**4 - 2*t**5 + 6*t - 2 - 4*t**3 + 8 - 8.
-2*(t - 1)**4*(t + 1)
Let b = -641/40 - -141/8. Factor -8/5*n**2 - 4*n - b.
-4*(n + 2)*(2*n + 1)/5
Let f(r) = -r + 16. Suppose 24 = 5*m - 3*m. Let w be f(m). Factor 2*i - 3*i**w - 41 + 41 + 12*i**3 + 4*i - 15*i**2.
-3*i*(i - 2)*(i - 1)**2
Let w be 513/(-180) + (-1 + 4 - 0). Let b(p) be the first derivative of w*p**4 + 3/5*p**3 - 3 + 3/5*p**2 + 0*p. Determine r, given that b(r) = 0.
-2, -1, 0
Let d(r) = 2*r**4 + 36*r**3 + 55*r**2 + 30*r + 3. Let p(b) = -3*b**4 - 34*b**3 - 55*b**2 - 30*b - 2. Let n(t) = 2*d(t) + 3*p(t). Factor n(w).
-5*w*(w + 1)*(w + 2)*(w + 3)
Let a(j) be the second derivative of j**9/15120 - j**7/1260 + j**5/120 - j**4/12 + 3*j. Let f(d) be the third derivative of a(d). Determine h so that f(h) = 0.
-1, 1
Suppose -3*w - 135 = -141. Let q(m) be the second derivative of 5*m**5 + 16/15*m**6 + 16*m**w + 0 - 8*m + 56/3*m**3 + 38/3*m**4 + 2/21*m**7. Factor q(b).
4*(b + 1)**2*(b + 2)**3
Suppose 0*k - 1/2*k**4 + 5/2*k**3 - 2*k**2 + 0 = 0. Calculate k.
0, 1, 4
Let h be 58/18 + 20/(-90). Determine r, given that 15*r**2 + 9*r**4 - h*r**5 + 3*r**3 - 25*r**2 - 11*r**2 + 12 = 0.
-1, 1, 2
Let w(j) be the second derivative of j**6/480 - 3*j**5/160 - 5*j**3/6 - j. Let a(h) be the second derivative of w(h). Factor a(u).
3*u*(u - 3)/4
Determine u so that 4 - 4*u + 2*u + 1410*u**3 - 6*u - 237*u**2 - 1050*u**3 = 0.
-2/15, 1/8, 2/3
Let r(y) be the first derivative of -y**4/4 + 8*y**3/3 - 19*y**2/2 + 12*y + 94. Factor r(m).
-(m - 4)*(m - 3)*(m - 1)
Let i be (-3)/(336/(-160)) - 1. Suppose -3/7*p**3 + 3/7 - i*p**2 + 3/7*p = 0. What is p?
-1, 1
Suppose -4*d - 3 = -7. Let x(o) = -4*o**3 + 8*o**2 + 6*o - 36. Let n(u) = -u**3. Let r(s) = d*x(s) - 2*n(s). Determine c so that r(c) = 0.
-2, 3
Let v be ((-8)/3)/((-1)/(-3)). Let j = v + 15. What is l in 16 - 2 + j + 25*l + 5*l**2 - 1 = 0?
-4, -1
Let s = 31/24 - -75/8. Factor 16/3*c**4 + s*c**2 + 10/3*c + 0 + 12*c**3 + 2/3*c**5.
2*c*(c + 1)**3*(c + 5)/3
Factor 85*i**3 - 14790*i + 6877/2*i**2 + 15138 + 1/2*i**4.
(i - 2)**2*(i + 87)**2/2
Let d(i) be the second derivative of i**10/241920 - i**9/60480 - i**8/53760 + i**7/10080 + 5*i**4/12 + i. Let w(l) be the third derivative of d(l). Factor w(f).
f**2*(f - 2)*(f - 1)*(f + 1)/8
Let v be (72/(-210))/(3/(-6) - 8/56). Factor -2/5*h**2 + 2/15*h**3 + v + 0*h.
2*(h - 2)**2*(h + 1)/15
Let f = -22334/3 - -89351/12. Let i be (-1 + (-10)/(-4))/6. Determine d, given that f*d**4 + 1/4*d + i - 3/4*d**5 - 3/2*d**2 + 1/2*d**3 = 0.
