5/20 - 9*s**4/4 + 61*s**3/6 - 56*s**2. Let j(p) be the first derivative of v(p). Let j(c) = 0. Calculate c.
18
Let b(v) = v**3 + 38*v**2 - 82*v - 78. Let y be b(-40). Let s be 18*y/(-8) + 6 + -1. Factor 2*l**2 - 3/4*l**3 + 0 - l + 1/4*l**5 - s*l**4.
l*(l - 2)*(l - 1)**2*(l + 2)/4
Let c(d) = 8*d**3 + 51*d**2 + 36*d - 89. Let i(x) = 6*x**3 + 50*x**2 + 38*x - 90. Let j(p) = 4*c(p) - 6*i(p). Factor j(u).
-4*(u - 1)*(u + 2)*(u + 23)
Let k(c) be the third derivative of 2*c + 0*c**3 - 1/42*c**4 + 1/210*c**6 + 0*c**5 + 0 - 4*c**2. Let k(l) = 0. What is l?
-1, 0, 1
Let a(b) be the third derivative of b**5/75 + 173*b**4/30 - 352*b**3/5 - 102*b**2. Determine f, given that a(f) = 0.
-176, 3
Let x(z) be the first derivative of z**4/8 - 193*z**3/6 - 389*z**2/4 - 195*z/2 - 4977. Solve x(k) = 0.
-1, 195
Let n be (-11)/(-4) + 25/100. Suppose n + 12 = 3*v. Suppose -4*x**v + 4*x**4 + 0*x**5 + 8*x**3 + 0*x**3 = 0. Calculate x.
-1, 0, 2
Let b = -666 - -669. Determine o so that 0*o**3 + 3*o**3 - 112 - o**b + 4*o**3 + o**2 - 40*o - 5*o**3 = 0.
-4, 7
Determine k so that -k**4 - 28 - 54*k**3 - 49*k**3 + 2*k**4 + 101*k**3 - 52*k - 27*k**2 = 0.
-2, -1, 7
Determine q so that 3324/7*q - 400/7*q**3 + 5360/7*q**2 + 72 = 0.
-3/10, 14
Let v(h) be the third derivative of 5/48*h**5 + 5/8*h**3 + 35/96*h**4 + 0 + 1/96*h**6 + 2*h - 19*h**2. Solve v(k) = 0.
-3, -1
Suppose -6*z - 15555 = 9*z. Let a = z - -1041. Solve 6/11 - 2/11*h**a - 8/11*h + 8/11*h**3 - 4/11*h**2 = 0 for h.
-1, 1, 3
Let x(w) = w**2 + 212*w + 6751. Let z be x(-39). Factor 15/7*v**3 - 18/7*v**2 - 12/7*v + 24/7 - 3/7*v**z.
-3*(v - 2)**3*(v + 1)/7
Let b = 316924 + -316919. Suppose 2*j**b - 50/3*j**4 - 10/3 - 44*j**2 + 62/3*j + 124/3*j**3 = 0. What is j?
1/3, 1, 5
Let c be -4 + 2 + (6 - (-6 - -441)). Let f = c - -436. Factor -4/11*o**4 + 2/11*o**f - 4/11*o**3 + 16/11*o**2 - 14/11*o + 4/11.
2*(o - 1)**4*(o + 2)/11
Let u(b) be the second derivative of -b**5/10 + 21*b**4/2 - b + 519. Factor u(l).
-2*l**2*(l - 63)
What is a in 1/4*a**3 - 9/4*a**2 + 11/4*a + 1/4*a**4 - 1 = 0?
-4, 1
Suppose 235*q = 237*q - 8. Suppose 10*h - 8 = 8*h, q*h - 31 = -d. Determine t, given that 0 - d*t + 10*t**2 - 5/4*t**4 + 5/4*t**3 = 0.
-3, 0, 2
Let f(g) be the second derivative of g**5/80 + 31*g**4/24 + 121*g**3/24 + 15*g**2/2 + 190*g + 5. Solve f(k) = 0 for k.
-60, -1
Factor 12*r**2 - 12736 - 450*r - 41*r**2 + 11*r**2 + 13*r**2 + 2611.
-5*(r + 45)**2
Let b(c) be the first derivative of 2*c**3/27 - 242*c**2/9 + 209. Determine p, given that b(p) = 0.
0, 242
Let y(q) be the second derivative of -q**6/165 + 13*q**5/55 - 2*q**4 + 248*q**3/33 - 160*q**2/11 - 2721*q. Factor y(x).
-2*(x - 20)*(x - 2)**3/11
Let i(d) = 2*d**2 - 163*d + 2462. Let o be i(20). Let c be 18/15 - (0 + 0). Factor 1/5*v**5 + c + 32/5*v**o + 2/5*v**4 - 18/5*v**3 - 23/5*v.
