j(d) be the second derivative of -2/5*d**6 - 6 + 0*d**3 + 4/21*d**7 + 0*d**2 + 0*d**5 + 8*d + 1/3*d**4. What is s in j(s) = 0?
-1/2, 0, 1
Let p(r) = -3*r**3 - 2*r**2 - 3*r - 4. Let x be p(-2). Factor 6*j**3 + 9*j**3 + 3*j**4 + x*j**3 + 20*j**2 + 10*j**2.
3*j**2*(j + 1)*(j + 10)
Let s(q) = 9*q**2 - 36*q - 29. Let h(c) = 15*c**2 - 72*c - 59. Let k be 6/2 + (-53 - -54). Let l(z) = k*h(z) - 7*s(z). Factor l(v).
-3*(v + 1)*(v + 11)
Factor -189/2 + 3/8*o**3 + 495/8*o + 129/4*o**2.
3*(o - 1)*(o + 3)*(o + 84)/8
Let x be (-1 + 28)*(-57 + 58). Let s(i) = 3*i - 79. Let d be s(x). Find r such that -2/3*r**4 + 8/3*r**3 - 2/3 - 4*r**d + 8/3*r = 0.
1
Let j(m) be the third derivative of 1/180*m**5 + 0*m**4 + 0*m - 1/630*m**7 + 0*m**6 + 125*m**2 - 2 + 0*m**3. Factor j(p).
-p**2*(p - 1)*(p + 1)/3
Let w(t) = 2*t**2 + 20*t + 2. Let j be w(-10). Factor -3*a**j - 249 + 110 + 91 + 24*a.
-3*(a - 4)**2
What is z in 39*z + 1/8*z**2 + 311/8 = 0?
-311, -1
Let a(g) be the first derivative of 3*g**5/5 - 870*g**4 + 504600*g**3 - 146334000*g**2 + 21218430000*g + 629. Factor a(c).
3*(c - 290)**4
Solve -13/4*y**3 + 0 - 1/4*y**4 + 48*y - 4*y**2 = 0.
-8, 0, 3
Let o(n) = -9*n**4 + 14*n**3 + 20*n**2 - 46*n. Let q(r) = -10*r**2 + 5*r**4 + 35*r + 5*r - 7*r**3 - 16*r. Let k(i) = 4*o(i) + 7*q(i). Factor k(d).
-d*(d - 8)*(d - 1)*(d + 2)
Let n(o) = 3*o**3 + 7*o**2 + 8*o - 4. Let v(k) = 128 + 4*k + 8*k**2 + 4*k**3 - 130 + 5*k. Let h(m) = -5*n(m) + 4*v(m). Factor h(s).
(s - 3)*(s - 2)*(s + 2)
Suppose 4*y + 3*n = 23, -9*y + 6*y = -5*n + 19. Let p(g) be the second derivative of 0 - 5*g + 1/4*g**4 + g**3 - 9/2*g**y. Factor p(f).
3*(f - 1)*(f + 3)
Let x(h) = -23 + 1 + 28*h**2 + 22 - 4*h**3 - 30*h. Let t(a) = -7*a**3 + 56*a**2 - 59*a. Let n(m) = 3*t(m) - 5*x(m). Factor n(b).
-b*(b - 27)*(b - 1)
Let i(v) be the second derivative of -5/4*v**2 + 3/8*v**3 + 5/24*v**4 + 2*v - 9/80*v**5 - 1. Find z, given that i(z) = 0.
-1, 1, 10/9
Suppose -n + 120997*a - 120993*a = -66, 0 = -2*n + 4*a + 68. Find o, given that 1369/2 + 1/8*o**n + 37/2*o = 0.
-74
Let n = -26006 + 286075/11. Find g such that -5/11*g**4 - n*g**2 + 12/11*g**3 + 0 + 2/11*g = 0.
0, 2/5, 1
Let x(y) = -4*y + 32. Let f be x(6). Solve -f*j**3 - 24*j**5 - 14*j**4 + 6*j**5 - 26*j**4 - 24*j**5 = 0 for j.
-2/3, -2/7, 0
Let t(u) be the first derivative of -u**3/3 + 27*u**2/2 - 241. Factor t(x).
-x*(x - 27)
Suppose -3*z + 4*i = -107, 2*z + 5*i - 55 = 47. Factor -40*x**3 + 45*x**2 - 100*x - z*x**3 - 40*x**3 + 135*x**2 + 40*x**3.
-x*(9*x - 10)**2
Let l = -101198 + 101200. Factor 2/5*v**l + 22/5*v + 4.
2*(v + 1)*(v + 10)/5
Let g = -16775/7 + 220609/91. Let y = 2742/91 - g. Solve -y*v - 4/7*v**2 - 16/7 = 0 for v.
-2
Suppose 10*i + 28 - 22030*i**2 - 22021*i**2 + 44049*i**2 = 0. What is i?
