 - i**3 + 0*i**5 + 1/40*i**6 - 3/8*i**4. Factor x(n).
3*(n - 2)*(n + 1)**2
What is i in 34/7*i**3 - 2/7*i**5 + 360/7*i - 16/7*i**4 + 408/7*i**2 + 0 = 0?
-6, -1, 0, 5
Let x be 2 + ((-160)/(-22))/(-4). Let c = -311493 + 311498. Let 0 + 2/11*w**c + 2/11*w**2 - x*w**4 + 0*w - 2/11*w**3 = 0. What is w?
-1, 0, 1
Let f = 6154/7 + -24615/28. Let t(x) be the second derivative of f*x**4 - 1/14*x**3 + 0 + 0*x**2 + 16*x. Let t(h) = 0. What is h?
0, 1
Let b = 4472 - 4467. Let g(u) be the second derivative of 1/55*u**b + 0 - 4*u + 2/33*u**4 - 1/165*u**6 - 2/33*u**3 - 3/11*u**2. Suppose g(z) = 0. What is z?
-1, 1, 3
Let u(n) = -6*n**2 + 216*n + 436. Let i(j) = 32*j**2 - 1081*j - 2180. Let l(q) = 2*i(q) + 11*u(q). Factor l(s).
-2*(s - 109)*(s + 2)
Let z(o) be the third derivative of 2*o**5 - 1/24*o**6 + 0*o**3 - 10/3*o**4 - 2*o**2 + 0*o - 1/7*o**7 - 2 - 5/336*o**8. Let z(n) = 0. Calculate n.
-4, 0, 1
Factor -95/2*d**2 - 315*d + 0 + 5/6*d**3.
5*d*(d - 63)*(d + 6)/6
Let o(t) be the first derivative of t**3/27 + 5*t**2/6 - 76*t/9 - 822. Suppose o(z) = 0. What is z?
-19, 4
Let k = 331/245 - -3239/245. Factor 1734/7*x - k*x**2 - 9826/7 + 2/7*x**3.
2*(x - 17)**3/7
Let z(s) = 9*s**2 - 30*s - 63. Let g(f) = -16*f**2 + 59*f + 127. Let v(i) = 3*i**2 - 24*i - 3. Let m be v(8). Let d(w) = m*g(w) - 5*z(w). Factor d(t).
3*(t - 11)*(t + 2)
Let w = -80 + 85. Let c be w/(-10)*4*(-2 + 0). Suppose -8*l**4 + 2*l + 5*l**4 + 2*l**c + 3*l**2 = 0. Calculate l.
-1, 0, 2
Let c = 11998/1165 + -2120/233. Determine b so that 63/5*b**4 - c*b**2 - 183/5*b**3 + 72/5 + 204/5*b = 0.
-2/3, -3/7, 2
Let k(h) be the first derivative of -2/15*h**3 + 44 - 27/5*h**2 + 56/5*h. Let k(i) = 0. Calculate i.
-28, 1
Suppose -5169*a = 5*c - 5168*a + 3, 0 = -3*c + 3*a + 45. Factor 4/11*q**3 - 6/11*q**4 + 0 + 0*q + 2/11*q**c.
-2*q**2*(q - 1)*(3*q + 1)/11
Let a(y) = 45*y**4 + 80*y**3 + 15*y**2 - 30*y + 40. Let k(q) = 2*q**4 + q**3 + 4*q**2 + q - 2. Let c(s) = a(s) - 25*k(s). Let c(r) = 0. Calculate r.
-1, 1, 2, 9
Let r(j) = -j**3 - 25*j**2 - 139*j + 4. Let t(x) = 2*x**2 + x + 4. Let u(n) = -2*r(n) + 2*t(n). Factor u(a).
2*a*(a + 7)*(a + 20)
Suppose 13 = 4*z + 1. Let s be -5 - -3 - (-2 - 3). Suppose -z*j + 8*j**s + 4 - 3*j - 2*j**5 - 32*j**2 + 28*j**2 = 0. What is j?
-2, -1, 1
Let r(m) = -m**2 - 38*m - 217. Suppose 57 = -2*z - 5*b, b = 2*z + 2*b + 61. Let g be r(z). Factor -1/3*n**2 + g - 2/3*n.
-n*(n + 2)/3
Let g = 56333/33798 + -1/11266. Let s be (92/15)/2 - (-6)/(-15). Factor 4/3*p + 0 - 1/3*p**4 + g*p**3 - s*p**2.
-p*(p - 2)**2*(p - 1)/3
Let z(t) be the second derivative of -t**7/105 - 2*t**6/25 - 4*t**5/25 + t**4/15 + 3*t**3/5 + 4*t**2/5 + 132*t. Let z(l) = 0. Calculate l.