(v - 1)**4*(v + 6)/5
Let h = -12724 - -12727. Let b(x) be the first derivative of -8/39*x**h + 4/13*x - 17 + 7/13*x**2. Factor b(r).
-2*(r - 2)*(4*r + 1)/13
Let l = 519 - 502. Factor -10*m + m**2 + 2 + 18 - 9*m + 15*m - l*m.
(m - 20)*(m - 1)
Factor -4*y**2 + 2*y**4 + 23*y + 33*y + 16*y + 6 - 8*y**3 - 4*y**4 - 64*y.
-2*(y - 1)*(y + 1)**2*(y + 3)
Let l = -1417 - -1422. Let h = -2 - -4. Factor -4*x - 6*x - 5*x + 15 - 5*x + l*x**h.
5*(x - 3)*(x - 1)
Suppose 83*a + 97*a = -49*a. Let d(u) be the third derivative of 0*u + a*u**3 + 0 + 1/180*u**5 + 1/36*u**4 - 1/360*u**6 - 22*u**2. Factor d(i).
-i*(i - 2)*(i + 1)/3
Let b(k) be the first derivative of 0*k**4 + 0*k + 16/3*k**3 + 0*k**2 - 1/440*k**5 - 15 - 7/3960*k**6. Let h(j) be the third derivative of b(j). Factor h(u).
-u*(7*u + 3)/11
Solve -176 - 1230/7*u + 2/7*u**2 = 0.
-1, 616
Let n(j) be the second derivative of -57/4*j**3 - 277/32*j**4 - 49/80*j**6 + 0 - 42*j + 399/80*j**5 - 27/4*j**2. Factor n(h).
-3*(h - 3)**2*(7*h + 2)**2/8
Let g be -6*((-2)/(-4) + -1). Suppose 2*y + 38 = -4*y + 68. Factor -18*n**g - 4*n + 5*n**4 + 7*n**2 - 6*n**5 + y*n**4 + 7*n**2 + 4*n**5.
-2*n*(n - 2)*(n - 1)**3
Let y = 212 + -199. Find g such that -6*g**2 + y*g - 3*g**2 + 3*g**3 - 9*g + 5*g - 3 = 0.
1
Let i be -40*49/392*7/((-140)/8). Find k, given that 2/13*k**i - 16/13 + 14/13*k = 0.
-8, 1
Let d(m) be the third derivative of -91/48*m**4 + 0 - 1/240*m**5 + 7*m**2 + 0*m - 8281/24*m**3. Let d(r) = 0. Calculate r.
-91
Let y(u) = -57*u - 440. Let z be y(-8). Let h(m) be the third derivative of -1/15*m**3 - z*m**2 + 1/40*m**4 + 0 - 1/300*m**5 + 0*m. Factor h(q).
-(q - 2)*(q - 1)/5
Let v = -1302/1963 + 121646/17667. Factor -8/3*o - v + 2/9*o**2.
2*(o - 14)*(o + 2)/9
Let h(o) be the second derivative of -239/24*o**4 - 899/9*o**3 + 29/60*o**5 - 1/180*o**6 + 0 - 961/3*o**2 - 163*o. Let h(c) = 0. What is c?
-2, 31
Let q be (-2970)/4158 - 4010/(-126). Factor 2/9*i**3 + q*i - 44/9*i**2 - 400/9.
2*(i - 10)**2*(i - 2)/9
Suppose 0 = -z + 149*c - 152*c + 20, -3*z + 3*c = 0. Find w such that -86*w**2 - 32*w**z + 1 + 22*w**3 + 25*w**2 - 6*w + 76*w**3 + 3 - 3*w**2 = 0.
-2, -1/4, 1/4, 1
Let d(y) = 4*y**2 - 15*y - 8. Let s be d(4). Let z be (10 - 2) + (s - 1). Find v such that 1 + z*v - 7/4*v**2 = 0.
-2/7, 2
Let b(k) be the second derivative of 2*k**6/45 - k**5/45 + 47*k**2 + 4*k - 9. Let c(j) be the first derivative of b(j). Factor c(v).
4*v**2*(4*v - 1)/3
Suppose u + 23489 = -5*a, 12*a - 23495 = 17*a - 5*u. Let f = 23568/5 + a. Factor 3/5*o**5 - 54/5*o**2 - 27/5*o**4 - 81/5*o + 81/5 + f*o**3.
3*(o - 3)**3*(o - 1)*(o + 1)/5
Let p(j) = 6*j**4 - 177*j**3 + 924*j**2 + 163*j - 1014. Let i(u) = 4*u**4 - 119*u**3 + 612*u**2 + 109*u - 676. Let q(h) = 7*i(h) - 5*p(h). Solve q(r) = 0 for r.
