b**5 - 1/9*b**4 + 5*b**2 + 0*b + 0 - 7/3*b**3.
b**2*(b - 3)**2*(b + 5)/9
Let z(y) = y**2 + y + 4. Let x be z(3). Let t be 4*-1*(-8)/x. Let -9*s**5 - 9*s + 15*s**3 + 2*s**2 - 3*s**2 + 4*s**t - 3*s**4 + 3*s = 0. Calculate s.
-1, 0, 2/3, 1
Let c(d) be the first derivative of 5*d**6/6 - 95*d**4/4 - 10*d**3/3 + 120*d**2 + 160*d - 319. Let c(u) = 0. What is u?
-4, -1, 2, 4
Let c(l) be the first derivative of l**6/2 + 3*l**5/5 - 33*l**4/16 - l**3 + 15*l**2/8 + 3*l/2 - 62. What is j in c(j) = 0?
-2, -1/2, 1
Let m(d) = d**3 - 5*d**2 - 5*d - 4. Let f be m(6). Suppose 0 = 13*b - 3*b + 2*b. Determine k, given that -5/6*k**4 + b + 1/2*k**3 + 0*k + 1/3*k**f = 0.
-2/5, 0, 1
Factor 49 + 49 - 16*p + p**2 - 70.
(p - 14)*(p - 2)
Let j = -10986 - -87895/8. Suppose 31/8*t**2 + 33/8*t**4 + j*t**5 + 53/8*t**3 + 0*t - 1/2 = 0. What is t?
-2, -1, 2/7
Let d be (-1537)/(-106) + (1 - 11). Let 0 + 3/2*z**4 + d*z**2 - 3/2*z - 9/2*z**3 = 0. What is z?
0, 1
Let c(o) be the first derivative of -o**6/10 - 3*o**5/4 + 3*o**4/4 + 13*o**3/2 - 15*o**2 - 6*o + 43. Let a(k) be the first derivative of c(k). Factor a(w).
-3*(w - 1)**2*(w + 2)*(w + 5)
Let a(g) be the third derivative of -g**7/210 + g**6/30 + 3*g**5/10 + 5*g**4/6 + 7*g**3/6 + 20*g**2 - 2*g. Factor a(p).
-(p - 7)*(p + 1)**3
Let t be ((-3 + 6)*-1 + 1)*-1. Let r be (-4)/(-6)*(t + (1 - 1)). Suppose r*s - 1/3 - s**2 = 0. Calculate s.
1/3, 1
Suppose -z - 249 + 251 = 0. Factor -14*u**2 - 46*u**z - 340*u + 352*u + 27*u**3.
3*u*(u - 2)*(9*u - 2)
Let g(f) be the third derivative of 1/12*f**5 + 0 - 5/6*f**3 - 4*f**2 + 1/24*f**6 - 5/24*f**4 + 0*f. Find q such that g(q) = 0.
-1, 1
Let q(c) = -188*c - 8831. Let d be q(-47). Solve 12/5 + 21/5*g**d - 24/5*g + 3/5*g**3 - 69/5*g**2 + 57/5*g**4 = 0 for g.
-2, -1, 2/7, 1
Let z(a) be the first derivative of a**6/6 + 7*a**5/5 - 9*a**4/2 + 2*a**3/3 + 17*a**2/2 - 9*a + 139. Factor z(s).
(s - 1)**3*(s + 1)*(s + 9)
Suppose 0 = -2*n + 5*y - 1, 3*n + 0*n = 5*y + 1. Factor -7*b + 4*b**2 + b + 4*b - n*b**2 - 4.
2*(b - 2)*(b + 1)
Let t(v) be the third derivative of v**7/9 - 89*v**6/180 + 23*v**4/9 - 32*v**3/9 + 45*v**2 - 8*v. Find u such that t(u) = 0.
-1, 2/5, 8/7, 2
Let b = 1001 - 5001/5. Find x such that -1/5 + b*x + x**2 = 0.
-1, 1/5
Let q(m) be the first derivative of -m**3/3 + 5*m**2/2 + 76. Factor q(j).
-j*(j - 5)
Suppose -16*k = -11*k - 5. Let d(b) = b**2. Let y(m) = -14*m**2. Let h(q) = k*y(q) + 10*d(q). Solve h(c) = 0 for c.
0
Let r = -39 - -61. Factor 0*y**2 - y**2 + r - 21.
-(y - 1)*(y + 1)
Let n(c) be the third derivative of -c**4/12 - 7*c**3/2 + 14*c**2. Let i be n(-13). Determine h so that 2*h + 1/2*h**4 + 2*h**i - h**2 - 4*h**3 + 1/2 = 0.
-1, -1/4, 1
Factor 1127*m - 180*m**2 + 7*m**3 + 1033*m - 2*m**3 - 8640.