-4, -1, 1
Let n be (-4764)/132 - 5/(-55). Let t be n/(-48)*40/15. Factor 0*v + 2/3*v**t + 0.
2*v**2/3
Let u be 20/14*(-14)/(-10). Let o(x) be the first derivative of 0*x + 3/20*x**5 + 0*x**u + 3/8*x**4 + 15 + 1/4*x**3. Let o(j) = 0. Calculate j.
-1, 0
Let x = -48377/108 - -12110/27. Let -5/12*i**5 + 0 - 7/12*i**4 + 11/12*i**3 - 1/2*i + x*i**2 = 0. What is i?
-2, -1, 0, 3/5, 1
Let s = 8454 - 8450. Let l(q) be the third derivative of -5*q**2 + 0 + 0*q + 1/280*q**6 - 1/140*q**5 + 2/7*q**3 - 1/14*q**s. Find j, given that l(j) = 0.
-2, 1, 2
Let p(k) be the second derivative of k**7/315 + 2*k**6/15 + 77*k**5/150 - 332*k**4/45 + 108*k**3/5 - 416*k**2/15 + 1570*k + 1. Suppose p(i) = 0. Calculate i.
-26, -8, 1, 2
Let a(f) be the first derivative of f**6/6 - 74*f**5/5 + 603*f**4/2 + 2100*f**3 - 3159*f**2/2 - 27378*f + 7518. Factor a(c).
(c - 39)**2*(c - 2)*(c + 3)**2
Let l(t) = 214*t**2 - t. Let g be l(1). Suppose -217 + g = -2*f. Let -6/19*j**f - 4/19*j + 0 - 2/19*j**3 = 0. What is j?
-2, -1, 0
Let i be 42/672 - 100/(-448). Factor -1/7*r - i*r**4 + 1/7*r**5 + 0 + 2/7*r**2 + 0*r**3.
r*(r - 1)**3*(r + 1)/7
Solve 0 - 2*i + 11/5*i**2 - 1/5*i**3 = 0 for i.
0, 1, 10
Let x = -352 - -484. Determine s, given that -x*s**5 - 6*s**4 - 131*s**5 + 260*s**5 - 3*s**3 = 0.
-1, 0
Let d = 695 - 707. Let a(r) = -r**2 - 43*r - 372. Let v be a(d). Factor 0*j + v - 4/15*j**3 + 2/15*j**4 + 2/15*j**2.
2*j**2*(j - 1)**2/15
Let w = 4353 - 4353. Let o(j) be the third derivative of 20*j**2 + 1/15*j**3 + w*j + 1/40*j**4 + 1/300*j**5 + 0. Solve o(u) = 0.
-2, -1
Let r = 93303 - 93299. Let 18/7*g**r - 18/7*g**2 + 24/7 - 72/7*g + 48/7*g**3 = 0. What is g?
-2, 1/3, 1
Suppose 17*j = 12*j + 40. Suppose j*g = -15 + 39. Determine d, given that -15*d + 0*d - 2*d**3 - 16 - 12*d**2 - 9*d + 0*d**g = 0.
-2
Let u(i) be the first derivative of 4/5*i**3 + 0*i + 51 - 1/10*i**4 - 9/5*i**2. Suppose u(q) = 0. Calculate q.
0, 3
Let n(q) = -q**3 + 10*q**2 - 6*q - 2. Let t be n(9). Factor 20*m**2 + 3*m - 15 - 63*m**2 - 3*m**3 + 33*m**2 + t*m**2.
-3*(m - 5)*(m - 1)*(m + 1)
Factor -2/13*c**3 - 190/13*c**2 + 0*c + 0.
-2*c**2*(c + 95)/13
Let x(g) be the first derivative of g**5/15 - 7*g**4/6 - 64*g**3/3 - 169*g**2/3 - 161*g/3 + 2733. Determine s so that x(s) = 0.
-7, -1, 23
Factor -326/7*b - 400/7*b**2 + 18/7*b**3 + 92/7.
2*(b - 23)*(b + 1)*(9*b - 2)/7
Suppose 1/3*d**3 - 98/3 - 46/3*d**2 - 145/3*d = 0. What is d?
-2, -1, 49
Let y be -28*(-629)/3808 + 5/(-8). Factor 0*b**3 + 32/7 + 0*b + 2/7*b**y - 16/7*b**2.
2*(b - 2)**2*(b + 2)**2/7
Let i(o) be the second derivative of o**7/63 + 19*o**6/45 + 22*o**5/5 + 200*o**4/9 + 448*o**3/9 + 2427*o. Factor i(x).
2*x*(x + 4)**3*(x + 7)/3
Let o(c) be the second derivative of -c**3/3 - c**2/2 + 59*c. Let t(r) = r**2 - 58*r + 673. Let j(z) = -3*o(z) + t(z). Determine s, given that j(s) = 0.
