4 + x*m**3 + 3*m**3.
2*m**3*(m - 2)**2
Let t = 187 - 187. Let f(r) be the third derivative of 0*r - 1/540*r**6 + 0*r**5 + 0*r**4 - 1/945*r**7 + 0*r**3 + t - 6*r**2. Factor f(w).
-2*w**3*(w + 1)/9
Let i be 4 + (-356)/(4/(-1)). Factor -i*h**3 - 16*h + 19*h**2 - 7*h**3 - 99*h**2.
-4*h*(5*h + 2)**2
Let t(w) be the second derivative of w**7/14 + 6*w**6/5 + 27*w**5/4 + 27*w**4/2 + 248*w. Factor t(n).
3*n**2*(n + 3)**2*(n + 6)
Determine t, given that -2*t**2 + 4*t + 4*t**3 + 2*t**5 + 1996*t**4 - 3988*t**4 - 10*t**3 + 1994*t**4 = 0.
-2, -1, 0, 1
Suppose -4*f - 3*o = 121, 0 = 2*o + 2 + 4. Let w = f - -30. Factor 2/11*p**w + 12/11*p + 18/11.
2*(p + 3)**2/11
Factor -5*o**2 + 16*o + 21*o**2 - 4*o**2 + 24 - 10*o**2.
2*(o + 2)*(o + 6)
Suppose -2*w - 3 + 7 = 0. Let f be -1*(-19 - -3)*(-5)/(-30). Determine s so that 4/3 - 5/3*s**w - f*s = 0.
-2, 2/5
Let v(s) be the third derivative of s**7/7560 - s**6/1080 + s**5/360 + 7*s**4/8 - 20*s**2. Let f(g) be the second derivative of v(g). Factor f(r).
(r - 1)**2/3
Let c(w) = 12*w - 202. Let x be c(17). Let i(u) be the first derivative of 6 + 10*u**x - 4*u - 25/3*u**3. Suppose i(g) = 0. Calculate g.
2/5
Let t(s) be the third derivative of -s**7/630 - s**6/180 - s**5/180 + 21*s**2 + 4. Find m such that t(m) = 0.
-1, 0
Determine d so that 4/5*d - 8/5 + 4/5*d**2 = 0.
-2, 1
Let v(r) = r - 4. Let p be v(3). Let z(f) = 1. Let o(g) = -4*g**2 + 12*g - 16. Let y(m) = p*o(m) - 8*z(m). Factor y(a).
4*(a - 2)*(a - 1)
Let p = 21/67 + 29/335. Factor -p + 2/5*n**3 - 6/5*n**2 + 6/5*n.
2*(n - 1)**3/5
Let l(a) = 8*a**2 + 17*a + 20. Let v be -2*(3 + 36/(-8)). Let k(b) = 55*b**2 + 120*b + 140. Let u(g) = v*k(g) - 20*l(g). Find j, given that u(j) = 0.
-2
Let x = -23 + 25. Let y(h) = -2*h**3 + 6*h. Let w(b) be the second derivative of -b**3/6 - 2*b. Let r(c) = x*y(c) + 12*w(c). Factor r(m).
-4*m**3
Suppose -2*x + 3 = -z, 5*x - 4 - 8 = z. Factor 4*g**3 + 40*g + 25*g**2 + 2*g**x - 6*g**3 + 5*g**3 + 20.
5*(g + 1)*(g + 2)**2
Let r(m) be the first derivative of m**7/1470 + m**6/90 + m**5/35 - 8*m**3 + 9. Let f(b) be the third derivative of r(b). Solve f(o) = 0.
-6, -1, 0
Suppose -9/2*r**3 - 99/2*r + 27/2 + 57/2*r**2 = 0. Calculate r.
1/3, 3
Let t(s) = 2*s**3 - 3*s**2 + s - 2. Let y(g) = -17*g**2 - 15*g + 30. Let c(l) = -t(l) + y(l). Factor c(j).
-2*(j - 1)*(j + 4)**2
Let y(r) = 5*r**3 - 13*r**2 + 7*r + 22. Let k(o) = -4*o**3 + 12*o**2 - 6*o - 20. Let d(w) = -6*k(w) - 4*y(w). Factor d(z).
4*(z - 4)*(z - 2)*(z + 1)
Factor 3 + 6 - 5 - 471*k + 9*k**2 + 483*k.
(3*k + 2)**2
Let z(v) be the third derivative of -v**7/140 - 5*v**6/12 - 187*v**5/20 - 363*v**4/4 - 1331*v**3/12 + 112*v**2. Suppose z(u) = 0. What is u?
-11, -1/3
Suppose 0*n + 1/2*n**2 + 0 + n**4 + 3/2*n**3 = 0. Calculate n.
