k, given that -9*k**2 - 4 - 31/3*k - 1/3*k**4 - 3*k**3 = 0.
-4, -3, -1
Let j(f) be the first derivative of -f**6/3 - 208*f**5/5 - 611. Suppose j(v) = 0. Calculate v.
-104, 0
Let z(d) be the second derivative of d**4/54 - 13*d**3/9 + 224*d**2/9 - 97*d - 7. Find j such that z(j) = 0.
7, 32
Suppose -12 = -2*s + s. Let o = -142759/2 - -71380. Factor 96*x + o*x**3 - 256 - s*x**2.
(x - 8)**3/2
Suppose 4*v + 1172 = 5*w, 937 = -6*w + 10*w - 3*v. Solve 29 - 8*o**3 + 115 + w*o - 68*o**2 - 12 = 0.
-11, -1/2, 3
Let n(d) be the first derivative of 1/15*d**5 + 1/4*d**4 - 1/2*d**2 - 53 - 1/9*d**3 + 0*d. What is m in n(m) = 0?
-3, -1, 0, 1
Let v be (120/100)/(((-4)/(-10))/1). Let -732*k**3 - v*k + 734*k**3 - 2 + 2*k**2 + k = 0. What is k?
-1, 1
Let p(i) = -7*i**2 - 147*i - 1296. Let j(n) = 6*n**2 + 146*n + 1296. Suppose 0 = 21*u + 13 + 50. Let f(b) = u*j(b) - 2*p(b). Factor f(a).
-4*(a + 18)**2
Let t = 6 - 3. Suppose t*v = 3*z, -z - 5*v + 3 = -9. Factor -16 + 0*s**2 - z*s**2 - 8*s + s**2.
-(s + 4)**2
Let q(a) = 28*a**2 - 1036*a - 471. Let f(b) = 7*b**2 - 241*b - 118. Let c(j) = -18*f(j) + 4*q(j). Factor c(h).
-2*(h - 15)*(7*h + 8)
Let r(a) be the third derivative of a**7/1260 - a**6/24 + 7*a**5/30 - a**4/24 + a**3/2 + 3*a**2 - 11. Let n(d) be the second derivative of r(d). Factor n(o).
2*(o - 14)*(o - 1)
Let c(s) = 2*s**3 - 6*s**2 - 5*s. Let j = -184 + 181. Let b(l) = -3*l**3 + 7*l**2 + 6*l. Let a(o) = j*b(o) - 4*c(o). Determine f, given that a(f) = 0.
-2, -1, 0
Let i be 117/(-12) + 9/(-36). Let p(l) = l + 19. Let j be p(i). Solve -36*d + 0*d**2 + 38*d - j*d**2 = 0 for d.
0, 2/9
Let d = 16684/37701 - -8/4189. Solve -d*g**3 - 1/9*g**4 - 2/9*g + 0 - 5/9*g**2 = 0 for g.
-2, -1, 0
Let h be ((-68)/10)/(16/(-60)) + (-12 - -9). Factor 5 - 55/2*n**2 + h*n.
-5*(n - 1)*(11*n + 2)/2
Let n be (-144)/(-360) - (-261)/2210. Let o = n + -4/221. Find v such that v**2 + 2*v - o*v**3 - 4 = 0.
-2, 2
Solve -1568 + 48*f**2 - f**4 - 606*f + 114*f - 374*f - 674*f + 19*f**3 = 0.
-8, -1, 14
Let z(d) be the third derivative of -18*d**7/175 + 111*d**6/5 - 368*d**5/25 - 37*d**4/3 + 82*d**3/5 + 72*d**2 + 4. Find n, given that z(n) = 0.
-1/3, 1/3, 123
Let s be ((-9)/2)/((-42)/84). Let w be 3/9*s/4. Solve -3/8*k**5 + 0*k**4 - 9/2*k + w*k**2 + 21/8*k**3 - 3 = 0 for k.
-2, -1, 2
Let b(t) = -t**3 + 16*t**2 + 37*t - 14. Let z be b(18). Determine m so that 4*m - z*m**3 - 100 + 164*m**2 - 40*m**2 - 24*m**2 = 0.
-1, 1, 25
Let q = 713110 - 713108. Factor 12/7*y - 4/7*y**q + 40/7.
-4*(y - 5)*(y + 2)/7
Let f(s) be the third derivative of -s**8/3024 - 17*s**7/378 - 83*s**6/1080 + 17*s**5/108 + 7*s**4/18 + s**2 + s + 219. Let f(i) = 0. Calculate i.
-84, -1, 0, 1
Let k(a) be the third derivative of a**6/300 + 2*a**5/5 - 319*a**4/60 + 26*a**3 - a**2 - a + 37. Factor k(z).
