 given that 8*g**2 - 2 + 20*g**3 + 16*g**4 + 40*g**5 - v*g**5 + 2 = 0.
-2, -1, 0
Let c(p) be the second derivative of -p**5/3 + 1291*p**4/9 - 55642*p**3/3 + 11094*p**2 + 3*p + 410. Factor c(k).
-4*(k - 129)**2*(5*k - 1)/3
Let r(l) be the first derivative of l**6/540 + l**5/360 + 25*l**3/3 - 255. Let u(o) be the third derivative of r(o). Factor u(x).
x*(2*x + 1)/3
What is v in v**2 - 6*v**2 - 2*v**4 - 19*v**3 + 4*v**2 + 9*v**2 + 4*v**3 = 0?
-8, 0, 1/2
Let v(p) = p**3 - 4*p**2 + 9*p - 33. Let m be v(4). Determine x, given that -12*x**2 + 6 - x - 2*x + 0*x - 2*x**3 + 6*x**4 - 3*x**5 + 8*x**m = 0.
-1, 1, 2
Let t be (-5 + -7)*((-1)/(-3) - 0). Let h be -2 + 161/42 - t/(-3). Factor -h*x**2 - 3/2*x - 1.
-(x + 1)*(x + 2)/2
Let g(z) be the first derivative of -7/4*z - 29 + 1/12*z**3 + 3/4*z**2. Factor g(f).
(f - 1)*(f + 7)/4
Determine p, given that 5/6*p**3 + 33/2*p + 1/6*p**4 - 19/2*p**2 + 0 = 0.
-11, 0, 3
Let j be 2473/10 - 63/210. Let s be (-19)/j*(-4)/2. Let 0 + 4/13*l - s*l**2 = 0. What is l?
0, 2
Let j = 16981 + -16977. Let n(h) be the third derivative of 1/24*h**j + 0 + 1/120*h**5 - 27*h**2 + 0*h**3 + 0*h. Factor n(u).
u*(u + 2)/2
Let f(h) be the second derivative of 0*h**2 - 55*h - 7/10*h**6 + 9/4*h**5 + 0*h**3 + 0 + 1/14*h**7 - 9/4*h**4. Solve f(v) = 0.
0, 1, 3
Find o such that -233*o**2 - 740*o - 342*o**2 + 23779*o**3 - 23909*o**3 + 5*o**4 - 300 = 0.
-2, -1, 30
Let w(h) be the third derivative of -h**5/30 + 221*h**4/4 - 662*h**3/3 - h**2 + 2000*h. Determine d so that w(d) = 0.
1, 662
Let 0 - 4/3*d - 2/9*d**2 = 0. What is d?
-6, 0
Suppose -198*v - 6 = -201*v + 3*c, -5*v + 4*c = -8. Let u(b) be the second derivative of 1/8*b**4 + 0*b**3 - 46*b - 3/4*b**2 + v. Factor u(n).
3*(n - 1)*(n + 1)/2
Let x be (-31)/((-1395)/(-350)) - (-10)/(-45) - (-624)/64. Suppose -1 - 11/4*n**3 + 13/4*n - 1/2*n**5 - x*n**2 + 11/4*n**4 = 0. What is n?
-1, 1/2, 1, 4
Let f(o) be the first derivative of 5/8*o**4 - 5/2*o**2 + 2*o**3 + 0*o + 1/20*o**5 - 31. Let l(b) be the second derivative of f(b). Factor l(w).
3*(w + 1)*(w + 4)
Factor 1191*j + 11*j**2 - 16*j**2 + 13*j**2 + 225*j + 62658.
2*(2*j + 177)**2
Let n = 14725 + -14722. Let r(q) be the third derivative of -13/40*q**6 + 0*q**n - 9/8*q**4 - 6/5*q**5 + 0*q + 0 - 1/35*q**7 - 14*q**2. Factor r(b).
-3*b*(b + 3)**2*(2*b + 1)
Let q(s) = 31*s**2 + 84*s - 79. Let d(g) = 7*g**2 + 21*g - 20. Let z = 403 + -405. Let f(x) = z*q(x) + 9*d(x). Factor f(l).
(l - 1)*(l + 22)
Let k(h) be the third derivative of -h**5/390 - 475*h**4/78 + 1904*h**3/39 - 86*h**2 + 6*h. Factor k(j).
-2*(j - 2)*(j + 952)/13
Let n(a) be the third derivative of -a**8/84 + 4*a**7/175 + 7*a**6/75 - 28*a**5/75 + a**4/2 - 4*a**3/15 - 3*a**2 + 416*a. What is z in n(z) = 0?