-1, -1/2, 0
Let p(l) = -l**2 - 15*l - 3. Let w be p(-15). Let o be 2 + w + 2 - 12/36. Solve o*k**2 + 6 + 4*k = 0.
-3
Let v(x) = -3*x + 8. Let l = 2 - 0. Let k be v(l). Factor 1/4*u - 1/2*u**k - 1/4*u**3 + 1/2.
-(u - 1)*(u + 1)*(u + 2)/4
Let x = 4/6017 + 11982/78221. Factor 0*f + x*f**2 - 2/13.
2*(f - 1)*(f + 1)/13
Let p(l) be the first derivative of -5*l**6/6 - 8*l**5 - 75*l**4/4 + 40*l**3/3 + 40*l**2 + 583. Suppose p(x) = 0. Calculate x.
-4, -1, 0, 1
Suppose -65*v + 21 = -64*v. Suppose 7*o + v*o + 4*o**3 - 24*o**2 - 24 + 0*o + 16*o = 0. Calculate o.
1, 2, 3
Solve -38*g + 9*g**4 - 7*g**4 - 50*g**2 - 4*g**4 - 28*g**2 - 42*g**3 = 0.
-19, -1, 0
Let z(s) be the first derivative of 3*s**4/4 + 23*s**3 - 3*s**2/2 - 69*s + 93. Let z(a) = 0. What is a?
-23, -1, 1
Let o(g) be the first derivative of -4*g**5/5 + 16*g**3/3 - 75. Factor o(h).
-4*h**2*(h - 2)*(h + 2)
Let i(j) = -3*j**3 + 5*j**2 + 22*j - 56. Let m(l) = 2*l**3 - 4*l**2 - 15*l + 37. Let a(p) = 5*i(p) + 8*m(p). Let a(b) = 0. What is b?
-2, 1, 8
Suppose 3*f = 22 - 16. Factor 50*p - 135*p - 75*p + 5*p**f + 1280.
5*(p - 16)**2
Let v(g) be the third derivative of -g**6/30 - 2*g**5/3 + g**4/6 + 20*g**3/3 - 22*g**2 + 2. What is n in v(n) = 0?
-10, -1, 1
Let n(h) = -8*h**3 + 17*h**2 - 34*h - 53. Let y(v) = -38*v**3 + 86*v**2 - 170*v - 266. Let i(t) = -28*n(t) + 6*y(t). Determine u, given that i(u) = 0.
-1, 4, 7
Let y(r) be the first derivative of -7*r**4/4 + 26*r**3/3 + 43*r**2/2 + 10*r - 87. Factor y(u).
-(u - 5)*(u + 1)*(7*u + 2)
Let i be (4/(-8) - 1)*-2. Find f such that -41*f**3 - 6*f**2 + 20 + 4 - 12*f + 44*f**i = 0.
-2, 2
Let c(b) be the third derivative of b**6/48 + 169*b**5/60 + 1411*b**4/12 - 578*b**3/3 - b**2 + 17. Find f such that c(f) = 0.
-34, 2/5
Let -4*y**2 - 52/5*y + 4/5*y**3 - 28/5 = 0. What is y?
-1, 7
Let w(r) be the second derivative of -2*r**6/9 + 7*r**5/15 - 2*r**4/9 + 2*r - 18. Factor w(z).
-4*z**2*(z - 1)*(5*z - 2)/3
Let c = 233 - 229. Let u(d) be the second derivative of 0*d**2 + 1/9*d**3 + 0 + 6*d + 1/180*d**6 - 1/40*d**5 + 0*d**c. Let u(t) = 0. What is t?
-1, 0, 2
Let y(f) = -2*f. Let r(u) = -3*u**3 + 17*u**2 + 30*u - 12. Let h(j) = 4*r(j) + 44*y(j). Let h(z) = 0. What is z?
-1, 2/3, 6
Let y(w) be the third derivative of w**8/20160 + w**7/2016 - w**6/480 - w**5/30 - w**4/24 + 10*w**2. Let j(b) be the third derivative of y(b). Factor j(a).
(a + 3)*(2*a - 1)/2
Let t be (-2)/(-4)*(10/2 + -5). Suppose t = 4*l + 2*l - 12. Determine v so that 4/3*v**l + v**3 - 2/3 - 1/3*v = 0.
-1, 2/3
Factor 16*q - 24*q**2 - 105 + 20*q - 17*q**2 + 38*q**2.
-3*(q - 7)*(q - 5)
Let i = -62/45 + 34/15. Let c(s) be the first derivative of -2/27*s**3 + 0*s**2 - 2 + i*s. Determine d so that c(d) = 0.
