0*q. Find r, given that o(r) = 0.
0, 1, 2
Let -532/3 + 16*c + 4/3*c**2 = 0. Calculate c.
-19, 7
Let l(n) be the first derivative of n**3/3 + 41*n**2/2 + 40*n - 2746. Factor l(k).
(k + 1)*(k + 40)
Let j(c) be the first derivative of 4/15*c**3 - 9/5*c**2 - 4/5*c + 9/10*c**4 - 40. Suppose j(t) = 0. Calculate t.
-1, -2/9, 1
Let p(a) be the first derivative of a**3 - 4365*a**2 - 8733*a + 10807. Determine n so that p(n) = 0.
-1, 2911
Let m(h) be the second derivative of 2/3*h**3 - 3/10*h**5 + 1/21*h**7 - 18 + 3*h + 1/15*h**6 - 1/6*h**4 + 0*h**2. Suppose m(q) = 0. Calculate q.
-2, -1, 0, 1
Let m be 16/(-9)*396/(-528). Let s(a) be the first derivative of 1/12*a**2 - 28 + 3*a**4 - 23/9*a**3 + a - m*a**5 + 7/36*a**6. What is d in s(d) = 0?
-2/7, 1, 3
Suppose -4*q = -5*j - 0*j - 10, -5*q = j - 27. Suppose -q*v = v - 12. Factor -849 - 2*m + 849 + m**3 + m**v.
m*(m - 1)*(m + 2)
Suppose -231*d**2 - 5*d**4 + 360 + 191*d**2 + 15 + 268*d**2 - 800*d - 40*d**3 + 242*d**2 = 0. Calculate d.
-15, 1, 5
Let y = 13 + -4. Let x(n) = -3*n**2 - 17*n + 8. Let u be x(-6). Determine i so that -y*i**2 + 3*i**3 + i**5 + 6*i**2 - 2*i**5 + i**u = 0.
-2, 0, 1
Let d(f) = 2*f**2 + 5*f - 22. Let h be d(-6). Find p such that 25*p**3 - 928*p**4 - h*p + 467*p**4 + 20 + 466*p**4 - 25*p**2 - 5*p**5 = 0.
-2, -1, 1, 2
Find w, given that -3483*w**4 + 170*w**3 + 3408*w**4 + 37*w - 15*w**2 + 85 - 202*w + 5*w**2 - 5*w**5 = 0.
-17, -1, 1
Suppose 5*y - 71 - 59 = 0. Suppose 5*j - 33 + 11 = -3*r, 5*j = -4*r + y. Factor -2*d**2 - d**2 - 7*d**2 + 10*d - 5*d**j + 35*d**4 - 15*d**5 - 15*d**3.
-5*d*(d - 1)**3*(3*d + 2)
Let t(b) be the third derivative of -b**5/15 + 1086*b**4 - 7076376*b**3 - 108*b**2 + 52*b. Let t(a) = 0. What is a?
3258
Let f(s) be the first derivative of 16*s**5/35 + 25*s**4/7 + 24*s**3/7 - 74*s**2/7 - 40*s/7 + 2414. Let f(x) = 0. What is x?
-5, -2, -1/4, 1
Suppose -4*k = 2*g + 46, -13*k = -9*k - 3*g + 31. Let z be 1140/252 - k/(-6). Factor 50/7 + z*b + 2/7*b**2.
2*(b + 5)**2/7
Let j be 1/(-2) - (-5 + (-6132)/(-16)). Let x = -378 - j. Factor -1/2 + x*p - 3/4*p**3 + 1/4*p**4 + 1/4*p**2.
(p - 2)*(p - 1)**2*(p + 1)/4
Let q(a) be the third derivative of a**6/300 - 1831*a**5/150 - 733*a**4/12 - 611*a**3/5 + a**2 - 8. Factor q(n).
2*(n - 1833)*(n + 1)**2/5
Suppose -3127*l + 2*l**4 + 1196*l - 2101*l + 36*l**3 + 286*l**2 - 4*l**4 - 25088 = 0. Calculate l.
-7, 16
Solve -28/11*s**2 + 8/11*s**4 + 0 + 2/11*s**5 - 6/11*s**3 - 16/11*s = 0.
-4, -1, 0, 2
Let o = -433654/297 - -39752/27. Find r, given that o + 2/11*r**2 - 136/11*r = 0.
1, 67
Let k(n) be the third derivative of -25/12*n**5 + 84*n**2 + 0*n**3 - 2/21*n**7 + 0*n + 7/6*n**6 + 5/4*n**4 + 0. Let k(i) = 0. What is i?
0, 1/2, 6
Find n, given that 92*n**3 + 481 - 1420*n**2 - 468*n + 239 - 552*n + 35*n**4 - 387*n**3 = 0.