5*(m - 12)**3
Let h(m) be the third derivative of -m**5/12 + 15*m**4/8 + 54*m**2. Let h(d) = 0. Calculate d.
0, 9
Let 4/7*a + 6/7*a**3 + 2/7*a**4 - 2/7*a**5 - 10/7*a**2 + 0 = 0. What is a?
-2, 0, 1
Let g = -1265 - -5063/4. Determine b, given that 3/4*b**2 + 1/4*b - 1/4*b**3 - g = 0.
-1, 1, 3
Let p(y) be the second derivative of -y**8/5376 - y**7/2016 - y**4/4 - 20*y. Let v(b) be the third derivative of p(b). Find c such that v(c) = 0.
-1, 0
Let -25/2*b**3 + 4 + 3*b + 3/2*b**4 - 23/2*b**2 + 7/2*b**5 = 0. What is b?
-1, 4/7, 2
Let d = -41 + 44. Let p(n) be the second derivative of 1/5*n**6 + 0 - d*n**2 - 3/10*n**5 - 2*n**4 - n - 7/2*n**3 + 1/14*n**7. What is z in p(z) = 0?
-1, 2
Let p be ((-3)/(-3))/(6/(-18)). Let c(m) = 2*m**3 + 4*m**2 - 6*m - 2. Let b(u) = -u**4 - 3*u**3 - 3*u**2 + 7*u + 3. Let r(h) = p*c(h) - 2*b(h). Factor r(d).
2*d*(d - 1)**2*(d + 2)
Let l = 74 + -72. Let i be (-5 - -4)/(-1) - (1 - l). Determine c so that -3*c - 3/2*c**i - 3/2 = 0.
-1
Let m(g) = -2 - 4*g**3 - 2*g**2 - 2*g**3 + 6*g + 8*g**3. Suppose -s - 1 = 4. Let y(p) = 3*p**3 - 2*p**2 + 7*p - 3. Let b(u) = s*m(u) + 4*y(u). Factor b(a).
2*(a - 1)*(a + 1)**2
Factor 2046/17*q + 1922/17 + 2/17*q**3 + 126/17*q**2.
2*(q + 1)*(q + 31)**2/17
Let u(w) = -3*w**4 + 5*w**3 - 67*w**2 + 81*w - 31. Let c(i) = 5*i**4 - 7*i**3 + 101*i**2 - 121*i + 46. Let h(s) = 5*c(s) + 8*u(s). Let h(r) = 0. Calculate r.
-9, 1, 2
Let o be (8/14 - 1080/1400)*-15. Solve 1/3*v - 2/3*v**2 + 0 - v**o = 0.
-1, 0, 1/3
Let m be 1*(-6)/8 - 1393/(-1820). Let u = m - -583/130. Factor -1/2*x - x**5 + 5/2*x**2 + 0 - u*x**3 + 7/2*x**4.
-x*(x - 1)**3*(2*x - 1)/2
Let m(a) be the third derivative of a**8/9240 + a**7/1540 + a**6/660 + a**5/660 + 5*a**3/6 - 14*a**2. Let k(p) be the first derivative of m(p). Factor k(z).
2*z*(z + 1)**3/11
Suppose -4*r + 0 - 8 = 0, v - 2*r - 7 = 0. Solve -5*g**5 - 150*g**4 - 200*g**2 - 24 + 40*g**5 + 26*g + 250*g**v + 49*g + 14 = 0 for g.
2/7, 1
Let -2/3*a**2 - 2048/3 + 128/3*a = 0. Calculate a.
32
Let t(w) = 2*w**2 - 6*w + 3. Let u be t(0). Determine a, given that 4/3 + 4/3*a**u - 4/3*a**2 - 4/3*a = 0.
-1, 1
Let k be (-6)/36*-1 + 3457/30. Let t = k + -115. Factor 1/5*g**4 - t*g**2 + 0*g + 0 + 1/5*g**3.
g**2*(g - 1)*(g + 2)/5
Suppose -h - 24 + 7 = 0. Let c = -14 - h. Factor 3*q + 2*q - 2*q**2 - c*q + 4 - 4*q.
-2*(q - 1)*(q + 2)
Let r(y) be the third derivative of -y**5/36 - 265*y**4/36 - 14045*y**3/18 + 547*y**2. Determine q, given that r(q) = 0.
-53
Let f be (-186)/(-1519)*(-28)/60*-5. Factor 1024/7 + 384/7*s + 48/7*s**2 + f*s**3.
2*(s + 8)**3/7
Let f(j) be the first derivative of -j**6/50 + 9*j**5/100 - 39*j - 45. Let r(n) be the first derivative of f(n). Factor r(l).
-3*l**3*(l - 3)/5
Factor 3/8*r**2 + 0 + 15/2*r.