-2, 1/5, 1
Let i(n) be the first derivative of -n**3 + 354*n**2 - 41772*n + 1086. Factor i(u).
-3*(u - 118)**2
Let v(u) be the second derivative of u**7/7140 + u**6/3060 - u**5/255 - u**4/51 - 29*u**3/2 - 44*u. Let a(l) be the second derivative of v(l). Factor a(h).
2*(h - 2)*(h + 1)*(h + 2)/17
Let v be (-19)/((-494)/(-325))*42/(-30). Solve -v - 15*d + 5/2*d**2 = 0 for d.
-1, 7
Let l(x) = -60*x**2 - 2405*x - 290410. Let n(y) = -71*y**2 - 2404*y - 290411. Let q(t) = 6*l(t) - 5*n(t). Factor q(a).
-5*(a + 241)**2
Let k(q) be the second derivative of -6/5*q**3 - 1/30*q**4 - 34 - 81/5*q**2 - q. Factor k(s).
-2*(s + 9)**2/5
Suppose 25*s + 2530 = 35*s. What is l in -128*l**2 - 38*l + 0*l + s*l**2 - 145*l**2 + 4 = 0?
-2, 1/10
Let k(w) = w**2 + 19408*w + 97017. Let s be k(-5). Factor 0 - 1/3*h**s + 7*h.
-h*(h - 21)/3
Let z(v) = -67*v**5 - 261*v**4 - 272*v**3 - 4*v - 8. Let m(j) = 67*j**5 + 263*j**4 + 272*j**3 + j**2 + 3*j + 6. Let k(i) = 4*m(i) + 3*z(i). Factor k(o).
o**2*(o + 2)**2*(67*o + 1)
Let m be (((-126)/(-420))/(3/(-24)))/((-24)/16). Factor 0 + 1/10*d + m*d**2.
d*(16*d + 1)/10
Let n(o) be the first derivative of -o**5/40 - 7*o**4/24 - 113*o - 55. Let f(r) be the first derivative of n(r). What is l in f(l) = 0?
-7, 0
Let q(t) be the third derivative of -t**5/20 - 1971*t**4/2 - 7769682*t**3 + t**2 + 1994. Find d such that q(d) = 0.
-3942
Let z(l) be the second derivative of l**7/1260 - l**6/60 + 3*l**5/20 + 5*l**4/6 + 10*l - 1. Let d(n) be the third derivative of z(n). Factor d(k).
2*(k - 3)**2
Solve 16/3*b + 16 - 4/3*b**2 = 0.
-2, 6
Let o(s) = s**3 - 14*s**2 + 4*s - 54. Let q be o(14). Factor 192*t**q + 76*t**3 + 78*t + 135*t + t**4 - 33*t + 54 + 9*t**4.
2*(t + 1)*(t + 3)**2*(5*t + 3)
Let -20/3 - 65/2*t**2 + 215/6*t**3 - 75*t = 0. What is t?
-1, -4/43, 2
Suppose 13*t - 28*t = -90. Suppose 10*g**2 + t*g**2 - 5*g**2 + 2*g**4 - 27*g**2 + 32 = 0. Calculate g.
-2, 2
Find r such that 168*r**2 + 2*r**3 + 33*r + 5*r - 804 - 32*r**2 + 41*r + 43*r = 0.
-67, -3, 2
Suppose 0 = -49*h + 79 + 68. Let f(g) be the first derivative of 3*g**2 + 37 + 0*g + 2/3*g**h. Factor f(a).
2*a*(a + 3)
Let s be (116/(-319))/((1 + 1)*(-21)/77). Let c(t) = t**2 + t + 2. Let n be c(0). Find l such that -14/9*l - s - 4/9*l**n = 0.
-3, -1/2
Let q(w) be the first derivative of w**4/2 + 26*w**3 + 75*w**2 + 74*w + 875. Determine p, given that q(p) = 0.
-37, -1
Suppose 16*a = 19*a + 3. Let v be (-2)/a*-2 + 7. Factor 0*k - v + 3/4*k**2.
3*(k - 2)*(k + 2)/4
Let s = 1/2037 - -221/10864. Let n(v) be the first derivative of 1 + 7/16*v**2 + s*v**6 - 1/4*v**4 - 1/12*v**3 - 1/20*v**5 + 1/2*v. Factor n(j).
(j - 4)*(j - 1)*(j + 1)**3/8
Let h(c) be the first derivative of c**2 - 7*c - 12. Let f be h(6). Factor -15*s**2 - 11*s**3 + 2*s**3 - s**3 + f*s**4.
