 - 0. Suppose 2*u**3 + u**3 + 3*u**2 - 5*u**3 + u**x = 0. Calculate u.
0, 2
Let d(v) be the third derivative of -v**5/150 + 11*v**4/60 + 5*v**2 - 11*v. Factor d(h).
-2*h*(h - 11)/5
Let u(a) be the third derivative of 0*a + 0 - 32/15*a**3 + 7/75*a**5 - 3*a**2 + 1/150*a**6 + 4/15*a**4. Factor u(v).
4*(v - 1)*(v + 4)**2/5
Let c(q) be the first derivative of q**4/4 - 5*q**3 - 17*q**2 + 2*q + 69. Let z be c(17). Factor 2/5*g**z - 4/5*g + 2/5.
2*(g - 1)**2/5
Let y = -56 + 60. Let t = 4 - y. Factor 1/3*i**3 - 1/3*i + 1/3*i**2 - 1/3*i**4 + t.
-i*(i - 1)**2*(i + 1)/3
Let t be (2 - 5)/3*-3. Suppose r + 18 = 3*l + t*r, 4*l + 2*r = 22. Let o**5 + 0 - 2*o**2 - 1 + o**l + o - 2*o**3 + 2 = 0. Calculate o.
-1, 1
Let 173*t**2 + 4*t**3 - 35*t**2 - 51*t**2 - 55*t**2 - 4*t**5 - 32*t**4 = 0. Calculate t.
-8, -1, 0, 1
Let t(s) be the second derivative of 0 - 3/70*s**5 - 1/28*s**4 + 0*s**2 + 8*s + 1/70*s**6 + 1/7*s**3. Factor t(j).
3*j*(j - 2)*(j - 1)*(j + 1)/7
Let j(m) = -2*m**2 + 3*m - 1. Let i(n) = 5*n**2 + 31*n - 118. Let s(u) = -i(u) - 2*j(u). Factor s(q).
-(q - 3)*(q + 40)
Let g = -525 + 738. Let x = g + -401/2. Factor -x - 1/2*t**2 - 5*t.
-(t + 5)**2/2
Let r(d) be the second derivative of -d**7/28 + 11*d**6/20 - 27*d**5/40 - 119*d**4/8 - 49*d**3/2 + 334*d. Determine f so that r(f) = 0.
-2, -1, 0, 7
Factor 3578*w**3 - 324 + 3132*w - 51*w**4 - 92*w**4 - 53*w**4 - 1142*w**3 - 8073*w**2.
-(w - 6)**2*(14*w - 3)**2
Suppose -5*d + 2*d - 9 = -v, 0 = 4*v + 2*d - 50. Factor k**3 - 7*k**3 - 3 + 6*k**2 + 3*k**5 + 8*k**4 - 23*k**4 + 3*k + v*k**4.
3*(k - 1)**3*(k + 1)**2
Let f be (-1)/(-1)*(-19 - -22). Let p(t) be the second derivative of 0*t**2 + 0 + t**f - 1/4*t**4 - 2*t. Solve p(u) = 0.
0, 2
Let w(l) be the second derivative of -24*l**2 - 38*l - l**4 + l**5 - 64/3*l**3 + 0. Factor w(p).
4*(p - 3)*(p + 2)*(5*p + 2)
Factor -4/5 + 4/5*f**2 - 1/5*f + 1/5*f**3.
(f - 1)*(f + 1)*(f + 4)/5
Let m(x) be the first derivative of -2*x**2 - 1/5*x**5 + 12 - x**3 + 4*x + x**4. Find r such that m(r) = 0.
-1, 1, 2
Let j = -16 - -20. Factor -173*m**j - 8*m**3 + 350*m**4 - 178*m**4 - 16*m**2.
-m**2*(m + 4)**2
Suppose -f + 4*f = 4*v - 219, 148 = -2*f + 2*v. Let j = f - -80. Let 1/2 - 1/2*r**2 - 1/2*r**j + 1/2*r = 0. What is r?
-1, 1
Let w(l) = -2*l**3 - l**2 - 2*l + 2. Let b be w(0). Factor -3/5*g**3 + 0 + 0*g + 0*g**4 + 3/5*g**5 + 0*g**b.
3*g**3*(g - 1)*(g + 1)/5
Let m(s) = 2*s**3 - 10*s**2 + 4*s + 4. Let u(a) = -6*a**2 - 4*a. Let h(f) = -f**2 - f. Let k(q) = 5*h(q) - u(q). Let x(r) = -6*k(r) - m(r). Factor x(w).
-2*(w - 2)*(w - 1)*(w + 1)
Let i(b) be the second derivative of b**4/6 - 280*b**3/3 + 19600*b**2 + b + 18. Suppose i(j) = 0. Calculate j.
