00/1600. Determine i, given that 3*i**3 - 3 + 6*i**l - 3*i**4 - 3/2*i**5 - o*i = 0.
-2, -1, 1
Suppose 1550*f - 1545*f = 0. Let l(y) be the second derivative of f*y**2 + 1/11*y**3 - 8*y + 1/66*y**4 + 0. Find j such that l(j) = 0.
-3, 0
Let l(b) = b**4 - b**3 - 3*b**2 + 2. Let g(n) = -n**3 - n**2 + 1. Suppose 0 = -2*o - 11 + 9. Let k(z) = o*g(z) + l(z). Factor k(d).
(d - 1)**2*(d + 1)**2
Factor 13/8*y**2 - 8*y + 1/8*y**3 + 17/2.
(y - 2)**2*(y + 17)/8
Let n(f) be the second derivative of -6*f + 0 + 2/17*f**3 - 5/17*f**2 - 1/102*f**4. What is u in n(u) = 0?
1, 5
Let o = 31592/5 - 6238. Let k = 4472/55 - o. Factor 0 - k*b**4 - 32/11*b**3 + 0*b + 50/11*b**5 - 8/11*b**2.
2*b**2*(b - 1)*(5*b + 2)**2/11
Let q = 11 - -5. Let t be (3/(-2))/((-4)/q). Suppose -6*h**3 - 3*h**5 + 3*h + t*h**4 - 3*h - 15*h**4 = 0. Calculate h.
-2, -1, 0
Let y = -2/22293 + 9474533/89172. Let f = 107 - y. Determine l, given that 0*l**3 - 3/4*l**2 + 0 + f*l**4 + 0*l = 0.
-1, 0, 1
Let f(t) be the third derivative of -13*t**5/15 - 11*t**4/3 + 16*t**3/3 - 50*t**2. Solve f(g) = 0.
-2, 4/13
Factor 350/3*f**4 - 220/3*f**3 - 344/3*f**2 - 80/3*f + 0.
2*f*(5*f + 2)**2*(7*f - 10)/3
Suppose -4*u - 5*k = -23, 9 = -u + 4*k - 1. Find x such that -4*x - 10*x**3 + 22*x**u - 6*x**2 - 6*x**3 = 0.
0, 1/2
Suppose 4*l = 13 - 5. Let g = -115/3 - -39. Find b such that 4/3*b**l + 5/3*b + 1/3*b**3 + g = 0.
-2, -1
Let z(l) be the first derivative of -2*l**6/15 - l**5/5 + l**4/3 + 2*l**3/3 - 4*l + 4. Let v(r) be the first derivative of z(r). Factor v(f).
-4*f*(f - 1)*(f + 1)**2
Let g(x) be the third derivative of -x**8/1344 - x**7/168 - x**6/72 + 11*x**4/24 + 20*x**2. Let a(k) be the second derivative of g(k). Factor a(z).
-5*z*(z + 1)*(z + 2)
Let q(o) be the third derivative of 0 - 45*o**2 - 17/448*o**8 + 0*o**3 + 0*o**5 + 0*o**6 + 1/140*o**7 + 0*o + 0*o**4. Determine d, given that q(d) = 0.
0, 2/17
Let y(b) be the second derivative of b**6/180 - b**4/24 + b**3/18 + 98*b. Determine i, given that y(i) = 0.
-2, 0, 1
Let r(t) be the second derivative of 0 + 6*t**2 + 18*t - 5/2*t**3 + 1/4*t**4. Factor r(b).
3*(b - 4)*(b - 1)
Let z be (-26 + 26)*13/52. Solve z - 2/3*t - 1/6*t**2 = 0.
-4, 0
Let t(i) be the third derivative of -i**5/12 - 35*i**4/6 - 490*i**3/3 + 23*i**2 - 3*i. Factor t(y).
-5*(y + 14)**2
Let 60*j**4 - 381*j**3 + 251*j**2 + 234*j**2 + 36*j**3 - 215*j + 37 - 7 - 15*j**4 = 0. What is j?
1/3, 1, 6
Let u be ((-285)/(-27) - (-2)/(-2))*-3. Let j = u + 31. Find r such that -2/3*r**3 - r - j*r**2 + 0 = 0.
-3, -1/2, 0
Let b = 207 + -290. Let k = 88 + b. Solve 4/11*z**4 + 0 + 2/11*z**k - 2/11*z + 0*z**3 - 4/11*z**2 = 0 for z.
-1, 0, 1
Let k(m) be the third derivative of -m**5/210 - 23*m**4/14 - 1587*m**3/7 - 77*m**2. Factor k(n).
-2*(n + 69)**2/7
Let k(f) be the third derivative of -119*f**5/90 - 16*f**4/9 + 28*f**3/9 + 17*f**2 + 9. Suppose k(t) = 0. What is t?
