m - 9*p + 13*p + p**2 + 2.
2*(p + 1)**2
Suppose -30 = -5*o + 2*m, 4*o - m + 2*m - 11 = 0. Suppose 3 = 4*i - i + 3*y, -2*y = -o*i + 10. Determine s so that -4*s + s + s - i*s**2 + 0*s = 0.
-1, 0
Suppose -12*d = -22 - 14. Let o(i) be the third derivative of 0*i**d + 0 - 14/135*i**5 - 1/27*i**4 - 49/540*i**6 + 0*i - 5*i**2. Solve o(s) = 0 for s.
-2/7, 0
Factor 1012/3*i - 6*i**2 - 224/3.
-2*(i - 56)*(9*i - 2)/3
Let i(b) be the second derivative of -b**4/3 - 64*b**3/3 + 65*b. Factor i(l).
-4*l*(l + 32)
Suppose n = -2*m + 6*n + 556, -2*m - 5*n + 536 = 0. Factor -5*d**2 - m*d + 11*d**2 - d**3 + 264*d.
-d*(d - 3)**2
Let r be ((-78)/(-10))/(12/(-60)). Let j = r - -64. Suppose j*q**2 + 4 + 45*q + 56*q**2 - 14 - 26*q**2 = 0. Calculate q.
-1, 2/11
Let b be 162/21 - 10/(-35). Suppose 5*v + 0*f = f + b, -4*v = 4*f - 16. Let -18*n**3 - 17*n**2 + 5*n**2 + 3*n - v*n - 3*n = 0. Calculate n.
-1/3, 0
Let i(p) be the third derivative of 1/96*p**6 + 1/6*p**3 + 0 - 7/240*p**5 + 7*p**2 + 0*p - 1/12*p**4. Factor i(z).
(z - 2)*(z + 1)*(5*z - 2)/4
Suppose 21*k = 24*k - 3. Let z(s) = 5*s**2 + 6*s. Let d(p) = p**2 + p. Let v(b) = k*z(b) - 6*d(b). Determine n so that v(n) = 0.
0
Solve 5*u**4 + 5*u - 34*u + 25 - 34*u + 90*u**2 - 40*u**3 - 17*u = 0 for u.
1, 5
Let t be -2*11/(-2) - (3 + -1). Factor -11*q**2 + 2*q + t*q**2 - 2*q**3 + 2*q.
-2*q*(q - 1)*(q + 2)
Let s(f) be the first derivative of -f**5/120 + f**4/6 - 4*f**3/3 + 3*f**2/2 - 13. Let y(t) be the second derivative of s(t). Factor y(u).
-(u - 4)**2/2
Let p(v) be the second derivative of -v**5/140 + v**4/12 + v**3/42 - v**2/2 + 2*v - 2. Suppose p(q) = 0. Calculate q.
-1, 1, 7
Let -4/11*y - 4/11*y**5 + 0 + 2/11*y**2 + 12/11*y**3 + 2/11*y**4 = 0. Calculate y.
-1, 0, 1/2, 2
Let h(r) be the first derivative of -r**3/3 + 9*r**2 - 81*r + 18. Factor h(x).
-(x - 9)**2
Let n(j) be the first derivative of j**5/4 - 5*j**4/3 + 10*j**3/3 + 8*j + 8. Let l(v) be the first derivative of n(v). Solve l(d) = 0 for d.
0, 2
Let n(z) be the third derivative of 0*z**4 - 1/40*z**5 + 22*z**2 + 0 + 0*z + 0*z**6 + 1/140*z**7 + 0*z**3. Factor n(r).
3*r**2*(r - 1)*(r + 1)/2
Suppose 5*m = 7*m. Suppose f = -2*o + 41, -3*f - 5*o + 100 + 28 = m. Factor 4 + 24*z + 12*z**5 + 84*z**3 + 4 - 5 + f*z**4 + 66*z**2.
3*(z + 1)**4*(4*z + 1)
Let t = 22 - 20. Suppose 0 = t*o + 4, 3*o = -5*s - o - 3. Suppose 0*n**3 + s - 2*n**2 + 3*n**2 + 2*n**2 - 3*n - n**3 = 0. What is n?
1
Let j = 1187 - 1177. Let y(i) be the second derivative of j*i + 0*i**3 + 0 - 1/60*i**4 + 2/5*i**2. Let y(r) = 0. Calculate r.
-2, 2
Let p(i) be the first derivative of -5*i**4/12 - 5*i**3/3 + 15*i**2/2 - 15*i + 3. Let k(x) be the first derivative of p(x). Factor k(q).