-2, 3/7, 12
Let x(z) = z**2 + 2*z - 5. Let o be x(-4). Suppose 0*n**2 + 3*n - 158*n**o - 4*n**2 - n**2 + 159*n**3 + n**4 = 0. Calculate n.
-3, 0, 1
Let t(r) be the first derivative of 9*r**4/26 + 686*r**3/13 + 29920*r**2/13 + 57800*r/13 - 3667. Factor t(s).
2*(s + 1)*(3*s + 170)**2/13
Let k(c) be the third derivative of -c**5/300 + 3*c**4/40 + 551*c**3/15 + c**2 - 1113. Find i, given that k(i) = 0.
-29, 38
Let u = 11428/9 - 399797/315. Let m = 32/35 - u. Factor -8/3*s - 16/3 - m*s**2.
-(s + 4)**2/3
Let s be 6 - (3 + (3 - (-2 - -4))). Find z, given that 900104*z + 41*z**4 + 840*z**3 - 20812295 - 16620*z**2 + 5253815 - 36300*z**s - 46*z**4 + 581656*z = 0.
42
Suppose -3*g - 57 = -65*w + 62*w, -g = 16. Factor -48/5*r**2 - 52/5*r - 12/5*r**w - 18/5 + 2/5*r**4.
2*(r - 9)*(r + 1)**3/5
Suppose -9*g + 35 + 82 = 0. Suppose 0 = -5*a + 3*q + g, a + 4*q - 40 = -42. Solve -1/4*s**3 + 0 - 3/2*s - 7/4*s**a = 0.
-6, -1, 0
Suppose 122*p - 25*p = 91 + 297. Let t(x) be the third derivative of 8/15*x**5 + 0*x + 4/105*x**7 + 16*x**2 - 2/3*x**3 + 0 - 1/4*x**6 - 1/4*x**p. Factor t(v).
2*(v - 2)*(v - 1)**2*(4*v + 1)
Let m = 12367/5 - 22288/15. Let n = -987 + m. Determine g so that -n + 2/15*g**2 + 0*g = 0.
-2, 2
Factor -244*b + 292/3 + 5/3*b**2.
(b - 146)*(5*b - 2)/3
Let q be (-24 - -28) + (-68)/5. Let l = q - -56/5. Solve 0*a - 2*a**3 - 4/5*a**2 - l*a**4 - 2/5*a**5 + 0 = 0.
-2, -1, 0
Let w(k) be the third derivative of k**8/1008 + k**7/252 - 7*k**6/216 + k**5/18 - 16*k**3 - 88*k**2. Let j(u) be the first derivative of w(u). Factor j(a).
5*a*(a - 1)**2*(a + 4)/3
Let a(f) be the second derivative of -37/4*f**4 + 2*f**5 - 31/3*f**3 - 81*f + 8/15*f**6 - 4*f**2 + 0. Factor a(k).
(k - 2)*(k + 4)*(4*k + 1)**2
Let r be 43/(-215)*(1 + -1)/(7 + -9). Let z(t) be the first derivative of -1/2*t**4 - 10 - t + 1/5*t**5 + t**2 + r*t**3. Factor z(u).
(u - 1)**3*(u + 1)
Find a, given that 12205*a**2 + 481*a - 35*a**4 - 270*a**3 - 2601*a - 10585*a**2 + 480 = 0.
-12, 2/7, 2
Factor -1 - 87 - 27*a + 0*a**2 - 41 - a**2 + 37.
-(a + 4)*(a + 23)
Let z(h) = h**3 - h - 2. Let i(m) = 8*m**3 - 2*m**2 - 12*m - 8. Let u(r) = 30*r + 5. Let w be u(1). Let n(j) = w*z(j) - 5*i(j). Solve n(v) = 0.
-2, 1, 3
Let x(l) be the second derivative of -l**7/42 + 7*l**6/15 - 13*l**5/20 + 647*l. Let x(g) = 0. What is g?
0, 1, 13
Let u(t) = 140*t**2 - 16880*t - 65. Let c(v) = 13*v**2 - 1535*v - 6. Let d(f) = 65*c(f) - 6*u(f). Let d(l) = 0. What is l?
-301, 0
Let x(u) = u**3 + 5*u**2 - 13*u + 16. Let m be x(-8). Let k = 80 + m. Factor 3*j**2 - 15 + k*j + 7*j - 3*j.
3*(j - 1)*(j + 5)
Suppose 4*c - 9*b = -5*b + 632, 0 = -2*c - 5*b + 323. Solve 200*r - 68 - 4*r**2 + c + 113 = 0.