140
Let o(z) = z - 59. Let w be o(63). Factor 0 - 1/4*b**w + b**3 - b**2 + 0*b.
-b**2*(b - 2)**2/4
Let n(g) be the second derivative of -1/95*g**6 + 1/399*g**7 - 2/57*g**3 + 1/38*g**4 + 0*g**2 + 1/190*g**5 + 0 + 12*g. Find v, given that n(v) = 0.
-1, 0, 1, 2
Let i(l) be the first derivative of -7*l**4/12 - 5*l**3/9 + l**2/3 + 12. Find t, given that i(t) = 0.
-1, 0, 2/7
Let u(q) = q**2 - 14*q - 13. Let m be u(11). Let f = m + 95/2. Factor 0 + 3*b**2 - 3/2*b**3 - f*b.
-3*b*(b - 1)**2/2
Let b = 159/4 - 32. Find t such that 5*t**3 + 0 + b*t**4 + 0*t + t**2 + 15/4*t**5 = 0.
-1, -2/3, -2/5, 0
Let v(x) = 3*x**3 - 27*x**2 - 61*x - 29. Let o(i) = -7*i**3 + 53*i**2 + 122*i + 57. Let g(q) = -2*o(q) - 5*v(q). Factor g(k).
-(k - 31)*(k + 1)**2
Factor -13 + w**3 - 177305*w + 177362*w + 41 + 30*w**2.
(w + 1)**2*(w + 28)
What is o in -122/15*o**2 - 2/15*o**4 - 28/15*o**3 - 24/5 - 56/5*o = 0?
-6, -1
Let x be (7/2)/(1015/1160). Factor -8/5 - 2/5*r**3 - 18/5*r**2 - 22/5*r + 2/5*r**x.
2*(r - 4)*(r + 1)**3/5
Let s(c) be the first derivative of -1/8*c**6 - 1/2*c**3 + 4/5*c**5 + 7/2*c**2 - 26 - 2*c - 23/16*c**4. What is u in s(u) = 0?
-1, 1/3, 2
Factor -72/5 - 84/5*w - 2/5*w**2 - 1/5*w**4 + 9/5*w**3.
-(w - 6)**2*(w + 1)*(w + 2)/5
Let a(h) be the second derivative of -h**6/20 - 3*h**5/20 + 3*h**4/8 + 2*h**3 + 3*h**2 + 49*h - 5. Suppose a(r) = 0. What is r?
-2, -1, 2
Let w = 101 - 47. Let p = 59 - w. Factor -8/7*u**3 + 4/7 - 4/7*u**2 + 6/7*u + 2/7*u**p + 0*u**4.
2*(u - 2)*(u - 1)*(u + 1)**3/7
Let r be ((-9)/162 - (-92)/360) + (-18)/(-10). Determine u so that 0 + 1/5*u**r + 4/5*u = 0.
-4, 0
Let y(p) be the second derivative of p**6/105 - p**5/35 - p**4/14 + 8*p**3/21 - 4*p**2/7 - 2*p - 91. Find z, given that y(z) = 0.
-2, 1, 2
Suppose -3 = 4*k - k. Let x be (3 - k) + 2/(-1). Factor 10*p**2 - x*p**2 - 7*p**2 + 2*p.
p*(p + 2)
Let t(r) be the first derivative of -r**3/18 - 9*r**2/4 - 99. Let t(z) = 0. What is z?
-27, 0
Factor 0*w - 48*w**3 + 0 + 40*w**4 + 32/3*w**2 + 100/3*w**5.
4*w**2*(w + 2)*(5*w - 2)**2/3
Let m(s) be the second derivative of -1/15*s**5 - 2/45*s**6 + 0*s**3 + 24*s + 0*s**2 + 2/9*s**4 + 0. Factor m(g).
-4*g**2*(g - 1)*(g + 2)/3
Let y be 12/6 + -2 + 2 + 2. Let r(q) be the first derivative of -1 + q**3 + 0*q**2 + 0*q + 3/4*q**y. Factor r(m).
3*m**2*(m + 1)
Find d such that -1/5*d**5 + 3/5*d**2 + d**4 - 7/5*d**3 + 0*d + 0 = 0.
0, 1, 3
Factor -4/3*g**3 + 0*g + 40*g**2 + 0.
-4*g**2*(g - 30)/3
Let d(t) be the second derivative of t**7/105 - 4*t**6/75 + 24*t. Factor d(z).
2*z**4*(z - 4)/5
Let x(i) be the third derivative of i**8/1680 + i**7/175 + 7*i**6/600 - 3*i**5/50 - 11*i**4/30 - 4*i**3/5 + 5*i**2 - 4. Find b such that x(b) = 0.
-3, -2, -1, 2
Solve -6115 + 6111 + 4*i**2 - i**4 + i**2 = 0 for i.