2*(z - 3)*(z - 2)*(z + 65)/5
Let a = -20 - -20. Suppose 2307 = -12*x + 2331. Let a - 8/9*u - 2/9*u**x = 0. What is u?
-4, 0
Let z(d) be the second derivative of d**4/60 - 31*d**3/15 - 64*d**2/5 - 1214*d. Find f such that z(f) = 0.
-2, 64
Let s be (2703/540 - 5)*2. Let n(v) be the second derivative of 0 - 1/36*v**4 + s*v**6 + 0*v**3 + 0*v**2 + 0*v**5 + 8*v. Factor n(j).
j**2*(j - 1)*(j + 1)/3
Let y = 7 - 4. Suppose -3*p - 1 = -s + 2*s, 0 = -4*s + p + 9. Let 6*a**3 + 4*a + s*a**y + 9*a**2 - 6 + 5*a**2 - 4*a**3 = 0. What is a?
-3, -1, 1/2
Solve 625/3*x**2 + 4/3*x**4 + 67*x**3 + 235/3 + 221*x = 0 for x.
-47, -5/4, -1
Let w(s) be the third derivative of s**4/6 - 7*s**3/3 + 16*s**2. Let o be w(4). Factor 6 - 4*f**2 + f - 5*f**2 + 7*f**o + 3*f.
-2*(f - 3)*(f + 1)
Find m, given that 2696/17*m + 10/17*m**2 - 1080/17 = 0.
-270, 2/5
Let q(x) be the second derivative of 3/2*x**2 + 44*x - 1/140*x**5 + 0 + 1/7*x**3 - 1/56*x**4. Let w(n) be the first derivative of q(n). Factor w(h).
-3*(h - 1)*(h + 2)/7
Find j, given that 140/9*j**2 - 32/9*j - 14/9*j**4 - 94/9*j**3 + 0 = 0.
-8, 0, 2/7, 1
Let f(a) = 3*a**2 + 39*a + 311. Let p(d) = 10*d**2 + 118*d + 940. Let t(l) = -16*f(l) + 5*p(l). Factor t(w).
2*(w - 23)*(w + 6)
Suppose -3*q - l = 24, -l = -8*q + 9*q + 10. Let z(b) = 3*b**2 - 9*b + 6. Let m(y) = -3*y**2 + 10*y - 7. Let x(n) = q*z(n) - 6*m(n). Solve x(p) = 0.
0, 1
Let y be (-105)/20*(481/(-9) - 1). Let v = -569/2 + y. Factor 10/3*t**2 - 4/3 + 2/3*t + v*t**3.
2*(t + 1)*(t + 2)*(2*t - 1)/3
Let a(t) be the second derivative of 3 - 16/51*t**4 - 1/170*t**5 + 67/51*t**3 - 2*t**2 + 16*t. Let a(z) = 0. Calculate z.
-34, 1
Factor -81/8*m**2 + 561/8 - 477/8*m - 3/8*m**3.
-3*(m - 1)*(m + 11)*(m + 17)/8
Let y(d) be the first derivative of -2*d**3/3 + 5*d**2 + 28*d + 168. Find v, given that y(v) = 0.
-2, 7
Suppose 100*o - 6896 = -6696. Factor 40 + 2/5*w**3 - 38/5*w**o + 32*w.
2*(w - 10)**2*(w + 1)/5
Let r(k) = 5*k**2 - 12605*k + 3269822. Let x(c) = -3*c**2 + 8407*c - 2179882. Let m(f) = 5*r(f) + 7*x(f). Solve m(z) = 0.
522
Let w(l) be the first derivative of l**4/10 - 4*l**3/3 - l**2/5 + 4*l + 59. Factor w(f).
2*(f - 10)*(f - 1)*(f + 1)/5
Factor -3362/5 - 164/5*n - 2/5*n**2.
-2*(n + 41)**2/5
Solve -1/4*p**2 - 42*p - 167/4 = 0.
-167, -1
Let f(l) be the third derivative of l**8/336 - 11*l**7/210 + 3*l**6/20 + l**5/30 - 19*l**4/24 + 3*l**3/2 - 2951*l**2. Determine r so that f(r) = 0.
-1, 1, 9
Let p(u) = -u**2 + 114*u - 739. Let x be p(7). Let b(z) be the first derivative of 8*z + x - 3/2*z**4 + 0*z**2 - 14/3*z**3. Factor b(w).
-2*(w + 1)*(w + 2)*(3*w - 2)
Let y = 405349 + -2842986/7. Let q = y - -793. Find n such that 16/7*n**3 - 20/7*n**2 - 4/7*n**4 + q*n + 0 = 0.