-1, 51
Let d be (-96)/(-33) - 0 - (-31)/(-62)*-4. Find x, given that 1/11*x**2 + 729/11 + d*x = 0.
-27
Factor 2/3*d**2 + 22/3*d - 8.
2*(d - 1)*(d + 12)/3
Let h(q) = q**2 + 5*q - 10. Let c be h(-7). What is f in 906 + 20*f**2 + 57*f + 322*f - c*f**3 - 74 - 27*f = 0?
-4, 13
Let h(i) = i**2 + 15*i - 98. Let c(q) = -8*q + 236. Let s be c(32). Let u be h(s). Factor 0 + 5/3*y - 5/3*y**u + 5/3*y**4 - 5/3*y**3.
5*y*(y - 1)**2*(y + 1)/3
Let d(u) be the first derivative of -u**4/4 + 2*u**2 - 653. Determine z, given that d(z) = 0.
-2, 0, 2
Let u be -11 - (-15 + 270/18 + -15). Factor -1/3*x**u + 17/3*x**2 + 1/3*x**3 - 12 - 7*x.
-(x - 3)**2*(x + 1)*(x + 4)/3
Let w be (-16385)/791 - (-24 - -3). Find p, given that 12/7*p**2 - w*p**3 + 0 + 0*p = 0.
0, 6
Let q(v) be the first derivative of -2*v**3/39 + 61*v**2/13 + 252*v/13 - 502. Determine j, given that q(j) = 0.
-2, 63
Let s = -182118 - -1639100/9. Factor -32/9*q - 50/9*q**2 - 8/9 - 14/9*q**4 - 2/9*q**5 - s*q**3.
-2*(q + 1)**3*(q + 2)**2/9
Let w be -1*(0 - 2/(4/6)). Factor -3*z**2 - 154*z**w + 5*z + 158*z**3 - 5*z**2 - z.
4*z*(z - 1)**2
Let s(n) be the first derivative of 4*n**3/3 + 7956*n**2 + 15824484*n + 1496. Factor s(h).
4*(h + 1989)**2
Let p be ((-12)/10 - 0)/(105/(-700)). Suppose -a = 5*k + p, 4*k + 9 = -a + 3. Factor 0 - 2/5*m**3 - 2/5*m**a + 0*m.
-2*m**2*(m + 1)/5
Let z be 0*(3/3)/(-1). Suppose -13143 = -623*t - 11897. Let -2/7*c**t - 22/7*c + z = 0. Calculate c.
-11, 0
Let n = 24558 + -24553. Let x(j) be the first derivative of 1/3*j**3 + 19/8*j**4 + 0*j + 19 + 0*j**2 + 22/5*j**n. Factor x(l).
l**2*(4*l + 1)*(11*l + 2)/2
Let y(v) be the second derivative of v**6/60 - 2*v**5/5 + 15*v**4/8 + 27*v**3/2 - 4023*v. Factor y(u).
u*(u - 9)**2*(u + 2)/2
Suppose 2/9*o**5 + 0 - 32/9*o**4 - 784/9*o + 28/9*o**2 + 46/3*o**3 = 0. What is o?
-2, 0, 4, 7
Let v(q) be the first derivative of -q**6/24 + 5*q**5/4 - 105*q**4/8 + 245*q**3/6 - 4*q**2 + 39. Let w(f) be the second derivative of v(f). Factor w(s).
-5*(s - 7)**2*(s - 1)
Let x(g) be the first derivative of g**3/15 + 8*g**2/5 - 1542. Suppose x(j) = 0. What is j?
-16, 0
Let a(x) be the second derivative of 0 - 1/6*x**3 + 19/96*x**4 - 211*x - 1/4*x**2 - 7/160*x**5. Factor a(t).
-(t - 2)*(t - 1)*(7*t + 2)/8
Let c(p) be the third derivative of p**6/72 + p**5/12 - 5*p**4/8 - 19*p**3/2 - p**2 + 11. Let w(t) be the first derivative of c(t). Factor w(g).
5*(g - 1)*(g + 3)
Let b(d) = 11*d**2 + 183*d + 537. Let z(w) = -52*w**2 - 916*w - 2686. Let o(g) = 14*b(g) + 3*z(g). Factor o(k).
-2*(k + 3)*(k + 90)
Let g(q) be the third derivative of -1/18*q**3 + 1/105*q**7 - 1/72*q**6 + 27*q**2 + 0*q + 5/72*q**4 - 1 - 1/36*q**5. Let g(v) = 0. What is v?
-1, 1/3, 1/2, 1
Let k(c) = 2*c**2 - 8*c + 7. Let z be k(-12). Factor 431*r - 2*r**2 - z*r + 3 - 3.
-2*r*(r - 