s c?
0, 1
Let q be 1/(-1 + 2) - -2. Factor q*j**2 + 4*j**2 + 21*j**5 - 36*j**4 + 9*j**3 - j**2.
3*j**2*(j - 1)**2*(7*j + 2)
Let r = 3125 + -18745/6. Determine u, given that r + u + 1/6*u**2 = 0.
-5, -1
Suppose -4*c = -2*z - 248, -3*z + 3*c = -50 + 431. Let d = 132 + z. What is t in 12/7 + 3/7*t**d + 15/7*t = 0?
-4, -1
Factor -56*c**3 - 2*c**4 - 3*c**5 - c**5 + 55*c**3 - 3*c**4.
-c**3*(c + 1)*(4*c + 1)
Let a(g) = g**2 + 3*g - 7. Let r be a(-5). Let p be (-24)/5 + -9*(-7 + (-19)/(-3)). Find b, given that -56/15*b - 16/15 - p*b**r - 4*b**2 = 0.
-2, -2/3
Let z(c) be the first derivative of c**8/2240 + c**7/560 + c**6/480 + 34*c**3/3 - 16. Let l(k) be the third derivative of z(k). Factor l(y).
3*y**2*(y + 1)**2/4
Let z = -441 - -447. Let m(w) be the first derivative of -1/20*w**5 + 1 + 0*w - 1/24*w**z + 0*w**2 + 0*w**3 + 1/8*w**4. Factor m(f).
-f**3*(f - 1)*(f + 2)/4
Determine h so that 36/7*h**4 + 2/7*h**5 + 0*h**3 + 0*h**2 + 0 + 0*h = 0.
-18, 0
Find q such that 235*q + 539*q + 366*q - 2888 + 144*q**2 + 4*q**3 = 0.
-19, 2
Suppose c = -3*u + 1, 0*c = 5*u + 2*c. Let g be 15/6*(u - 38/20). Factor 0*s**2 + 0*s + g*s**3 + 0.
s**3/4
Let y(j) be the first derivative of -2/33*j**3 + 36 - 2/11*j**2 + 6/11*j. Factor y(p).
-2*(p - 1)*(p + 3)/11
Find i, given that -69*i**2 - 354*i**3 + 27/2*i**5 + 345/2*i - 36 - 63*i**4 = 0.
-3, -1, 1/3, 8
Let u be ((-1292)/(-153) + -9)*(-6)/5. Solve 2/9*j**4 - 2/3*j + u*j**3 - 4/9 + 2/9*j**2 = 0.
-2, -1, 1
Let o(u) = 147*u**4 + 363*u**3 - 63*u**2 - 336*u - 84. Let k(h) = -21*h**4 - 52*h**3 + 9*h**2 + 48*h + 12. Let r(x) = 27*k(x) + 4*o(x). What is t in r(t) = 0?
-2, -1, -2/7, 1
Let w(y) be the first derivative of 0*y**3 - 1/30*y**5 - 1/60*y**6 - 2*y**2 + 0*y + 0*y**4 - 4. Let u(x) be the second derivative of w(x). Solve u(m) = 0 for m.
-1, 0
Suppose 0 = 13*o - 28 - 24. Let c(a) be the first derivative of 0*a + 0*a**2 - 2/75*a**5 - 10 - 2/15*a**o - 8/45*a**3. Determine n, given that c(n) = 0.
-2, 0
Factor -625*p**2 + 56 + 48*p + 629*p**2 + 45 + 43.
4*(p + 6)**2
Let m(g) be the third derivative of -1/54*g**5 + 13*g**2 + 0 + 0*g - 1/135*g**6 + 7/108*g**4 + 2/27*g**3. Factor m(v).
-2*(v - 1)*(v + 2)*(4*v + 1)/9
Let n = -5 - -5. Suppose 3*f = 6 - n. Factor -3*r + 3*r**3 + 5*r**3 - 7*r**3 + f.
(r - 1)**2*(r + 2)
Let y = 11 - 7. Suppose 4*u = -n + 2, 5*u - 8*u = 0. Factor 0 - 1/2*t**y - 3/2*t**n + 3/2*t**3 + 1/2*t.
-t*(t - 1)**3/2
Let r(j) = -j**3 - 4*j**2 + 82*j - 31. Let d be r(7). Let z(c) be the second derivative of 1/3*c**3 + 0*c**d + 0 + 2/3*c**2 - 1/30*c**5 - 9*c. Factor z(q).
-2*(q - 2)*(q + 1)**2/3
Let a = 271 + -267. Let f(s) be the third derivative of 0 - 1/140*s**7 + 1/40*s**6 - 1/8*s**a + 1/4*s**3 + 0*s + 0*s**5 - 5*s**2. Factor f(b).
