 = 0. Calculate u.
-3, 5
Let b(h) be the second derivative of -h**6/18 + 53*h**5/60 - 3*h**4 + 14*h**3/9 + 16*h**2/3 + 4*h + 3. Determine k, given that b(k) = 0.
-2/5, 1, 2, 8
Let w = 36928 + -36926. Find o, given that 0*o - 1/5*o**w + 1/5 = 0.
-1, 1
Suppose -2 = k - 5. Suppose 2*n = -n + 3*u + 6, -4*n = 2*u - 8. What is s in 2 - 6*s + 5*s**3 - s**k - 3*s**2 - 3*s**2 + n = 0?
-1, 1/2, 2
Let t be 39/(-273)*(0 + (-14)/4). Let 0 - t*m**3 + 0*m + 0*m**2 - 1/2*m**4 = 0. Calculate m.
-1, 0
Let t(s) be the first derivative of 4*s**6/3 - 20*s**5 + 231*s**4/2 - 931*s**3/3 + 343*s**2 - 58. What is o in t(o) = 0?
0, 2, 7/2
Let g = -70 - -98. Factor -g*a**2 - 36*a**3 - 283 - 8*a - 20*a**4 + 283 - 4*a**5.
-4*a*(a + 1)**3*(a + 2)
Let q(x) = -x - 9. Let p be q(-6). Let f(g) = -g**2 + g - 1. Let z(a) = 4*a**2 + 12*a - 1. Let v(w) = p*f(w) + z(w). Solve v(h) = 0 for h.
-1, -2/7
Solve 0 + 1/5*t**5 - 1/5*t + 2/5*t**2 + 0*t**3 - 2/5*t**4 = 0 for t.
-1, 0, 1
Let x(q) = -4*q**4 + 2*q**3 + 0*q**4 + 5*q**4 - 3*q**3. Let i(w) = 3*w**3 + 6*w**3 + 2*w**4 - 14*w**4 + w**3. Let p(u) = 2*i(u) + 22*x(u). Factor p(f).
-2*f**3*(f + 1)
Let s(q) be the first derivative of -q**5/180 + q**4/18 - q**3/6 - 19*q**2/2 - 15. Let f(k) be the second derivative of s(k). Let f(j) = 0. Calculate j.
1, 3
Let j(r) be the second derivative of -7*r**7/12 - 973*r**6/90 - 649*r**5/15 - 62*r**4 - 364*r**3/9 - 40*r**2/3 + 431*r. Find b such that j(b) = 0.
-10, -2, -2/3, -2/7
Let k = -20578/3 + 6860. Factor -c**2 - k*c + 1/3.
-(c + 1)*(3*c - 1)/3
Let g(n) be the third derivative of 1/1512*n**8 + 0*n + 0*n**5 + 12 + 0*n**3 + 0*n**4 - 3*n**2 - 1/945*n**7 + 0*n**6. Factor g(c).
2*c**4*(c - 1)/9
Let q(w) = 4*w + 1. Let o be q(2). Let n = -6 + o. Factor -6*c**3 + 11*c**2 - n*c + 2*c**5 + 0*c**2 - c**2 - c - 2*c**4.
2*c*(c - 1)**3*(c + 2)
Let c(u) be the third derivative of u**5/120 - 13*u**4/16 - u**2 + 70. Suppose c(b) = 0. Calculate b.
0, 39
Let d(w) = 9*w**2 + 69*w - 66. Let m(i) = i**2 - i + 1. Let p(j) = -d(j) + 12*m(j). Factor p(v).
3*(v - 26)*(v - 1)
Let c(h) be the third derivative of h**7/315 - h**6/90 - 7*h**5/90 - h**4/9 - 210*h**2. Find i, given that c(i) = 0.
-1, 0, 4
Let b(o) be the first derivative of -1/14*o**4 + 1 + 0*o**3 + 0*o**2 + 0*o. Solve b(i) = 0.
0
Let p be 8 + -48*10/150. Solve -2/15*g**2 - p + 8/5*g = 0 for g.
6
Let -10 - 6*n + 18/5*n**2 - 2/5*n**3 = 0. What is n?
-1, 5
Let i(u) be the third derivative of 1/210*u**5 + 0*u + 23*u**2 + 1/42*u**4 + 0*u**3 + 0. Find r, given that i(r) = 0.
-2, 0
Let v = -1179 - -1182. Let r(t) be the first derivative of -2 - 1/6*t**2 + 1/6*t**v + 0*t. Suppose r(f) = 0. Calculate f.
0, 2/3
Let h(x) = x**3 - x**2 + x + 1. Let c(i) = 2*i**4 + 78*i**3 + 120*i**2 + 74*i + 10. Let j(q) = -c(q) + 10*h(q). Factor j(f).