-2, 2
Let q(t) be the third derivative of t**6/480 + 17*t**5/240 - 37*t**4/96 + 19*t**3/24 - 6*t**2 - 2. Solve q(h) = 0 for h.
-19, 1
Let a be 6/8 + 20/16. Determine r, given that r**a + 92*r**3 - 93*r**3 + r**5 + 0*r**4 - r**4 = 0.
-1, 0, 1
Let b = 1801 - 1801. Factor -1/7*p**2 + 1/7*p**3 + 0*p + b.
p**2*(p - 1)/7
Factor 1187*z**3 - 15*z - 1186*z**3 + 23*z - 3*z**2 - 3*z**2.
z*(z - 4)*(z - 2)
Suppose -3*j = -l - 11, 207*l - 210*l = j - 7. Let 8/7*f + 8/7*f**5 - 2/7*f**j - 2/7 + 4/7*f**2 - 16/7*f**3 = 0. Calculate f.
-1, 1/4, 1
Suppose -158*l = -156*l. Suppose 0*i - 3*i + 9 = w, l = -4*w - 2*i + 16. Factor 3/2*o**w + 7/2*o**2 + 0 + o.
o*(o + 2)*(3*o + 1)/2
Let k(f) be the third derivative of 1/30*f**5 + 12*f**3 + 0 + 0*f - 37*f**2 - f**4. Factor k(a).
2*(a - 6)**2
Let k be 3/(-2)*14*(-62)/651. What is t in 0 - 10/7*t**k + 4/7*t + 8/7*t**3 - 2/7*t**4 = 0?
0, 1, 2
Let m(w) be the third derivative of -w**7/420 - w**6/36 + w**5/60 + 5*w**4/12 + 2*w**3 - 18*w**2. Let l(t) be the first derivative of m(t). Factor l(p).
-2*(p - 1)*(p + 1)*(p + 5)
Suppose -s - 37 = -39. Let u(h) be the second derivative of 1/66*h**4 - 4/33*h**3 + 6*h + 3/11*h**s + 0. Let u(w) = 0. Calculate w.
1, 3
Suppose k + 20*i + 28 = 15*i, k + 4 = -i. Factor 1/4*f**k - 1/4 - 1/4*f**3 + 1/4*f.
-(f - 1)**2*(f + 1)/4
Let m(p) = 6*p**2 - 8*p + 2. Let b(t) = -5*t**2 + 7*t - 2. Let q(l) = 7*b(l) + 6*m(l). Factor q(y).
(y - 1)*(y + 2)
Let p(g) be the first derivative of 3/140*g**5 + 0*g**3 + 0*g + 1/28*g**4 + 1/280*g**6 - 5 - 1/2*g**2. Let f(l) be the second derivative of p(l). Factor f(h).
3*h*(h + 1)*(h + 2)/7
Let b(s) be the first derivative of -1/3*s**3 + 8 + 0*s + 0*s**2. Factor b(r).
-r**2
Let x(u) = 28*u + 284. Let m be x(-10). Let h(q) be the first derivative of 0*q + 81/2*q**2 + 27/4*q**4 - m + 27*q**3 + 3/5*q**5. Factor h(z).
3*z*(z + 3)**3
Let x = -2281/2 + 1142. Solve -x*k**5 + 3/2*k**2 - 3/2*k**4 + 0 - 3*k + 9/2*k**3 = 0 for k.
-2, -1, 0, 1
Let q(n) be the second derivative of -1/20*n**5 + 1/6*n**3 + 1/24*n**4 + 0 - 2*n - 3/8*n**2 + 1/120*n**6. Determine j so that q(j) = 0.
-1, 1, 3
Let m(v) be the second derivative of -10*v**7/21 + 23*v**6/6 - 21*v**5/2 + 35*v**4/3 - 5*v**3/3 - 15*v**2/2 - 12*v + 11. Find t such that m(t) = 0.
-1/4, 1, 3
Let x(g) be the first derivative of g**6/24 - g**5/20 - 15*g**4/8 + 8*g**3/3 + 20*g**2 + 157. Factor x(i).
i*(i - 4)**2*(i + 2)*(i + 5)/4
Let v(z) be the second derivative of z**5/50 + 7*z**4/10 + 33*z**3/5 - 121*z**2/5 - 218*z. Solve v(m) = 0.
-11, 1
Let k(p) be the second derivative of 0*p**2 - 3/4*p**5 + 0*p**3 + 1/6*p**6 - 6*p + 5/6*p**4 + 0. Factor k(t).
5*t**2*(t - 2)*(t - 1)
Suppose 2*o - 2 = -2*f + 3*o, f = 2*o - 2. What is r in -3*r**3 + 85 + 18*r**f - 85 + 0*r**3 = 0?
0, 6
Let i(b) be the third derivative of -b**6/360