-5*(q - 1)*(q + 3)
Suppose 16*a + 112 = 0, 2*d = -4*a + 7*a + 25. Determine m, given that -1/3*m**3 + 5/3*m**d - 7/3*m + 1 = 0.
1, 3
Let q(s) be the third derivative of -s**5/60 + 7*s**4/12 - 5*s**3/3 - 3*s**2 - 12*s. Let r be q(13). Factor 2/3*z**4 + 0 + 0*z**r + 0*z - 2/3*z**2.
2*z**2*(z - 1)*(z + 1)/3
Suppose 5*r - 10 = -5*g, 30 - 7 = 4*r - g. Let p(j) be the second derivative of -2*j - 2/7*j**2 + 0*j**3 + 1/28*j**4 + 0 - 1/140*j**r. Factor p(m).
-(m - 2)**2*(m + 1)/7
Let x(s) be the third derivative of -s**7/1260 + 13*s**6/720 - 2*s**5/15 + 17*s**4/36 - 8*s**3/9 - 9*s**2 - 6*s. Suppose x(v) = 0. Calculate v.
1, 2, 8
Let u(i) be the third derivative of i**8/840 - i**7/1050 - i**6/100 + 7*i**5/300 - i**4/60 - 81*i**2. Solve u(g) = 0.
-2, 0, 1/2, 1
Let b(c) be the second derivative of c**4/3 + 104*c**3/3 + 1352*c**2 - 90*c. Factor b(a).
4*(a + 26)**2
Let k = -19069 - -19072. Determine g, given that -6/5*g + 0*g**2 + 2/5*g**k + 4/5 = 0.
-2, 1
Solve -402/11*u**2 + 290/11*u**3 + 14/11*u**5 - 102/11*u**4 - 72/11 + 272/11*u = 0.
1, 9/7, 2
Suppose 6*d - 6 = 3*d. Suppose -8*o**3 - 2 - 9*o**2 - 5*o**4 - 8*o + o**4 + d*o**4 - 3*o**2 = 0. Calculate o.
-1
Let p(q) = -q**2 + q - 26. Let d be p(0). Let u = 30 + d. Factor 4*h + u*h**2 - 6*h**2 - 6*h - 2*h**3 + 6*h.
-2*h*(h - 1)*(h + 2)
Let n = 23 + -23. Determine s, given that 10*s + n*s**2 + 3*s**2 + 12 - 6 - s = 0.
-2, -1
Let t(j) be the first derivative of -5*j**3/3 - 507*j**2/2 - 202*j + 555. Factor t(o).
-(o + 101)*(5*o + 2)
Let w(k) be the third derivative of 14/15*k**4 + 16/15*k**3 + 10*k**2 + 0 + 0*k + 1/30*k**6 + 22/75*k**5. Factor w(z).
4*(z + 2)**2*(5*z + 2)/5
Let v(f) = 9*f**2 + 7*f - 53. Let y(p) = 8*p**2 + 6*p - 50. Let b(m) = 6*v(m) - 7*y(m). Find o such that b(o) = 0.
-4, 4
Let w(c) be the third derivative of c**7/315 + c**6/90 - 4*c**5/45 + 92*c**2. Suppose w(f) = 0. Calculate f.
-4, 0, 2
Let x(z) be the third derivative of -z**8/168 - 4*z**7/105 - z**6/10 - 2*z**5/15 - z**4/12 - 9*z**2 + 6. Determine c so that x(c) = 0.
-1, 0
Solve 37*r - 10*r - 3*r - 8*r + r**2 = 0.
-16, 0
Let f be (-2)/(-4)*(-39)/(-1170). Let q(b) be the third derivative of -5*b**2 + 1/30*b**5 + 0*b + 0*b**3 + 0 - f*b**6 + 1/6*b**4. Factor q(u).
-2*u*(u - 2)*(u + 1)
Suppose -13*w = -63 - 0 + 37. Let 0*q**w + 0 + 0*q - 5/2*q**5 + 15/2*q**4 + 10*q**3 = 0. What is q?
-1, 0, 4
Let o(z) be the third derivative of -z**6/840 - z**5/105 - z**4/42 + 2*z**2 - 54*z. Factor o(i).
-i*(i + 2)**2/7
Let j(c) be the third derivative of c**5/20 - 9*c**4/8 + 9*c**3 - 70*c**2 + c. Suppose j(f) = 0. Calculate f.
3, 6
Suppose -3*w - 42 = -57. Let v(j) be the second derivative of 4*j**3 + 2/5*j**6 + 9/2*j**2 - 9/5*j**w + 0 - 6*j - 3/4*j**4. Find o, given that v(o) = 0.
-1/2, 1, 3
Let b(d) be the second derivative of -d**7/112 + 17*d**6/240 - 11*d**5/80 + d**4/12 + 288*d. Determine o so that b(o) = 0.