-3*(b - 1)**3*(b + 1)/2
Let y be (-4)/((-12)/(-25))*-3. Let h = y - 21. Suppose 5*a + 8 - h*a + 20*a**2 + 27*a = 0. What is a?
-1, -2/5
Suppose -5*l - 4*t = 1, 4*t = -222*l + 224*l - 22. Factor -f - 1/4*f**4 + 0 + 1/4*f**l + f**2.
-f*(f - 2)*(f - 1)*(f + 2)/4
Let t(u) be the second derivative of u**7/42 + u**6/10 - 3*u**5/10 - 5*u**4/6 + 7*u**3/2 - 9*u**2/2 + 67*u. Determine f so that t(f) = 0.
-3, 1
Let o(k) be the third derivative of -1/180*k**6 + 0*k**4 + 2/315*k**7 - 1/504*k**8 + 10*k**2 + 0*k**3 + 0 + 0*k + 0*k**5. Factor o(i).
-2*i**3*(i - 1)**2/3
Find f, given that -4*f**2 - 31/2*f - 11 + 1/2*f**3 = 0.
-2, -1, 11
Let t be ((-240)/(-1080))/((-4)/(-72)*10). Suppose 8/5*u + 0 - t*u**2 = 0. Calculate u.
0, 4
Let w be 3 + (-147)/(-441) + 668/30. Suppose 131072/5 + 3072/5*r**2 + w*r**3 + 2/5*r**4 + 32768/5*r = 0. What is r?
-16
Let a(x) be the first derivative of 2*x**5/25 + x**4/10 - 2*x**3/5 - x**2/5 + 4*x/5 + 62. Let a(u) = 0. What is u?
-2, -1, 1
Let k be (-10 + (6 - -4))*(-1 - -2). Let q(w) be the third derivative of 3/20*w**5 + 1/40*w**6 + 5*w**2 + k + 0*w**4 + 0*w - 2*w**3. Factor q(r).
3*(r - 1)*(r + 2)**2
Let u(k) = -4*k**4 + 6*k**3 + 20*k**2 - 21*k - 1. Let t(w) = -w**4 - w**3 + w + 1. Suppose -2 = -4*r - 6. Let v(g) = r*u(g) - t(g). Factor v(l).
5*l*(l - 2)*(l - 1)*(l + 2)
Let a be 2/15*(-2 + 228/84). Let n(v) be the second derivative of 0*v**2 - 9*v + a*v**7 + 0*v**3 - 1/5*v**5 + 1/3*v**4 - 2/15*v**6 + 0. Factor n(r).
4*r**2*(r - 1)**2*(r + 1)
Determine q so that 4*q**4 + 32/7*q**3 - 32/7*q - 4*q**2 + 0 = 0.
-8/7, -1, 0, 1
Let -93*i**2 - 3/2*i**4 - 144 + 192*i + 39/2*i**3 = 0. What is i?
2, 3, 4
Let a(y) = -y**2 - 9*y + 4. Let z be a(-11). Let p be (-6)/z - (-2)/6. Factor p*b**2 + 1/3*b**5 - 1/3 - 1/3*b**4 - 2/3*b**3 + 1/3*b.
(b - 1)**3*(b + 1)**2/3
Suppose -4*p = m - 6*p + 106, 2*m + 209 = 5*p. Let r = m - -115. Factor 1/5*b**r - 4/5*b**2 - 2/5 + b.
(b - 2)*(b - 1)**2/5
Let a(l) be the third derivative of 5*l**7/42 + 13*l**6/24 + l**5/3 - 5*l**4/6 - 94*l**2. Suppose a(q) = 0. What is q?
-2, -1, 0, 2/5
Let q(n) be the second derivative of -n**5/6 + 16*n**4/9 - 37*n**3/9 + 10*n**2/3 + n + 218. Factor q(j).
-2*(j - 5)*(j - 1)*(5*j - 2)/3
Let -1/3*i + 1/9*i**2 + 0 = 0. What is i?
0, 3
Suppose 4*c - 51 = -15. Let y be c/12*(11 - 7). Find q, given that -1/3*q**y + 0 + 0*q + 1/3*q**2 = 0.
0, 1
Let v(t) be the first derivative of 2 - 39/10*t**2 + 18/5*t + 8/5*t**3 - 3/20*t**4. Factor v(g).
-3*(g - 6)*(g - 1)**2/5
Let w(x) be the third derivative of -x**6/360 - x**5/20 - x**4/3 - 8*x**3/9 + 9*x**2 + 4. Factor w(g).
-(g + 1)*(g + 4)**2/3
Let c(d) = d**3 - d**2 - 5. Let p(k) = -9. Let y(a) = 5. Let l(v) = -3*p(v) - 5*y(v). Let h(x) = 2*c(x) + 5*l(x). Factor h(n).