0, 1, 2
Let r(b) = -410*b**2 + 48*b - 3. Let n(p) = 5332*p**2 - 624*p + 40. Let g(l) = 3*n(l) + 40*r(l). Factor g(o).
-4*o*(101*o - 12)
Let r be (-5)/(-60) + (-38390)/(-792) + -33. Factor -r*k**2 - 4/9*k**4 + 0 - 44/9*k**3 - 100/9*k.
-4*k*(k + 1)*(k + 5)**2/9
Let z(j) be the second derivative of -j**5/20 + j**4/12 - j**3/6 - j**2/2 + 99*j. Let o(w) = -4*w**3 - 17*w**2 - 3*w - 3. Let k(i) = o(i) - 3*z(i). Factor k(l).
-l**2*(l + 20)
Let 658*b - 716*b**3 + 12 + 338*b**4 + 399*b**5 - 274*b**3 - 350*b**2 - 67*b**5 = 0. Calculate b.
-2, -1, -3/166, 1
Let h = -19585 - -19589. Let z(v) be the second derivative of 0 - 1/48*v**h + 0*v**2 - 1/4*v**3 - 2*v. Suppose z(y) = 0. What is y?
-6, 0
Let n = 207321/40 - 5183. Let o(j) be the third derivative of 1/80*j**6 + 1/4*j**3 - 19*j**2 - 1/16*j**4 + 0 + 0*j - n*j**5. Factor o(i).
3*(i - 1)**2*(i + 1)/2
Let 1276/13*k - 1278/13 + 2/13*k**2 = 0. Calculate k.
-639, 1
Let b(y) be the third derivative of -361/12*y**5 - 10/3*y**3 + 0*y - 95/6*y**4 - 50*y**2 + 0. Find r such that b(r) = 0.
-2/19
Find b such that -9*b**2 - 3/7*b**5 + 75/7*b**3 - 9/7*b**4 + 0*b + 0 = 0.
-7, 0, 1, 3
Let h = -588 + 592. Factor -k**5 - 180*k**3 - 8 - k**4 + 10*k**2 + 179*k**3 - 2*k**h + 4*k - k**4.
-(k - 1)**2*(k + 2)**3
Factor z**4 + 13*z**2 - 12*z**2 - 9*z**2 - 16*z + 16 - 5*z**4 + 16*z**3 - 4*z**2.
-4*(z - 2)**2*(z - 1)*(z + 1)
Let m(d) be the first derivative of 20/7*d + 1/3*d**3 - 1/28*d**4 + 2*d**2 + 52. Suppose m(a) = 0. Calculate a.
-2, -1, 10
Let j(z) be the first derivative of z**2 + 41*z - 14. Let h be j(-18). Factor -6*g**5 - 6*g**h + 12*g**2 + 15*g**5 - 9*g**4.
3*g**2*(g - 2)**2*(g + 1)
Let s(a) = 2332*a**2 + 499*a + 2. Let m(o) = -2336*o**2 - 500*o - 7. Let c(n) = -5*m(n) - 4*s(n). Factor c(y).
3*(28*y + 3)**2
Determine l so that 104 - 158*l + 56*l + 136 + 3*l**3 - 15*l**2 = 0.
-5, 2, 8
Let d(u) be the third derivative of -3*u**7/140 + 23*u**6/40 + 33*u**5/40 - u**4 + 15*u**2 + 27. Let d(c) = 0. What is c?
-1, 0, 1/3, 16
Suppose 30*t**4 + 510*t**3 + 1650 + 12*t**4 + 310*t**2 - 2715*t + 1013*t**5 + 206*t**2 - 1016*t**5 = 0. Calculate t.
-5, 1, 22
Let a(h) = h**3 - 3*h**2 - 9*h - 2. Let j be a(5). Let l(d) be the first derivative of 5*d**3 + 4 - 100*d + 91*d - 6*d**j + 6*d**2. Factor l(b).
-3*(b - 3)*(b - 1)
Let d be (-156)/(-24) - (-5)/3. Let z(g) be the first derivative of 4*g**2 + 20*g**3 + 61/2*g**4 + 0*g - d*g**6 + 21/5*g**5 + 35. Determine h so that z(h) = 0.
-1, -2/7, 0, 2
Let k(i) = 6*i**2 - 96*i + 8*i - 58*i + 4915 - 28*i + 34*i. Let x(s) = 7*s**2 - 140*s + 4918. Let r(l) = 6*k(l) - 5*x(l). Factor r(v).
(v - 70)**2
Determine t so that -4/3 - 5/3*t**4 + 41/3*t - 49/6*t**3 - 5/2*t**2 = 0.
-4, -2, 1/10, 1
Let z(h) be the third derivative of 0 - 1/3*h**3 - 7/270*h**5 + 156*h**2