-2*f*(f + 1)**2*(f + 32)
Let g(m) be the first derivative of -8/15*m**3 - 1/300*m**5 - 5/2*m**2 + 1/15*m**4 + 0*m - 9. Let u(f) be the second derivative of g(f). Factor u(w).
-(w - 4)**2/5
Factor -3/2*c**2 + 5/2 + 7*c.
-(c - 5)*(3*c + 1)/2
Let f(y) be the first derivative of y**7/70 - 11*y**6/120 + y**5/10 - 19*y**2/2 + 5. Let r(l) be the second derivative of f(l). Factor r(w).
w**2*(w - 3)*(3*w - 2)
Let g(a) = -2*a**2 + 5*a + 1. Suppose 0 = -3*d + d - 8. Let l = -7 - d. Let c(k) = 3*k**2 - 9*k - 2. Let p(z) = l*c(z) - 5*g(z). What is m in p(m) = 0?
-1
Let g(j) = 6*j**2 - 2*j - 1. Let q be g(-1). Solve q*w + 4 + 23*w**2 - 17*w - 15*w**2 - 2*w**3 = 0 for w.
1, 2
Let y(a) = -14*a - 20. Let o(g) = -5*g - 7. Let f(z) = 11*o(z) - 4*y(z). Let j be f(17). Factor 6*q**2 + 11*q - 3*q**2 - j*q.
3*q*(q - 3)
Factor 95476*x + 198*x**2 - 99832*x - 3*x**3 + 19500 + 12444.
-3*(x - 22)**3
Let y = 81 - 77. Let b = -5 + 8. Factor -1 + 2*o**5 - 9*o + b*o - 4*o**2 + y*o**3 + 6*o**4 - 1.
2*(o - 1)*(o + 1)**4
Let j(g) = 9*g**2 - 15*g + 16. Let z be j(1). Let m(y) be the first derivative of z + 2/15*y**3 + 1/10*y**4 - 2/5*y**2 + 0*y. Solve m(b) = 0.
-2, 0, 1
Factor 45/2*s - 15/4*s**2 + 50 - 5/4*s**3.
-5*(s - 4)*(s + 2)*(s + 5)/4
Suppose 18*s - 2*p = 16*s + 4, -5*s + 2*p + 10 = 0. Let r(y) be the first derivative of -7 + 2/33*y**3 - 2/11*y**s + 1/22*y**4 + 0*y. Factor r(t).
2*t*(t - 1)*(t + 2)/11
Let d(s) = -10*s**4 + 35*s**3 - 125*s**2 + 145*s - 55. Let h(t) = -t**4 - 2*t**3 + 2*t - 1. Let y(z) = d(z) - 5*h(z). Factor y(q).
-5*(q - 5)*(q - 2)*(q - 1)**2
Factor 0*q + 2/5*q**5 + 8/5*q**4 + 0 + 2*q**3 + 4/5*q**2.
2*q**2*(q + 1)**2*(q + 2)/5
Let b(g) be the third derivative of -7*g**7/165 - 7*g**6/44 + 13*g**5/165 + 8*g**4/11 + 32*g**3/33 + 320*g**2. Let b(h) = 0. Calculate h.
-2, -4/7, 1
Let w be 32/(-160) - (-4)/5. Let -1/5*s**5 - 1/5*s**2 - 3/5*s**3 + 0 - w*s**4 + 0*s = 0. What is s?
-1, 0
Let b(f) be the second derivative of f**5/90 - 5*f**4/36 - 2*f**3/3 - 15*f**2 + 13*f. Let r(j) be the first derivative of b(j). Determine u so that r(u) = 0.
-1, 6
Let l(y) be the third derivative of -y**8/112 + 2*y**7/25 + 7*y**6/200 - 61*y**5/50 - 16*y**4/5 - 16*y**3/5 + 393*y**2. Let l(i) = 0. Calculate i.
-1, -2/5, 4
Let v(k) be the first derivative of 2*k**5/15 - 5*k**4 + 314*k**3/9 + 340*k**2 + 2312*k/3 - 148. Factor v(s).
2*(s - 17)**2*(s + 2)**2/3
Let l = 40 + -36. Let f be (l/(-10))/(24/(-30) + 0). Factor 0*q + 1/2*q**5 + 0 - f*q**3 - 1/2*q**4 + 1/2*q**2.
q**2*(q - 1)**2*(q + 1)/2
Suppose -17 = -2*m - 5. Let 25 - 3*x - 3*x**2 + m - 13 = 0. Calculate x.
-3, 2
Suppose -4*y + 0*y + 640 = 0. Let q be 12/9*90/y. Find z, given that -11/4*z**2 - 3*z - q*z**3 - 1 = 0.
-2, -1, -2/3
Suppose 4*b - 12 - 12 = -5*d, 0 = -5*d. Factor 9*m**3 - 4*m - m**3 + 2*m - b*m**3.