-2, -1, 1, 2
Let v = 161 - 156. Suppose -v*z - 2*o - 8 = 2*o, -3*z + o + 2 = 0. Factor 0*u - 1/3*u**5 + 0*u**2 + 4/3*u**4 - 4/3*u**3 + z.
-u**3*(u - 2)**2/3
Let u(x) be the first derivative of 2*x**5/75 + x**4/5 + 16*x**3/45 - 7. Factor u(w).
2*w**2*(w + 2)*(w + 4)/15
Let p(k) be the second derivative of 1/14*k**5 + 1/21*k**3 + 0*k**2 + 2/21*k**4 - 6*k + 2/105*k**6 + 0. Factor p(z).
2*z*(z + 1)**2*(2*z + 1)/7
Let y(p) be the first derivative of -8*p**5/55 - p**4/22 + 8*p**3/11 + p**2 + 4*p/11 - 151. Let y(x) = 0. Calculate x.
-1, -1/4, 2
Let t(n) be the first derivative of 4/21*n**3 - 16/7*n + 6/7*n**2 - 8. Factor t(s).
4*(s - 1)*(s + 4)/7
Let m(j) be the third derivative of j**5/90 + j**4/36 - 2*j**3/9 + 24*j**2 + j. Let m(p) = 0. What is p?
-2, 1
Factor 1/3*u**2 + 10 + 13/3*u.
(u + 3)*(u + 10)/3
Suppose 2*t + c = 8, 12 = 3*t - 3*c + c. Let l(s) be the first derivative of 8/15*s**3 + 1/20*s**t + 18/5*s + 21/10*s**2 - 14. Determine k, given that l(k) = 0.
-3, -2
Let p(o) be the second derivative of -o**8/43680 - o**7/8190 - o**6/4680 - 7*o**4/12 + 17*o. Let w(z) be the third derivative of p(z). Factor w(a).
-2*a*(a + 1)**2/13
Factor -8*d**4 + 2*d**4 + 0*d**4 + 2*d**3 - 35*d**2 + 2*d**4 + 5*d**4.
d**2*(d - 5)*(d + 7)
Let y(l) be the first derivative of 2*l**5/55 - l**4/22 - 4*l**3/11 + 4*l**2/11 + 16*l/11 + 118. Determine x, given that y(x) = 0.
-2, -1, 2
Let q(i) = 89*i**3 - 169*i**2 + 81*i + 9. Let y(b) = 179*b**3 - 341*b**2 + 163*b + 17. Let t(r) = 9*q(r) - 5*y(r). Find n, given that t(n) = 0.
-2/47, 1
Let s(q) = 13*q**4 - 18*q**2 - 13*q - 8. Let r(f) = -11*f**4 + f**3 + 18*f**2 + 14*f + 8. Let c(a) = -7*r(a) - 6*s(a). Suppose c(g) = 0. What is g?
-2, -1
Let t(f) be the second derivative of 5*f**8/504 - 4*f**7/105 + f**6/20 - f**5/45 - 15*f**2/2 - 12*f. Let v(q) be the first derivative of t(q). Factor v(a).
2*a**2*(a - 1)**2*(5*a - 2)/3
Let g(a) = 9*a**2 + 33*a + 67. Let h(b) = 5*b**2 + 17*b + 34. Let k(d) = 6*g(d) - 11*h(d). Let j be k(13). Suppose 1/2*f**j - 1/2*f + 0 = 0. Calculate f.
0, 1
Let v(r) be the third derivative of r**5/12 + 5*r**4/2 + 50*r**3/3 + 33*r**2. Let v(p) = 0. What is p?
-10, -2
Factor 15*t + 4 - 3*t**2 + 7 + 6 + 14 - 13.
-3*(t - 6)*(t + 1)
Factor 3*s**3 - 13 + 6*s**2 - 207*s - 11 + 195*s.
3*(s - 2)*(s + 2)**2
Let b = 147 - 150. Let p(m) = -m**3 - m**2 + m + 1. Let l(z) = -z**4 + 2*z**3 - 12*z**2 + 10*z + 1. Let o(u) = b*p(u) + l(u). Solve o(k) = 0 for k.
1, 2
Suppose -5*f + 246 = 2*k, -9 = -f + 3*k + 47. Let p = f + -48. Let -3/7 + 3/7*u**p + 0*u = 0. Calculate u.
-1, 1
Let p(a) = -a. Let d be (-2 - -3)/((-11)/44). Let z(r) = -2*r + r**2 - 2*r - 4*r**2. Let u(b) = d*p(b) + z(b). Let u(g) = 0. Calculate g.
0
Let i(k) be the third derivative of -k**8/151200 + k**7/37800 + k**5/60 + 9*k**2. Let c(z) be the third derivative of i(z). Factor c(