0, 2/3, 1, 4
Let b = 25 - 20. Suppose a - b*a = -8. Factor -8*u**2 - 12 - 15*u**3 - 21*u**a + 44*u + 0*u**2.
-(u + 3)*(3*u - 2)*(5*u - 2)
Let c = 353 - -2146. Determine a, given that a**2 - c + a + 4*a + 2505 = 0.
-3, -2
Let p be (6/(-24))/(1 + (-26)/24). Solve -4*b**4 - p*b**4 + 3*b**4 + 6*b**3 - 8*b**2 - 18*b**3 = 0.
-2, -1, 0
Let s(q) = 128*q + 2434. Let c be s(-19). Find h, given that 0 - 3/2*h - 3/2*h**4 + 3/2*h**c + 3/2*h**3 = 0.
-1, 0, 1
Determine i, given that -268/13*i + 2/13*i**2 + 8978/13 = 0.
67
Let o be (-39)/(-2)*(-10 - (-324)/30). Let j = -141/10 + o. Let 3/2*v**2 - j*v + 3/2*v**3 - 3/2 = 0. What is v?
-1, 1
Let b(s) = 2*s**2 + 8*s + 5. Let t(f) = -30*f - 4*f**2 + 2*f**2 - 4*f**2 + 6*f - 14. Let w(q) = 10*b(q) + 3*t(q). Solve w(c) = 0 for c.
-2
Let d(w) be the first derivative of w**6/21 + 2*w**5/5 - w**4/7 - 4*w**3/3 + w**2/7 + 2*w + 344. Find v, given that d(v) = 0.
-7, -1, 1
Let h(i) be the third derivative of 0*i + 0 + 0*i**3 - 1/60*i**6 + 15*i**2 + 2/15*i**5 - 1/4*i**4. Determine j, given that h(j) = 0.
0, 1, 3
Find a, given that -a**2 + 18*a**3 + 10*a**4 - 9 - 37/2*a + 1/2*a**5 = 0.
-18, -1, 1
Let c(p) be the second derivative of 3*p**5/20 + 41*p + 1. Determine t, given that c(t) = 0.
0
Let t(k) be the third derivative of -1/10*k**5 + 0 + 0*k + 0*k**3 - 22*k**2 + 0*k**4 - 1/40*k**6 + 1/70*k**7. What is z in t(z) = 0?
-1, 0, 2
Suppose u - 2*u - 5 = 2*p, 5*u = p + 19. Factor 5 - b**2 + 28*b**4 + 101*b**2 + 18*b**5 - 22*b**5 + 11 - 64*b - 76*b**u.
-4*(b - 2)**2*(b - 1)**3
Determine n so that -177/2*n + 3/2*n**3 - 45 - 42*n**2 = 0.
-1, 30
Let d(i) be the third derivative of i**7/70 - 17*i**6/240 - 3*i**5/40 + 17*i**4/48 + i**3/4 - 428*i**2. Let d(s) = 0. What is s?
-1, -1/6, 1, 3
Suppose -3*k - 10 = 5*o - 0*o, -5*o + 2*k = -15. Let b(l) = l**2 + l. Let d(m) = -10*m**2 + 6*m - 4. Let n(w) = o*d(w) + 4*b(w). Factor n(x).
-2*(x - 1)*(3*x - 2)
Let o = -203 - -208. Let z(b) be the second derivative of 3*b - 1/50*b**o - 1/45*b**3 + 0 + 0*b**2 - 1/225*b**6 - 1/30*b**4. Factor z(n).
-2*n*(n + 1)**3/15
Let k be -4 - 2*1*8589/(-45570). Let u = -5/217 - k. What is n in -27/5 - 3/5*n**2 + u*n = 0?
3
Let j(r) be the third derivative of -r**6/840 + 11*r**5/420 - 5*r**4/84 - 50*r**2. What is h in j(h) = 0?
0, 1, 10
Let j be (51/(-238))/(36/(-7)). Let z(b) be the third derivative of j*b**4 + 0*b - 2*b**2 + 0*b**3 - 1/120*b**5 + 0. Factor z(f).
-f*(f - 2)/2
Suppose 5*m + 5 = 0, -m = -5*x + 3*x + 107. Let r = 53 - x. Factor -1/7*d**3 + 0*d + r*d**2 + 0 - 1/7*d**4.
-d**3*(d + 1)/7
Factor -105*n**2 - 3*n**4 + 243*n**3 + 290*n**3 - 476*n**3 + 51*n.
-3*n*(n - 17)*(n - 1)**2
Suppose -9*r = 9 - 36. Let c(v) be the first derivative o