3*r*(r + 20)/8
Let x(j) be the third derivative of 0 - 1/35*j**7 + 0*j + 1/336*j**8 + 11/120*j**6 + 4/3*j**3 - 1/30*j**5 - 14*j**2 - 1/2*j**4. Factor x(h).
(h - 2)**3*(h - 1)*(h + 1)
Find v such that 235/2*v + 11045/4*v**4 - 2760*v**2 - 5/4 - 235/2*v**3 = 0.
-1, 1/47, 1
Let n(y) be the first derivative of y**5/5 + 25*y**4/4 + 63*y**3 + 407*y**2/2 + 242*y + 120. Factor n(g).
(g + 1)*(g + 2)*(g + 11)**2
Let 80*u**2 + 166 - 2*u**3 - 428*u + 486 + 1292 - 436*u - 2*u**2 = 0. What is u?
3, 18
Determine c so that -27848/9 - 2/9*c**2 + 472/9*c = 0.
118
Let s(y) be the second derivative of -y**5/20 - 13*y**4/8 - 6*y**3 + 25*y**2 + 2*y + 51. Let l(x) be the first derivative of s(x). Let l(j) = 0. What is j?
-12, -1
Let u(b) be the third derivative of b**5/45 - 4*b**4/9 + 10*b**3/3 - 106*b**2. Find i, given that u(i) = 0.
3, 5
Let u**2 + 2*u - 1/2*u**3 - 4 = 0. Calculate u.
-2, 2
Let l be (-84*(-2)/8)/7. Factor 0*u**2 + 8/7*u**4 + 0*u + 0 + 8/7*u**l + 2/7*u**5.
2*u**3*(u + 2)**2/7
Suppose 512*u - 509*u - 18 = -3*n, -2*u + 16 = 4*n. Factor -4/7*p**3 - 1/7*p**u + 0 + 0*p**2 + 0*p.
-p**3*(p + 4)/7
Let v(a) be the first derivative of 4*a**3/3 - 40*a**2 - 176*a + 223. Factor v(l).
4*(l - 22)*(l + 2)
Let b(l) = l**2 - 5*l + 5. Let r(v) = 4*v**2 - 9*v + 5. Let k(c) = 5*c**2 - 10*c + 4. Let q(j) = 2*k(j) - 3*r(j). Let n(s) = -7*b(s) - 5*q(s). Factor n(z).
3*z**2
Let b(i) be the second derivative of 8*i + 16/3*i**3 + 32/3*i**2 + 1/9*i**4 - 2/5*i**5 + 2/45*i**6 - 2. Solve b(q) = 0 for q.
-1, 4
Let a(s) = s**4 - s**3 + s - 1. Let c = -8 - -32. Let y(j) = 15*j**4 + 8*j**3 - 3*j**2 - 8*j - 12. Let g(p) = c*a(p) - 3*y(p). Suppose g(l) = 0. Calculate l.
-2, -1, -2/7, 1
Let h(u) be the third derivative of -41*u**2 - 5/2*u**3 - 1/12*u**5 + 5/6*u**4 + 0*u + 0. Solve h(z) = 0.
1, 3
Let x = 123/7 - 121/7. Let x - 1/7*n**3 + 3/7*n + 0*n**2 = 0. Calculate n.
-1, 2
Let n be (2224/160 - 17) + (-12)/(-8) + 2. Factor 14*f + n*f**3 + 22/5*f**2 + 10.
2*(f + 1)*(f + 5)**2/5
Let o = 6 + -1. Suppose 24 - 44 = -4*w - f, f = 5*w - 16. Suppose 3*r**3 - 5*r**5 + 0*r**5 - 3*r**2 - 3*r**2 + 2*r**o + 6*r**w = 0. Calculate r.
-1, 0, 1, 2
Let m(u) be the first derivative of -7*u**2/2 - 5*u + 2. Let r be m(-1). Find n, given that -12/7*n - 20/7*n**3 + 0 - 4*n**r - 4/7*n**4 = 0.
-3, -1, 0
Let z(w) be the third derivative of -w**6/60 + 3*w**4/4 + 484*w**2. Factor z(p).
-2*p*(p - 3)*(p + 3)
Let i(l) be the third derivative of -l**5/4 + 11*l**4/8 - l**3 + 104*l**2. Factor i(a).
-3*(a - 2)*(5*a - 1)
Let m be 1 + 24/(-20)*(-5)/2. Suppose -4*h = -4*n - h + 4, 5*n + 3*h = 32. Find y, given that 4*y - m + y - 7*y - 6*y - n*y**2 = 0.
-1
Let b = -17 - -3. Let s = b + 15. Let k(v) = -3*v**2 + 23*v - 49. Let a(d) = -d - 1. Let o(u) = s*k(u) - a(u). Factor o(w).
-3*(w - 4)**2