-2, 7
Let o = 175690/9 + -1229794/63. Suppose 0 + 0*y**2 + 0*y + 24/7*y**3 - o*y**5 + 20/7*y**4 = 0. Calculate y.
-1, 0, 6
Let l(t) be the first derivative of 4*t**3/3 - 44*t**2 - 2567. Factor l(g).
4*g*(g - 22)
Factor t**3 - 247*t - 94*t**2 + 237*t + 85*t**2.
t*(t - 10)*(t + 1)
Factor -256/5 + 102/5*s + 13/5*s**2.
(s - 2)*(13*s + 128)/5
Let f(k) be the second derivative of -k**6/3 + 227*k**5/4 + 875*k**4/2 + 3530*k**3/3 + 1180*k**2 + 1250*k + 3. Suppose f(i) = 0. Calculate i.
-2, -1/2, 118
Factor -44/5 + 1/5*x**2 + 43/5*x.
(x - 1)*(x + 44)/5
Let a be ((-3266)/2556)/(3 - 114/36). Solve -1/3*m**2 - a - 8*m = 0 for m.
-23, -1
Let r = 510459 - 117915487/231. Let v = r + -68/33. Factor 0 - 2/7*m**3 + 2/7*m**4 - v*m**2 + 2/7*m.
2*m*(m - 1)**2*(m + 1)/7
Let z(p) = -11*p**3 - 5*p**2 - 59*p + 7. Let t(y) = -2*y**3 - y**2 - 10*y + 1. Let o be 9/(-3)*(-374)/(-33). Let x(h) = o*t(h) + 6*z(h). Factor x(q).
2*(q - 1)**2*(q + 4)
Suppose -30 = 6*k - 21*k. Suppose k*u - 4*n - 10 = -16, 3*u + 3*n = 18. Find w such that 0*w + 0*w**2 + 25/2*w**u + 5/2*w**4 + 0 = 0.
-5, 0
Let o(n) be the first derivative of -3*n**5/5 - 7743*n**4/2 - 6666721*n**3 - 19976940*n**2 - 19969200*n + 8008. Factor o(g).
-3*(g + 1)**2*(g + 2580)**2
Let h = -30 + 61. What is l in -22*l**4 + 5*l + 15*l**2 + 0*l**2 + 26*l**3 - h*l**3 + 7*l**4 = 0?
-1, -1/3, 0, 1
Let b(l) = 2*l**5 - 1314*l**4 - 112860*l**3 - 326640*l**2 - 6*l - 6. Let c(i) = -i**5 - 3*i**4 - 10*i**2 + i + 1. Let j(o) = b(o) + 6*c(o). Factor j(f).
-4*f**2*(f + 3)*(f + 165)**2
Find g, given that -5145*g**3 + 5149*g**3 + 171*g - 26 + 54*g**2 - 147*g = 0.
-13, -1, 1/2
Let b be (-1)/((-48)/(-374)) - (2*-12)/3. Let c(z) be the third derivative of -1/24*z**6 - 1/12*z**5 + 0 - 40*z**2 + 0*z + b*z**4 + 5/6*z**3. Factor c(i).
-5*(i - 1)*(i + 1)**2
Let g be ((-621)/(-36) + -17)*(1 + -2)*144/(-54). Determine w so that -g + w - 1/3*w**2 = 0.
1, 2
Factor 657072*u**2 + 0*u + 5619/4*u**4 - 658476*u**3 + 0 - 3/4*u**5.
-3*u**2*(u - 936)**2*(u - 1)/4
Let x(a) be the first derivative of a**6/2 + 31*a**5/5 + 91*a**4/4 + 27*a**3 + 9*a**2 + 2257. Determine p, given that x(p) = 0.
-6, -3, -1, -1/3, 0
Find p, given that 324/7*p**2 - 640/7*p**5 + 0 - 1184/7*p**4 - 234/7*p**3 + 0*p = 0.
-9/8, 0, 2/5
Let q = -2343461/11 - -213047. Factor q - 2/11*f**2 + 24/11*f.
-2*(f - 14)*(f + 2)/11
Let j = 672811 - 3364053/5. Solve 4/5*t**4 + j*t - 2*t**3 - 2/5 + 6/5*t**2 = 0.
-1/2, 1
Let f = 309 - 289. Find l, given that 26*l**3 + 18*l - 26*l**3 - f*l**3 + 2*l**5 = 0.
-3, -1, 0, 1, 3
Suppose 98*v = -71 + 105 + 260. Let i(l) be the first derivative of 9/34*l**4 + 50/17*l - 14/17*l**v + 31 - 5/17*l**2. Determine k, given that i(k) = 0.
-1, 5/3
Let z(s) be the second derivative of -s**6/10 - 3*s**5/20 + 3*s**4/4 + s**3/2 - 3*s**2 + 83*s + 1. Factor z(h).