-14/17, 2/7
Suppose 3*h + 3*w + 12 = 0, h + 6 = w - 3*w. Let m(y) = -13*y - 22. Let g be m(h). Factor 0 - 7/3*k**g - 13/3*k**2 + 17/3*k**3 + k.
-k*(k - 1)**2*(7*k - 3)/3
Let t(h) = 25*h**4 + 15*h**3 - 115*h**2 - 195*h - 80. Let z(j) = 8*j**4 + 5*j**3 - 38*j**2 - 65*j - 27. Let x(v) = 3*t(v) - 10*z(v). Factor x(g).
-5*(g - 3)*(g + 1)**2*(g + 2)
Let g(h) be the first derivative of -3/35*h**5 + 0*h**2 + 0*h + 42 + 2/7*h**3 + 3/28*h**4. Factor g(a).
-3*a**2*(a - 2)*(a + 1)/7
Find w such that 2/13*w**3 + 0 + 0*w - 2/13*w**2 = 0.
0, 1
Suppose 5*p - 81 = -66. Find y, given that -11*y + 2*y**3 - 7*y**3 + 2*y**p + 14*y = 0.
-1, 0, 1
Let b(i) = i**3 + i**2 + 1. Let q be ((-1)/(-2))/(3/6). Let d(j) = -22*j**3 + 58*j**2 - 39*j + 12. Let g(y) = q*d(y) - 3*b(y). Factor g(k).
-(k - 1)*(5*k - 3)**2
Let v(u) be the first derivative of u**7/105 + u**6/180 - 2*u**3/3 + 7. Let o(y) be the third derivative of v(y). Determine b so that o(b) = 0.
-1/4, 0
Let p(q) = -13*q**3 - 37*q**2 - 45*q - 16. Let d = -36 + 31. Let n(u) = 6*u**3 + 18*u**2 + 22*u + 8. Let w(g) = d*n(g) - 2*p(g). Factor w(z).
-4*(z + 1)**2*(z + 2)
Let b(v) be the first derivative of 2*v**5/55 - 5*v**4/11 + 64*v**3/33 - 32*v**2/11 + 111. Factor b(k).
2*k*(k - 4)**2*(k - 2)/11
Let l(h) = 4*h**2 - 16*h - 35. Let j(t) = -3*t**2 + 16*t + 31. Let u(n) = -5*j(n) - 4*l(n). Determine d so that u(d) = 0.
-15, -1
Let q = 26887 + -26884. Factor 147/2*g**5 + 60*g + 705/2*g**q - 6 - 435/2*g**2 - 525/2*g**4.
3*(g - 1)**3*(7*g - 2)**2/2
Let c(i) = -8*i + 232. Let r be c(29). Let s(t) be the second derivative of 0 + 1/24*t**4 - 9*t + 0*t**2 + r*t**3 + 0*t**5 - 1/60*t**6. Factor s(w).
-w**2*(w - 1)*(w + 1)/2
Suppose -v - 12 = 3*v + l, -3*v - 2 = -l. Let j(w) = -5*w - 10. Let a be j(v). Factor 0*y**2 + 2/3*y**4 + 0*y**3 + 0 + a*y + 2/3*y**5.
2*y**4*(y + 1)/3
Let i(m) = -15*m**3 - 36*m**2 + 29*m. Let n(x) = 4*x**3 + 9*x**2 - 7*x. Let p(u) = 3*i(u) + 11*n(u). Let p(d) = 0. What is d?
-10, 0, 1
Let n = -957/5 + 192. Let i = -3235 - -3238. Suppose -6/5*x**i + 0*x**2 + 3/5*x**4 + 6/5*x - n = 0. What is x?
-1, 1
Let k(m) = -m**4 - m**2 - 2*m. Let g(f) = f**5 - 40*f**4 - 142*f**3 - 225*f**2 - 161*f - 37. Let h(v) = -4*g(v) + 28*k(v). Factor h(j).
-4*(j - 37)*(j + 1)**4
Let i(g) be the second derivative of -1/80*g**5 + 0 - 1/24*g**4 - 10*g + 0*g**2 - 1/24*g**3. Factor i(y).
-y*(y + 1)**2/4
Let l = 78 - 542/7. Let p(i) be the first derivative of -l*i**2 - 2/21*i**3 - 8/7*i + 3. Determine a, given that p(a) = 0.
-2
Suppose 0 = -4*x + z + 7, -13 = -5*x - 5*z + 2. What is q in -5*q**3 - 55 + 112 - 3*q**x - 53 + 5*q - q**4 = 0?
-4, -1, 1
Let c(a) be the first derivative of -8 - 1/12*a**3 + 1/20*a**5 + 1/4*a**2 - 1/8*a**4 + 0*a. Find k, given that c(k) = 0.