2*n**2*(n - 1)
Let m(z) = -z**2 + z. Let c(d) = 2*d**3 - 12*d - 6. Let n(o) = -c(o) - 2*m(o). Factor n(x).
-2*(x - 3)*(x + 1)**2
Suppose 0*x + 1/2*x**3 + 11*x**4 - 1/2*x**5 - 11*x**2 + 0 = 0. What is x?
-1, 0, 1, 22
Let f(x) = x**4 + x**3 - 2*x**2 - x - 1. Let m(t) = 8*t**4 + 29*t**3 - 38*t**2 - 29*t + 16. Let o(p) = 21*f(p) - 3*m(p). Determine c so that o(c) = 0.
-23, -1, 1
Let s(b) be the first derivative of 0*b**3 + 0*b + b**2 + 1/270*b**5 - 1/108*b**4 - 9. Let f(a) be the second derivative of s(a). Factor f(k).
2*k*(k - 1)/9
Let a(c) be the second derivative of -3*c**5/100 - 19*c**4/60 - c**3 - 4*c**2/5 - 3*c - 77. Find g, given that a(g) = 0.
-4, -2, -1/3
Let w be ((2 + 7)*(-24)/72 + 3)/1. Suppose -4/11*g**2 + 0 + 2/11*g**4 + w*g - 2/11*g**3 = 0. What is g?
-1, 0, 2
Let -4/21*u**4 + 4/21*u**3 - 4/21 - 2/21*u + 8/21*u**2 - 2/21*u**5 = 0. Calculate u.
-2, -1, 1
Let y = 757 - 753. Let 0*i**2 + 9/2*i**y + 0*i + 0 + 0*i**3 - 3/2*i**5 = 0. What is i?
0, 3
Let i(g) = -g**2 + g + 1. Let u(j) be the second derivative of j**3/6 - 10*j. Let l(y) = -i(y) + u(y). Find z such that l(z) = 0.
-1, 1
Suppose -10 = 8*m + 6. Let d = 5 + m. Suppose 5*x**3 - 3*x - d*x**5 + 2*x**3 - x**3 = 0. Calculate x.
-1, 0, 1
Let q(u) = -5*u**5 + 17*u**4 - 33*u**3 + 33*u**2 - 3*u - 2. Let l(n) = -n**4 + n**3 + n**2. Let m(z) = 14*l(z) - 2*q(z). Factor m(f).
2*(f - 2)*(f - 1)**3*(5*f + 1)
What is v in 11/2*v**2 + 49/4*v**4 + 21*v**3 + 1/4 - 3*v = 0?
-1, 1/7
Factor 6*l - 2/17*l**2 - 100/17.
-2*(l - 50)*(l - 1)/17
Let w(k) = k**4 - 32*k**3 + 385*k**2 - 1944*k + 3645. Let y(j) = j**2. Let i(t) = -4*w(t) + 28*y(t). Factor i(u).
-4*(u - 9)**3*(u - 5)
Let v(t) be the third derivative of -t**7/315 - 7*t**6/60 - 59*t**5/45 - 5*t**4/3 + 200*t**3/9 + 140*t**2 + t. Solve v(f) = 0 for f.
-10, -2, 1
Let c be (((-15)/4)/5)/(8/800). Let l = -72 - c. Let -2/11*s + 0 + 4/11*s**2 - 2/11*s**l = 0. Calculate s.
0, 1
Find j, given that -2*j**3 + 4/5 + 2*j + 2/5*j**2 - 6/5*j**4 = 0.
-1, -2/3, 1
Suppose -3*a - 18 = -2*p, -p + 129*a = 132*a + 9. Factor 8/5*q**2 + 0 + 0*q + 4/5*q**p - 4/5*q**4.
-4*q**2*(q - 2)*(q + 1)/5
Let k(m) be the second derivative of -1/36*m**3 + 0 + 1/60*m**6 + 1/120*m**5 + 10*m + 1/6*m**2 - 5/72*m**4. What is n in k(n) = 0?
-1, 2/3, 1
Let s(d) be the second derivative of -1/2*d**3 + 11*d - 23/48*d**4 + 33/40*d**5 + 1/2*d**2 - 7/24*d**6 + 0. Let s(j) = 0. Calculate j.
-2/5, 2/7, 1
Let d(p) be the first derivative of -2*p**7/735 + p**6/105 - p**5/105 + 9*p**2/2 - 8. Let i(u) be the second derivative of d(u). Suppose i(q) = 0. Calculate q.
0, 1
Determine n, given that 57*n**3 + 363 - 27*n**4 + 3/2*n**5 + 1683/2*n + 564*n**2 = 0.
-2, -1, 11
Let x(k) = -2*k**3 + k**2 + 3*k - 2. Let p be x(-4). Let r = -1166/9 + p. Factor -8/9*z**3 + 2/3*z + r - 4/9*z**2 + 2