2*m*(m - 1)*(m + 1)
Factor 0 + 10/9*t + 8/9*t**2 - 2/9*t**3.
-2*t*(t - 5)*(t + 1)/9
Let b be ((-117)/27 + 3)*(-12)/8. Factor 16/7*l - 2/7*l**b - 32/7.
-2*(l - 4)**2/7
Let h(o) be the third derivative of o**8/784 + 13*o**7/490 + 23*o**6/140 + 11*o**5/35 - 5*o**4/7 - 32*o**3/7 + 544*o**2. Factor h(y).
3*(y - 1)*(y + 2)**3*(y + 8)/7
Let j(l) = 20*l**3 - 954*l**2 - 37440*l + 38400. Let x(s) = 3*s**3 - 159*s**2 - 6240*s + 6400. Let d(z) = 6*j(z) - 39*x(z). Factor d(t).
3*(t - 1)*(t + 80)**2
Let i(o) be the first derivative of 3*o + 1/4*o**2 + 1 - 1/6*o**3. Solve i(d) = 0.
-2, 3
Let d be (1 - 18/(-3)) + -4. Factor -17*u**2 + 5*u**3 - 7*u**d + 19*u**2.
-2*u**2*(u - 1)
Let m = 148 + -445/3. Let g = m + 17/33. What is d in 0 - g*d**2 + 0*d = 0?
0
Factor -618*m**3 + 227*m**3 + 5*m**2 + 5*m**4 - 30*m + 208*m**3 + 203*m**3.
5*m*(m - 1)*(m + 2)*(m + 3)
Let u(l) be the first derivative of -1/4*l**4 + 19 + 0*l**2 - l**3 + 0*l. Let u(b) = 0. What is b?
-3, 0
Suppose 3*u - 15 = -2*s - 1, -s + 6 = u. Suppose -8 - 4 = -u*i + 5*x, 0 = -4*x. Determine z, given that 2*z**2 + 5*z - z - i + 0*z**2 = 0.
-3, 1
Let n be (-10)/(-4)*132/165. Factor -f**2 + 131*f**3 + 12*f**4 - 6 + 33*f - 134*f**3 - 35*f**n.
3*(f - 1)**2*(f + 2)*(4*f - 1)
Let a be (-9)/216 + 15/360. Factor 0*i - 2/7*i**3 + 6/7*i**2 + a.
-2*i**2*(i - 3)/7
Let f(h) be the second derivative of -h**8/112 - h**7/70 + h**6/40 + h**5/20 - 7*h**2 - 8*h. Let r(v) be the first derivative of f(v). What is q in r(q) = 0?
-1, 0, 1
Let r(b) = 10*b**4 + 6*b**3 - 30*b**2 + 6*b + 21. Let p(q) = 37*q**4 + 26*q**4 - 61*q**4 - 6*q**2 + q + 4 + q**3. Let v(l) = 11*p(l) - 2*r(l). Factor v(g).
(g - 2)*(g + 1)**2*(2*g - 1)
Let v(x) = 5*x**2 + 15*x + 13. Let o(m) = m**2 - m - 1. Let f(n) = 3*o(n) - v(n). Solve f(y) = 0 for y.
-8, -1
Determine i, given that -231*i**2 + 57*i**4 + 58739 + 1095*i**2 - 60035 + 3*i**5 + 372*i**3 = 0.
-6, -2, 1
Let z be (-5424)/(-339) - 152/10. Factor 0*k**3 + 4/5*k**2 + 0 - z*k**4 + 0*k.
-4*k**2*(k - 1)*(k + 1)/5
Suppose -3*k + 7*k = a + 9, -2*k - a = -3. Factor 2*q + 2*q**2 + q**3 + q + k*q**2 + 0*q**3.
q*(q + 1)*(q + 3)
Let d(y) be the third derivative of y**6/180 + y**5/135 - y**4/9 - 8*y**3/27 + 209*y**2. Factor d(q).
2*(q - 2)*(q + 2)*(3*q + 2)/9
Let i(l) = -10*l**3 + 2*l**2 + 20*l - 4. Let r(p) = 10*p**3 - 4*p**2 - 19*p + 3. Let b(x) = 5*i(x) + 4*r(x). Factor b(y).
-2*(y - 1)*(y + 2)*(5*y - 2)
Factor 107/5*z - 106/5 - 1/5*z**2.
-(z - 106)*(z - 1)/5
Let s be (((-3)/(-2))/((-18)/(-24)))/2. Let b(j) = 4*j**3 + j**2 - 4*j + 2. Let a be b(s). Factor a + 0*i - 9/4*i**2 + 3/4*i**3.
3*(i - 2)**2*(i + 1)/4
Suppose a = -s + 2, -15*s + 20*s - 8 = -4*a. Let f(c) be the third deriva