-3*(h - 1)**2*(h + 1)*(h + 2)
Let c(z) = -7*z**2 - 31*z - 124. Let a(n) = 8*n**2 + 33*n + 133. Let m(k) = 6*a(k) + 7*c(k). Suppose m(p) = 0. Calculate p.
-14, -5
Let v = 20 - 10. Find p, given that -2*p**4 + 5*p**2 + 35*p + v*p**2 - 30 - 3*p**4 - 15*p**3 + 0*p**4 = 0.
-3, -2, 1
Suppose 5*a - 9 - 6 = 0. Suppose -3*o + a*c = 4*c - 64, 0 = 3*o + 4*c - 49. Factor -22*b**2 - b**4 - 5*b + 4*b + o*b**2 + b**3.
-b*(b - 1)**2*(b + 1)
Let y(u) be the second derivative of 2*u - 1/8*u**3 - 7/48*u**4 - 1/16*u**5 - 1/120*u**6 + 0*u**2 + 51. Factor y(g).
-g*(g + 1)**2*(g + 3)/4
Let w be 79 - ((-22)/(-33) + 8/(-3)). Factor -36 - 82*d**2 - 75*d**2 + 33*d - w*d**2 + 241*d**2.
3*(d - 1)*(d + 12)
Let w be (-144)/630*(-175)/100. Find j such that 14/5*j**3 + 0*j + w*j**4 + 12/5*j**2 + 0 = 0.
-6, -1, 0
Factor 198/13*b**2 + 2/13*b**4 + 194/13*b + 70/13*b**3 + 64/13.
2*(b + 1)**3*(b + 32)/13
Suppose -17*g = 21*g + 27*g. Factor -1/2*r**4 - 1/4*r + 0*r**3 + 1/4*r**5 + g + 1/2*r**2.
r*(r - 1)**3*(r + 1)/4
Let s(x) be the third derivative of -1/240*x**5 - 625/6*x**3 - 2*x + 0 - 25/24*x**4 + 3*x**2. Factor s(t).
-(t + 50)**2/4
Let d be 30*(0 - (-2)/25). Suppose 0 = 5*y + 5*z - 70, -111*y - 34 = -112*y - 3*z. Factor -9/5*j**3 + 0*j**2 + 0 + d*j + 3/5*j**y.
3*j*(j - 2)**2*(j + 1)/5
Let q = -6400 - -6403. Let t(p) be the second derivative of -16*p + 0 - 2/9*p**q - 5/9*p**2 - 1/54*p**4. Determine m, given that t(m) = 0.
-5, -1
Let l = -2822/311 + 21620/2177. Factor -12/7*i**4 + l*i - 12/7*i**3 + 9/7*i**2 - 3/7.
-3*(i + 1)**2*(2*i - 1)**2/7
What is g in -26*g - 5*g**3 + 0*g**3 - 125*g**2 - 135 + 262*g + 0*g**3 + 29*g = 0?
-27, 1
Suppose -3*j = -9*q + 13*q + 3, 3*q + 11 = -4*j. Let o be (-1)/7 + 115/315. Suppose -2/9*f**2 - 8/9*f**q + 8/9*f + o = 0. Calculate f.
-1, -1/4, 1
Let t = 2829/5 + -19713/35. Find y such that -3*y + 9/7*y**3 + t + 3/7*y**4 - 9/7*y**2 = 0.
-3, -2, 1
Let g(d) be the first derivative of 2*d**5/5 - 9*d**4 + 54*d**3 - 1029. What is a in g(a) = 0?
0, 9
Suppose 3*z = 6*i + 69, -4*z = 5*i - 653 + 691. Suppose 0 - 19/4*a**z + 0*a + 9/2*a**2 + 1/4*a**4 = 0. What is a?
0, 1, 18
Let s = -96 - -312. Let z = s + -143. Factor 36*a**3 + 15*a**2 + 32*a**3 - z*a**3 - 10*a.
-5*a*(a - 2)*(a - 1)
Let w be 9 + (-1573)/221 - (-4)/34. Let n = 61 - 32. Suppose 65*f - f**3 + 2 - 2*f**w - 35*f - n*f = 0. What is f?
-2, -1, 1
Let j be (-85)/20 - 9/(-2). Let q(d) be the third derivative of 3/2*d**3 - j*d**4 + 0*d + 0 + 32*d**2 + 1/60*d**5. Let q(f) = 0. What is f?
3
Factor 11776/11 - 1984/11*r + 10*r**2 - 2/11*r**3.
-2*(r - 23)*(r - 16)**2/11
Let g(d) be the third derivative of -d**5/12 - 15*d**4/2 - 150*d**3 + 1072*d**2. Factor g(v).
-5*(v + 6)*(v + 30)
Let o be 488/11712 - 3/1