10/50400 - i**8/2240 + i**7/840 - 79*i**5/20 - 197*i**2. Let q(n) be the third derivative of d(n). Solve q(y) = 0 for y.
-2, 0, 1
Let d(q) be the third derivative of 0*q - 1/6*q**7 + 0 - 5/12*q**4 - 89*q**2 + 1/12*q**6 + 7/12*q**5 + 0*q**3. Factor d(p).
-5*p*(p - 1)*(p + 1)*(7*p - 2)
Let w = 18317 - 18309. Let g(t) be the second derivative of 1/108*t**4 - 2/27*t**3 + w*t - 5/18*t**2 + 0. Solve g(k) = 0 for k.
-1, 5
Suppose 85*x = 82*x + 39. Factor 5*g**3 - 55*g + x + 67 + 18*g - 23*g.
5*(g - 2)**2*(g + 4)
Let h(q) be the third derivative of -8/15*q**3 - 1/30*q**4 + 0 + 1/150*q**5 + 0*q - 19*q**2. Let h(o) = 0. What is o?
-2, 4
Let d(i) be the second derivative of -i**7/168 + i**5/24 + i**3 + 11*i**2/2 + 122*i. Let j(o) be the second derivative of d(o). Let j(h) = 0. What is h?
-1, 0, 1
Factor 382/3*j**2 - 2/3*j**3 + 2/3*j - 382/3.
-2*(j - 191)*(j - 1)*(j + 1)/3
Let n be ((-18568)/924 - -20)/(3/(-21)). Factor 0 + 0*h - 4/3*h**2 + 0*h**4 - n*h**5 + 2*h**3.
-2*h**2*(h - 1)**2*(h + 2)/3
Determine d, given that -3*d**2 + 0*d**2 - 650*d + 193 + 1148*d - 645*d - 1987 = 0.
-26, -23
Suppose -30*x**4 + 80*x + 109*x - 3*x**5 + 11 - 273*x - 78*x**2 + 109 + 6*x**5 + 93*x**3 = 0. Calculate x.
-1, 2, 5
Factor 274/3*n - 268/3*n**2 - 2/3*n**3 + 180.
-2*(n - 2)*(n + 1)*(n + 135)/3
Let m(u) = u**3 - 36*u**2 - 205*u + 4. Let p be m(41). Let o(f) be the first derivative of 0*f - 1/10*f**p - 4/15*f**3 + 12 + 3/5*f**2. Let o(a) = 0. What is a?
-3, 0, 1
Let f(b) = 9*b**2 - 57*b + 12. Let u(w) = -5 + 66 - 200*w + 80*w + 44*w**2 - 165*w. Let q(z) = -11*f(z) + 2*u(z). Factor q(g).
-(g - 5)*(11*g - 2)
Let y(r) be the first derivative of 0*r**3 + 0*r + 15 + 1/15*r**5 + 1/6*r**4 - 6*r**2. Let v(n) be the second derivative of y(n). Factor v(w).
4*w*(w + 1)
Let l(t) be the second derivative of t**6/105 - 38*t**5/35 + 37*t**4/21 + 76*t**3/21 - 75*t**2/7 - t - 622. Let l(f) = 0. Calculate f.
-1, 1, 75
Let z = -2/213929 + 737413267/427858. Let g = z - 1686. Determine q, given that g*q**2 - 10 + 10*q**3 + 30*q = 0.
-2, 1/4
Let 5/7*w**2 + 4/7 - 8/7*w - 1/7*w**3 = 0. What is w?
1, 2
Let o(l) be the first derivative of -l**3/15 + 21*l**2/5 + 43*l/5 - 365. Find p, given that o(p) = 0.
-1, 43
Let p(l) = -13*l - 127. Let c be p(-10). Factor 2112*g + 144*g + 43*g**3 - 22293*g**2 + 17*g**c + 21565*g**2 - 288.
4*(g - 6)**2*(15*g - 2)
Let -6*i - 517/6 + 1/6*i**2 = 0. Calculate i.
-11, 47
Let s = 8894/19 + -468. Determine h so that -10/19*h - 6/19 - 2/19*h**2 + s*h**3 = 0.
-1, 3
Let o(j) be the third derivative of -j**6/240 + 11*j**5/120 - j**4/3 - 7*j**3 - 530*j**2 - j. Factor o(n).
-(n - 7)*(n - 6)*(n + 2)/2
Suppose -25*d - d - 7670 = 0. Let o = 298 + d. Let -1/2*p**2 - o*p + 0 = 0. What is p?
-6, 0
Let z(m) be the first derivative of -5*m**3/3 + 305*m**2/2 + 630*m + 1333. Determine o, given that z(o) = 0.
-2, 63
Let q(d) be the first derivative of d**5/60 + d**4/3 - 9*d**2/2 - 2*d - 21. Let n(s) be the second derivative of q(s). Solve n(a) = 0 for a.
-8, 0
Let h = -766975 + 767005. Let -36*f - 16*f**2 - 2/9*f**4 - h - 28/9*f**3 = 0. What is f?
-5, -3
Let g(d) = 961*d**2 + 62*d + 7. Let h(u) = 961*u**2 + 62*u + 6. Suppose -43*j - 5 = -42*j. Let c(w) = j*g(w) + 6*h(w). Let c(q) = 0. What is q?
-1/31
Let v = -164 + 167. Let r = -666 + 668. Factor 1/2*y**4 + 3/2*y**v + 2 - 5/2*y**r - 3/2*y.
(y - 1)**2*(y + 1)*(y + 4)/2
Let i = 218 - 214. Solve -82*w + i + 5041*w**2 + 68*w + 298*w = 0 for w.
-2/71
Let j(h) be the first derivative of -h**6/300 - h**5/150 + 3*h**4/20 + 3*h**3/5 - 2*h**2 + 4*h + 24. Let d(u) be the second derivative of j(u). Factor d(a).
-2*(a - 3)*(a + 1)*(a + 3)/5
Let c(r) be the third derivative of -3*r**2 - 13/9*r**3 - 8*r - 1/180*r**5 - 3/8*r**4 + 0. Factor c(v).
-(v + 1)*(v + 26)/3
Let c(d) be the second derivative of -d**8/10080 - 13*d**7/1260 - d**6/3 + 20*d**5/9 + 25*d**4/3 - d - 1. Let r(i) be the third derivative of c(i). Factor r(w).
-2*(w - 1)*(w + 20)**2/3
Find j, given that -55/7*j - 376/7 - 1/7*j**2 = 0.
-47, -8
Let u(i) = i**2 - i**3 + 316 + i - 160 - 153. Let g be u(0). Factor -5*x**g + 15/4*x**2 + 5/2 + 45/4*x.
-5*(x - 2)*(x + 1)*(4*x + 1)/4
Let q(z) be the third derivative of 1/80*z**6 - 1/12*z**4 + 1/168*z**7 + 0*z + 0 - 1/60*z**5 + 1/1344*z**8 - 52*z**2 + 0*z**3. Factor q(r).
r*(r - 1)*(r + 2)**3/4
Let g(q) be the second derivative of 2*q**5/15 + 79*q**4/18