5*s**2*(s - 3)*(s + 1)
Suppose 92*r - 16 = 84*r. Suppose -8 + 9 + 8*p + 4*p**r - 6 - 27 = 0. Calculate p.
-4, 2
Let v(x) be the second derivative of -x**6/60 + 5*x**5/8 - 149*x**4/24 + 227*x**3/12 - 51*x**2/2 + 4*x + 135. Suppose v(t) = 0. What is t?
1, 6, 17
Suppose -55*r + 2*d - 42 = -69*r, r = -3*d + 3. Factor 0 + 1/2*h**2 + 5/6*h**4 + 0*h - 1/6*h**5 - 7/6*h**r.
-h**2*(h - 3)*(h - 1)**2/6
Suppose 2 = -4*x - 2*z, 0 = 4*x - 6*z + 10*z + 12. Solve -40*q**2 + 8 + 58*q**2 + 192*q + 76*q**x = 0.
-2, -2/47
Let q(s) be the second derivative of s**4/72 + 67*s**3/9 - 269*s**2/12 + 4*s - 157. Factor q(c).
(c - 1)*(c + 269)/6
Suppose 3*c = -3*g - 6, -5*c - 3*g = -8*c + 18. Let x be (-63)/10*15*c/(-18). Find b such that -30*b - x*b**3 + 3/2*b**4 + 12 + 27*b**2 = 0.
1, 2
Let t(a) be the third derivative of -1 + 0*a**3 + 0*a - a**4 + 1/10*a**6 - 35*a**2 - 1/6*a**5 - 1/105*a**7. What is q in t(q) = 0?
-1, 0, 3, 4
Let h(r) = -19*r + 595. Let i be h(31). Let t(p) be the first derivative of i + 125/18*p**4 - 50/9*p**3 + 0*p**2 + 8/9*p. Solve t(g) = 0 for g.
-1/5, 2/5
Let c(p) be the second derivative of -1/30*p**4 - 181*p - 144/5*p**2 + 0 - 8/5*p**3. Factor c(u).
-2*(u + 12)**2/5
Let v be (-35)/(-14)*16/20. Let q be 3/9*v/(16/28). Factor q*s**2 - 5/2*s - 1/6*s**3 + 3/2.
-(s - 3)**2*(s - 1)/6
Let 181*a + 349*a**3 - 9*a**4 + 189*a + 256*a**2 + 182*a - 492*a - 414*a**3 = 0. What is a?
-10, -2/9, 0, 3
Let v(t) be the second derivative of -9*t - 5/24*t**4 + 0*t**2 + 13/6*t**3 + 1/72*t**6 + 0 + 0*t**5. Let b(q) be the second derivative of v(q). Factor b(f).
5*(f - 1)*(f + 1)
Factor -r**2 + 451*r + 1335 + 11*r**2 + 544*r + 800*r + 10*r**2.
5*(r + 89)*(4*r + 3)
Let j(f) = f**2 - 21*f - 38. Let p be j(-2). Let o be 0 - (459/(-1080) + (-3)/p). Solve 2/5*t**2 - 6/5*t + o = 0 for t.
1, 2
Let n(l) be the second derivative of 169*l**6/360 + 13*l**5/45 + l**4/18 - 59*l**2 - 56*l. Let s(y) be the first derivative of n(y). Factor s(v).
v*(13*v + 2)**2/3
Solve -370*u**2 - 210*u**3 + 1854*u + 95 + 15*u**5 + 111*u**4 - 2812*u + 1153*u + 164*u**4 = 0.
-19, -1, -1/3, 1
Let p(j) be the first derivative of -j**6/39 + 54*j**5/65 - 95*j**4/26 - 2614*j**3/39 + 96*j**2/13 + 2560*j/13 + 648. What is g in p(g) = 0?
-5, -1, 1, 16
Let n(h) be the second derivative of h**7/189 - 2*h**6/135 - 3*h**5/10 - 26*h**4/27 - 28*h**3/27 - 200*h. Determine m so that n(m) = 0.
-2, -1, 0, 7
Let a = -965599 - -965601. Find p such that 0 + 1/4*p**3 - a*p**2 - 9/4*p = 0.
-1, 0, 9
Let s = -6259517/7 - -894245. Suppose -6*l + 158/7*l**2 - 262/7*l**3 + s*l**4 + 4/7 - 8*l**5 = 0. What is l?
1/4, 2/7, 1
Let h(c) = -c**3 + 5*c**2 + 6*c - 15. Let l be h(5). Determine p, given that 16*p + 4*p**2 - l*p - 5*p**2 = 0.
0, 1
Let d be ((-40)/(-100))/(46/460). Suppose -