o**4/3 + 529*o**3/3 - 2*o + 5. Solve i(f) = 0.
0, 23
Let a(t) be the third derivative of t**7/420 - 7*t**6/240 + 3*t**5/20 - 5*t**4/12 + 2*t**3/3 - 18*t**2 - 5*t. Factor a(z).
(z - 2)**3*(z - 1)/2
Let y(x) be the third derivative of -x**6/600 - x**5/75 - x**4/24 - x**3/15 - 136*x**2 + 3. Factor y(i).
-(i + 1)**2*(i + 2)/5
Factor 2930*m**2 + 1571*m**5 - 3225*m - 789*m**5 - 135*m**4 - 787*m**5 - 690*m**3 + 1125.
-5*(m - 1)**3*(m + 15)**2
Let g = -128 - -132. Let z(h) be the first derivative of 3 - 5/2*h**2 - 7/16*h**g + 3/2*h**3 + 1/20*h**5 + 2*h. Factor z(p).
(p - 2)**3*(p - 1)/4
Let k(j) be the first derivative of -j**7/1960 + j**6/210 - j**5/56 + j**4/28 - 17*j**3/3 - 18. Let c(i) be the third derivative of k(i). Solve c(s) = 0 for s.
1, 2
Let t be (-94)/2209 - (-1293)/564. Suppose -3/4*x**2 + 3*x - t = 0. What is x?
1, 3
Let t(y) = -y**3 - 7*y**2 - 6*y + 8. Let x be t(-6). Suppose -7*w**3 + x*w**3 - 3*w**5 + 2*w**3 = 0. What is w?
-1, 0, 1
Factor 0 - 3/7*w**3 + 0*w + 9/7*w**2.
-3*w**2*(w - 3)/7
Factor -12 + 62/5*v - 2/5*v**2.
-2*(v - 30)*(v - 1)/5
Let n(z) be the second derivative of 3*z**5/20 + 3*z**4/2 + 9*z**3/2 + 6*z**2 - 73*z. Factor n(i).
3*(i + 1)**2*(i + 4)
Let l(n) = -1. Let a(y) = y**2 - 5*y + 9. Let m(g) = -a(g) - 3*l(g). Factor m(p).
-(p - 3)*(p - 2)
Let n(t) be the third derivative of 0*t + 9/20*t**5 - 1/40*t**6 - 43*t**2 - 15/8*t**4 + 7/2*t**3 + 0. Factor n(a).
-3*(a - 7)*(a - 1)**2
Let t(x) = x**2 - 6*x - 59. Let o be t(11). Let h be (16/102)/(o/(-6)). Determine g so that 2/17*g**2 + 2/17 + h*g = 0.
-1
Let m(g) = -g**3 + g**2 - g - 1. Let a(h) = 14*h**3 + 124*h**2 + 95*h - 29. Let b(d) = -5*a(d) - 35*m(d). Find v, given that b(v) = 0.
-18, -1, 2/7
Let o(r) be the first derivative of 3*r**4 + 20*r**3/3 + 2*r**2 - 4*r + 72. Factor o(b).
4*(b + 1)**2*(3*b - 1)
Let t(j) = 9*j**2 - 1421*j - 83539. Let y(g) = 12*g**2 - 2131*g - 125309. Let p(c) = 7*t(c) - 5*y(c). Suppose p(q) = 0. Calculate q.
-118
Let g(q) = -6*q + 3. Let i(l) = l**2 + 11*l - 6. Let c(z) = 5*g(z) + 3*i(z). Let n be 6/9 + 4/12. Let p(r) = r + 1. Let h(y) = n*c(y) + 3*p(y). Factor h(a).
3*a*(a + 2)
What is j in -368758*j**2 + 8*j - 31*j + 31 - 7*j + 368757*j**2 = 0?
-31, 1
Let c = -9346 - -18811/2. Factor -6 + 40*p - 49/2*p**3 - c*p**2.
-(p + 3)*(7*p - 2)**2/2
Let f(v) = 3*v**4 + 69*v**3 + 15. Let c(m) = m**4 + 17*m**3 + 4. Let t(g) = 15*c(g) - 4*f(g). Factor t(a).
3*a**3*(a - 7)
Let z(j) = j**2 - 5*j + 1. Suppose -4*y = 3*y - 14. Let x(s) = -s**2 + 4*s - 1. Let n(o) = y*z(o) + 3*x(o). Let n(k) = 0. What is k?
1
Let w(v) be the second derivative of -2*v**5/5 - 5*v**4/3 + 8*v**3/3 + 6*v**2 + 107*v - 1. Find l such that w(l) = 0.
-3, -1/2, 1
Let n be ((-2299)/(-133) - 17)/(-1 + (-19)/(-14)). Factor 16/5 + 1/5*o**5 + 3/5*o**4 - n*o**3 - 16/5*o**2 + 0*o.