26
Determine o so that -20407*o**2 - 75076*o + o**4 - 321*o**3 - 74*o**3 + 96031*o**2 - 154*o**3 = 0.
0, 1, 274
Let w be 2/9*(131 - -31)/18. Let -2/5 - 3/5*f - 1/5*f**w = 0. Calculate f.
-2, -1
Let o = 18984 + -18956. Let p(y) be the second derivative of 5/3*y**3 - 5/2*y**2 - o*y + 0 - 5/12*y**4. Factor p(q).
-5*(q - 1)**2
Let y(h) be the third derivative of 0*h + 0 + 12/5*h**3 + 7*h**2 - 8/15*h**4 + 1/30*h**5 + 1/300*h**6. Factor y(u).
2*(u - 2)**2*(u + 9)/5
Let j(x) be the first derivative of 8/5*x**5 + 10*x**2 + 16*x**3 + 26*x - 2/5*x**6 + 10*x**4 - 30. Let b(h) be the first derivative of j(h). Solve b(w) = 0.
-1, -1/3, 5
Suppose -19 = -0*v - v. Let i = -13590 - -13593. Factor -12*o**i - 5*o - v*o**4 - 15*o**2 + 34*o**4 + 17*o**3.
5*o*(o - 1)*(o + 1)*(3*o + 1)
Let c(j) = -22*j**3 - 2*j**2 + 10*j + 2. Let g(m) = 21*m**3 + 3*m**2 - 10*m - 1. Suppose -l - 1 - 3 = 0. Let x(z) = l*g(z) - 3*c(z). Factor x(w).
-2*(w + 1)*(3*w - 1)**2
Determine s, given that 248/7*s**2 + 4/7*s**3 + 0 + 480/7*s = 0.
-60, -2, 0
Let w(n) be the third derivative of 1/728*n**8 + 0*n - 8/65*n**5 + 16/13*n**3 - 16/39*n**4 + 0 + 5/273*n**7 + 134*n**2 + 3/65*n**6. Let w(a) = 0. Calculate a.
-6, -2, 2/3, 1
Suppose 0 = s - 3, 0 = 3*b + 4*s + 4 - 25. Let g be 10/(-45) + 2112/27. Factor -3*l**5 - 79*l**b + 4*l**5 + g*l**3.
l**3*(l - 1)*(l + 1)
Let x(p) = p**2 + 8*p - 161. Let i be x(10). Suppose -6*b = -i*b + 26. Determine w so that -25/4 - 1/4*w**b + 5/2*w = 0.
5
Let j(s) = s**3 - 14*s**2 + 50*s - 4. Let u be j(6). Suppose u*v = -2 - 6, v = -5*y + 19. Factor -y*k**3 + 16/3*k + 0 + 10/3*k**4 - 8/3*k**2 - 2/3*k**5.
-2*k*(k - 2)**3*(k + 1)/3
Let j(d) = -13*d**2 + 231*d + 18. Let x(w) = -24*w**2 + 461*w + 33. Let z(a) = 11*j(a) - 6*x(a). Let z(y) = 0. Calculate y.
0, 225
Let u(m) be the second derivative of -m**6/6 - 3*m**5/4 + 5*m**4/4 + 35*m**3/6 - 15*m**2 + 868*m. Determine d, given that u(d) = 0.
-3, -2, 1
Factor -25*l**2 - 24*l**2 - 28*l**2 - 15*l**4 + 70*l**3 + 12*l**2 - 30*l.
-5*l*(l - 3)*(l - 2)*(3*l + 1)
Let m be (329/(-42) - -8)/(2/24). Factor -31*z**m - 11*z**3 - 573*z + 4*z**3 - z**4 - 4*z**3 + 552*z.
-z*(z + 1)*(z + 3)*(z + 7)
Let i = -233 + 235. Find q such that 5*q**3 - 165*q**i + 260*q**2 + 28 - 4*q**4 + q**4 + 115*q = 0.
-4, -1, -1/3, 7
Let o(s) = -s**3 - 8*s**2 - 12*s + 4. Let q be o(-6). Suppose -5*u + 23 - 8 = 0. Factor -1/5*z**5 + 3/5*z**2 + 0 + z**u + 1/5*z**q + 0*z.
-z**2*(z - 3)*(z + 1)**2/5
Let p(b) = -b**2 + 4*b + 24. Let q be p(7). Let d(g) be the first derivative of -2/9*g**2 + 4 + 0*g - 2/27*g**q. Suppose d(n) = 0. What is n?
-2, 0
Let v(w) be the second derivative of -w**6/75 - 3*w**5/25 + 2*w**4 - 136*w**3/15 + 96*w**2/5 - 1342*w - 2. Let v(k) = 0. Calculate k.
-12, 2
Let b(v) = 6*v +