-1, 0, 1, 2
Let s be (-6)/4*(0 + -2). Let n = -1 + s. Factor -2*i**n - 6*i + 3*i + i.
-2*i*(i + 1)
Suppose -36 = -3*a - 4*l, -a + 14 = -0*a + 2*l. Let g(w) = 5*w**2 + 6*w - 8. Let d(j) = -2*j**2 - 2*j + 3. Let h(t) = a*d(t) + 3*g(t). Factor h(k).
-k*(k - 2)
Factor 102/13*j - 2/13*j**2 + 8.
-2*(j - 52)*(j + 1)/13
Let u = -112 - -673/6. Factor 1/6*f - u*f**3 - 1/6*f**2 + 0 + 1/6*f**4.
f*(f - 1)**2*(f + 1)/6
Suppose 0 = 3*y + 5*j - 9, 0 = 2*y - y - j - 3. Let z be 28*2/(4 - (1 - y)). Determine r so that -4*r + 8/3 - z*r**3 - 16*r**2 = 0.
-1, 2/7
Let a(v) be the first derivative of -11 - 2*v - 1/18*v**3 - 2/3*v**2. Suppose a(m) = 0. What is m?
-6, -2
Let z(b) = -2*b**2 + 7*b + 7. Let p be z(4). Let c(u) = -u**3 + 27*u**2 + 27*u + 30. Let r be c(28). Let -q**p + 9/4 - 23/4*q**r - 15/2*q = 0. Calculate q.
-3, 1/4
Let b = 8 + -5. Factor -4*j + 2*j**b - 12*j**2 + 5*j + 15*j.
2*j*(j - 4)*(j - 2)
Let k(s) be the third derivative of 0 + 0*s + 3/20*s**5 + 1/2*s**4 - 8*s**2 + 1/70*s**7 - 1/10*s**6 - 2*s**3. Suppose k(a) = 0. Calculate a.
-1, 1, 2
Suppose -3*v + v = 4*a, v + 15 = -5*a. Let v*f - 5*f**2 - 18 - 22 + 50 - 15 = 0. What is f?
1
Let p(r) = -4*r**5 - r**4 - 3*r**3 + 15*r**2 - 7*r. Let l(b) = 2*b**5 + b**4 + b**3 - 7*b**2 + 3*b. Let x(v) = 7*l(v) + 3*p(v). Factor x(i).
2*i**2*(i - 1)*(i + 1)*(i + 2)
Let u(x) be the first derivative of -x**6/6 - 5*x**5/4 - 15*x**4/4 - 35*x**3/6 - 5*x**2 - x - 4. Let f(q) be the first derivative of u(q). Solve f(z) = 0 for z.
-2, -1
Let m(p) be the second derivative of -p**4/36 - 7*p**3 - 125*p**2/6 + p + 343. Factor m(x).
-(x + 1)*(x + 125)/3
Factor -5*f**3 + 560*f - 5*f**4 + 27*f**2 + 27*f**2 + 127*f**2 + 64*f**2 - 45*f**2.
-5*f*(f - 7)*(f + 4)**2
Let g(n) be the third derivative of 0*n**5 + 1/240*n**6 + 0*n**3 - 4*n**2 + 0 + 0*n**7 + 0*n**4 + 0*n - 1/672*n**8. Factor g(y).
-y**3*(y - 1)*(y + 1)/2
Let v = -275/7 - -9082/231. Let p(g) be the second derivative of 0 + 0*g**2 - 1/110*g**5 - 1/33*g**3 + 2*g - v*g**4. Factor p(y).
-2*y*(y + 1)**2/11
Let l(j) = -j**3 + 4*j**2 - 2*j. Let o be l(3). What is s in -1567*s**3 - 9*s - 4*s**2 + 1557*s**o + 7 + 9 + 49*s = 0?
-2, -2/5, 2
Let g be -24*8/(-48) - 4/(-1). Let d(j) be the second derivative of 3/20*j**5 + 0*j**2 - j**3 - g*j + 0 - 1/4*j**4. Suppose d(n) = 0. Calculate n.
-1, 0, 2
Factor 0 + 2/9*i**2 + 88/9*i.
2*i*(i + 44)/9
Let v(d) be the second derivative of -1/120*d**6 + 0 + 29*d + 1/6*d**3 + 1/16*d**5 + 0*d**2 - 1/6*d**4. Determine u so that v(u) = 0.
0, 1, 2
Let y(j) be the first derivative of j**4/2 - 20*j**3/3 + 28*j**2 - 48*j - 20. Suppose y(n) = 0. What is n?
2, 6
Let j(v) = v**3 - 2*v**2 - 4*v 