(o - 2)*(o - 1)*(o + 2)**3/5
Let v be (16/9)/(8/12). Let w(n) be the first derivative of 0*n**2 + 0*n**4 - v*n**3 + 4/5*n**5 - 8 + 4*n. Factor w(a).
4*(a - 1)**2*(a + 1)**2
Let d = 14701/95303 + -3/7331. Factor d*f**2 + 72/13 + 24/13*f.
2*(f + 6)**2/13
Let -2/9*k**3 + 8/9*k + 8/9*k**2 - 32/9 = 0. Calculate k.
-2, 2, 4
Factor -430/3*y + 205/3*y**2 + 20/3*y**3 - 40.
5*(y - 2)*(y + 12)*(4*y + 1)/3
Let u(i) be the third derivative of 23*i**6/120 - i**5/30 - 23*i**4/24 + i**3/3 - 4*i**2 + 9. Find a such that u(a) = 0.
-1, 2/23, 1
Let l(q) be the first derivative of 4*q**5/5 + 572*q**4 + 163592*q**3 + 23393656*q**2 + 1672646404*q + 24. Factor l(y).
4*(y + 143)**4
Find u, given that -2839714/5 - 1156*u**3 - 34*u**4 - 167042*u - 19652*u**2 - 2/5*u**5 = 0.
-17
Factor 3*m**2 - 80*m + 41*m + 42*m - 2*m**2.
m*(m + 3)
Let c(b) = -35*b**2 + 15*b - 5. Let v(o) = o**2. Suppose 5*z + 342 = -u, 2*z + 3*u = -0*u - 142. Let h = z + 43. Let j(s) = h*v(s) - c(s). Factor j(g).
5*(g - 1)*(2*g - 1)
Let s = 971/24 - 297/8. Suppose -s + 25/3*r - 20/3*r**2 + 5/3*r**3 = 0. Calculate r.
1, 2
Solve 1/4*l**3 + 0*l**2 + 0*l + 1/4*l**4 + 0 = 0 for l.
-1, 0
Let q(m) be the second derivative of m**7/273 + 17*m**6/195 + 31*m**5/130 + 5*m**4/26 - 2*m - 68. Factor q(v).
2*v**2*(v + 1)**2*(v + 15)/13
Factor 0*h + 5/9*h**4 + 0 + 11/9*h**3 + 2/9*h**2.
h**2*(h + 2)*(5*h + 1)/9
Let w(k) be the third derivative of -k**8/42 + 11*k**7/105 + 19*k**6/60 - 22*k**5/15 - k**4 + 130*k**2 - 2. Determine i so that w(i) = 0.
-2, -1/4, 0, 2, 3
Suppose 0*b - 2*t = 5*b - 207, -4*t = -2*b + 102. Solve 27*z**3 + 7*z**2 + 3*z**2 - 2*z**4 + 5*z**5 + 35 - 43*z**4 + b*z**3 - 75*z = 0.
-1, 1, 7
Let o(c) = 3*c + 20. Let g be o(-5). Factor -25 + 2*r**3 + g*r - 5 - 4*r**3 - 3*r**3 + 30*r**2.
-5*(r - 6)*(r - 1)*(r + 1)
Let j(s) be the first derivative of -s**5/4 - 35*s**4/12 - 55*s**3/6 - 25*s**2/2 + 18*s - 18. Let b(p) be the first derivative of j(p). Factor b(l).
-5*(l + 1)**2*(l + 5)
Let p = -56/3 + 113/6. Let q(t) be the first derivative of 0*t + 1/9*t**3 - 1/15*t**5 + 2 + p*t**2 - 1/12*t**4. Factor q(k).
-k*(k - 1)*(k + 1)**2/3
Let a = -49 + 48. Let t(w) = w**2 - 2. Let q(v) = -20*v**2 + 28*v + 32. Let o(s) = a*q(s) - 16*t(s). Factor o(r).
4*r*(r - 7)
Solve 18 - 6*u + 1/2*u**2 = 0.
6
Let m(w) be the first derivative of w**6/3 + 32*w**5/5 + 63*w**4/2 - 32*w**3/3 - 64*w**2 - 203. Find d, given that m(d) = 0.
-8, -1, 0, 1
Let m be (-84)/(-135)*45/18. Factor -4/9 + m*n - 2/9*n**4 - 2*n**2 + 10/9*n**3.
-2*(n - 2)*(n - 1)**3/9
Let o = 8234/6171 + -2/2057. Factor 0 - o*i**3 - 4/3*i - 8/3*i**2.
-4*i*(i + 1)**2/3
Suppose -h + 3*h = -3*v + 60, -v + 21 = h. Factor -v*i**2 - 54*i**3 - 710 + 710 - 2*i - 54*i**4.