-1, 1, 13
Suppose -3*o - 18 = -7*o + 5*g, -2*o = -2*g - 8. Let 34*v**3 - 6*v**3 - 4*v**5 - 7*v**5 + 12*v**4 - 60*v**o - 72*v + 7*v**5 = 0. Calculate v.
-2, -1, 0, 3
Let b be ((-3)/(-42))/(16 - -15*247/(-234)). Let -b*l**2 + 18/7*l + 3 = 0. What is l?
-1, 7
Let f = -1086283 + 1086286. Factor 0 + 6/7*d**f + 2/7*d**4 + 0*d + 0*d**2.
2*d**3*(d + 3)/7
Suppose 19*p = 4*z - 12818 + 12799, 4*z - 5*p - 5 = 0. Factor -4*b**5 + z*b**2 + 4/3*b**3 + 8/3*b**4 + 0 + 0*b.
-4*b**3*(b - 1)*(3*b + 1)/3
Let i(f) be the third derivative of f**7/315 - 26*f**6/45 - 24*f**5/5 - 278*f**2 + f. Solve i(a) = 0 for a.
-4, 0, 108
Let u be 75/15750*28 + 2/10. Factor u*i**2 + 14/3*i + 11.
(i + 3)*(i + 11)/3
Let h(o) be the third derivative of -4*o**2 + 0*o**3 + 0 - 3*o + 4/45*o**5 - 7/36*o**4 - 1/180*o**6. Determine d so that h(d) = 0.
0, 1, 7
Let h(m) = -34*m**2 + 10*m + 92. Let k(p) = -22*p**2 + 7*p + 62. Let t(x) = 5*h(x) - 8*k(x). Let n(w) = w**2 + 2*w. Let v(r) = 3*n(r) - t(r). Factor v(a).
-3*(a - 6)*(a + 2)
Let w(x) be the first derivative of -66 + 800/17*x + 40/17*x**2 + 2/51*x**3. Determine t, given that w(t) = 0.
-20
Suppose -3*k - 56*k = 26*k. Let w(g) be the first derivative of k*g + 1/3*g**3 - 7 + 1/2*g**2. Determine a, given that w(a) = 0.
-1, 0
Suppose -2*c - 15 = -4*a - 5, 4*a - 11 = c. Factor 254*v**2 - 254*v**2 - 3*v**4 - 3*v**a.
-3*v**3*(v + 1)
Suppose -184*t = 37*t - 663. Let l(w) be the first derivative of -2/9*w**2 + 18 - 2/27*w**t + 0*w + 1/18*w**4. Suppose l(q) = 0. What is q?
-1, 0, 2
Factor -46/3*x**2 - 2600/3 + 1/3*x**3 + 620/3*x.
(x - 26)*(x - 10)**2/3
Let x(p) be the second derivative of 8*p + 1/6*p**4 + 0 - 7*p**2 + 2/3*p**3 - 1/15*p**5 - 1/30*p**6. Let f(h) be the first derivative of x(h). Factor f(v).
-4*(v - 1)*(v + 1)**2
Suppose -82 = -6*w - 28. Suppose -3*v + 3*m + w = 0, -m = -2*m + 1. Factor -v*n**2 + 6*n**2 - n + 0*n**2 - 9*n**2.
-n*(7*n + 1)
Suppose -63*k - 132 = -6*k - 417. Suppose -4*w + w = -12. Solve 0 - 1/2*g**k - 5/2*g**w - 7/2*g**2 - 9/2*g**3 - g = 0 for g.
-2, -1, 0
Let s = 823 + -827. Let o be 32 + -40 - 109/s. Find l such that 9*l + 2*l**4 + o*l**2 + 27/2*l**3 + 5/4 = 0.
-5, -1, -1/2, -1/4
Suppose -12*q - 9 = -15*q. Suppose 14*n**3 - 12*n + n**q - 1264*n**5 + 1261*n**5 - 30*n**2 + 24 + 6*n**4 = 0. What is n?
-2, -1, 1, 2
Suppose -4*v + 4*v**4 - 160*v**3 + 462*v**2 + 10*v + 4*v**4 + 2*v - 616 - 6*v**4 = 0. What is v?
-1, 2, 77
Let k be 17/(17/36)*(-1)/(-3). Solve 100*n**3 - 375*n**2 + 137*n**3 + 3*n**5 - 45*n**4 - k*n**3 = 0 for n.
0, 5
Let s(b) = 5*b**4 - 34*b**2 + 40*b - 19. Let p(y) = -15*y**4 + 101*y**2 - 120*y + 56. Let q = -177 + 181. Let t(i) = q*p(i) + 11*s(i). Factor t(a).
-5*(a - 1)**3*(a + 3)
Factor