-2*i*(3*i + 1)**3
Let n(y) = -9*y**3 + 197*y**2 + 70*y - 130. Let l(r) = -10*r**3 + 199*r**2 + 71*r - 131. Let m(o) = -6*l(o) + 7*n(o). Determine t so that m(t) = 0.
-1, 2/3, 62
Let h(i) be the first derivative of 24*i**5/5 - 25*i**4 - 4*i**3/3 + 44*i**2 - 32*i + 60. Suppose h(l) = 0. Calculate l.
-1, 1/2, 2/3, 4
Let u(i) = -4*i**3 + 106*i**2 - 22*i - 145. Let y(z) = z**3 - 27*z**2 + 5*z + 36. Let r(a) = 6*u(a) + 26*y(a). Factor r(o).
2*(o - 33)*(o - 1)*(o + 1)
Let o(s) = -10 - 4*s - 6*s + 21 + 0*s**2 + s**2. Let x be o(9). Suppose x*f**2 + 1 - 2*f + 1 - 6 = 0. Calculate f.
-1, 2
Let m(r) be the third derivative of -r**6/240 + r**5/60 + r**4/16 + 163*r**2. Factor m(j).
-j*(j - 3)*(j + 1)/2
Let j(x) be the first derivative of -2 + 1/3*x + 5/6*x**4 + 5/6*x**2 + 10/9*x**3 + 1/3*x**5 + 1/18*x**6. Let j(d) = 0. What is d?
-1
Let p(i) be the third derivative of i**6/540 + 2*i**5/135 - 7*i**4/108 - 10*i**3/27 - 22*i**2 + 3. Suppose p(d) = 0. What is d?
-5, -1, 2
Let v(c) = -c**2. Let f(i) = 8*i**2 + 16*i. Let k(j) = f(j) + 12*v(j). Factor k(a).
-4*a*(a - 4)
Let p(l) = -6*l**4 - 7*l**3 - 8*l**2 + 11*l - 10. Let s(c) = -7*c**4 - 7*c**3 - 8*c**2 + 10*c - 12. Let g(q) = 6*p(q) - 5*s(q). Find i, given that g(i) = 0.
-4, 0, 1
Let j(c) be the first derivative of 0*c + 1/4*c**6 - 9/8*c**4 - 3/2*c**2 - 5/2*c**3 - 8 + 3/10*c**5. What is k in j(k) = 0?
-1, 0, 2
Let i(z) be the second derivative of 0 + 0*z**2 - 3/80*z**5 + 14*z + 1/8*z**3 + 0*z**4. Factor i(o).
-3*o*(o - 1)*(o + 1)/4
Factor -2/3*t**2 + 5/3*t - 1/3*t**3 + 2.
-(t - 2)*(t + 1)*(t + 3)/3
Let u(c) = c**5 + 442*c**4 - c**3 - 481*c**2 - 13*c + 26. Let w(q) = 74*q**4 - 80*q**2 - 2*q + 4. Let s(r) = 4*u(r) - 26*w(r). Suppose s(y) = 0. What is y?
-1, 0, 1, 39
Let v(b) be the third derivative of -2*b**3 - 14*b**2 + 0*b + 0 - b**4 + 1/70*b**7 + 1/8*b**6 - 1/112*b**8 - 1/20*b**5. Factor v(p).
-3*(p - 2)**2*(p + 1)**3
Let v = -9 + 13. Suppose -4*z + w + w = -10, v*z + 2*w = 6. Solve -j + j**2 + j - z*j - 3 = 0 for j.
-1, 3
Let c(g) be the second derivative of -1/70*g**5 + 0 + 0*g**3 - 1/42*g**4 + 0*g**2 + 38*g. Find t, given that c(t) = 0.
-1, 0
Suppose -5*g**2 + 0*g + 150 - 62*g - 3*g + 0*g**2 = 0. What is g?
-15, 2
Let k be (2/4)/(1/18). Let f = 12 - 10. Factor 3*n**3 - 6 + 13 + 7*n - 10*n**2 + 2*n**f - k.
(n - 1)**2*(3*n - 2)
Suppose -3*l = -6*l. Suppose l*y = 2*y. Factor 2/5*i**2 + y*i + 2/5*i**3 + 0.
2*i**2*(i + 1)/5
Factor 26/11*g - 24/11 - 2/11*g**2.
-2*(g - 12)*(g - 1)/11
Let t(x) be the second derivative of -x**4/6 + 4*x**3/3 + x**2/2 + 20*x. Let h(n) = -n**2 + 7*n + 2. Let g(d) = -3*h(d) + 2*t(d). Factor g(y).
-(y + 1)*(y + 4)
Let j(m) be the first derivative of m**6/900 - m**4/60 + 4*m**3 + 10. Let g(b) be the third derivative of j(b). Fin