-1, -1/3, 1
Let v = 33 - 74. Let n = 43 + v. Solve 4/5*r - 2/5*r**n - 2/5 = 0 for r.
1
Let t(d) = 16*d**4 - 42*d**3 - 92*d**2 - 84*d - 68. Let o(v) = v**4 - v**3 + 2*v - 1. Let h(i) = 36*o(i) - 2*t(i). Suppose h(g) = 0. What is g?
-5, -1
Let p(s) = -s**5 - 15*s**4 + 16*s**3 + 6*s + 3. Let d(a) = -a**5 + a**4 + 2*a + 1. Let u(l) = 3*d(l) - p(l). Determine q so that u(q) = 0.
0, 1, 8
Let s(c) be the third derivative of 0*c + 1/630*c**7 + 0 + 0*c**4 + 1/80*c**6 - 2*c**2 - 1/9*c**3 + 11/360*c**5. Factor s(g).
(g + 1)*(g + 2)**2*(2*g - 1)/6
Let q be 80/36 + (-2)/9. Suppose 6 = q*d - 2*w, 2*d - w - 12 = -5*w. Determine g so that 62*g**d - 170*g**4 - 83*g**2 - 33*g**2 - 24*g - 180*g**3 - 20*g**5 = 0.
-3, -1, -2/5, 0
Let i = 518 - 1553/3. Suppose 2/3*o - i - 1/3*o**2 = 0. Calculate o.
1
Let f(k) be the third derivative of k**7/70 + 23*k**6/40 + 6*k**5 - 18*k**4 + 236*k**2. Factor f(x).
3*x*(x - 1)*(x + 12)**2
Let b(w) = 5*w**5 - w**4 - 11*w**3 + 10*w**2 - 3*w - 1. Suppose -g + 5 = 4. Let l(z) = -z**5 - z**3 + z**2 + z + 1. Let j(o) = g*b(o) + l(o). Factor j(p).
p*(p - 1)**2*(p + 2)*(4*p - 1)
Let q(j) be the second derivative of j**4/54 - 8*j**3/27 + 16*j**2/9 + 5*j. Factor q(i).
2*(i - 4)**2/9
Suppose -5*u = -2*k - 315, 2*k + 2*u = -0*k - 322. Let q = k - -162. Factor 186/5*j**4 + 864/5*j + 1206/5*j**q + 216/5 + 18/5*j**5 + 142*j**3.
2*(j + 3)**3*(3*j + 2)**2/5
Let n(g) = 2*g**2 + 1. Let i(f) = -f**2 - 32*f + 5. Let r(k) = 5*i(k) + 35*n(k). Solve r(q) = 0 for q.
6/13, 2
Let s = 115272/41165 + -2/8233. Factor 32/5 - s*h**2 + 108/5*h.
-2*(h - 8)*(7*h + 2)/5
Let b(v) be the second derivative of -v**4/78 - v**3/39 + 2*v**2/13 + 12*v. Factor b(y).
-2*(y - 1)*(y + 2)/13
Let i be 20/8*(-8)/10. Let f be i/(-3) - ((-40)/(-21))/5. Solve -f*a**2 - 2/7 - 4/7*a = 0.
-1
Let j be -2 + (-6 - ((-24)/3 - 0)). Factor -1/4*f**4 + 0 + 1/4*f**2 + j*f + 0*f**3.
-f**2*(f - 1)*(f + 1)/4
Let c(v) = -3*v**3 + 30*v**2 - 9*v + 2. Let b(w) = 2*w**3 - 15*w**2 + 6*w. Let u(l) = -5*b(l) - 2*c(l). Determine h so that u(h) = 0.
-1/4, 2
Solve 10/11*a**2 - 10/11 - 2/11*a**3 + 2/11*a = 0.
-1, 1, 5
Factor 1/8*f**4 + 9/2 + 13/8*f**2 - 15/2*f + 5/4*f**3.
(f - 1)**2*(f + 6)**2/8
Let 14/11*x**3 + 192/11*x - 108/11*x**2 + 64/11 = 0. What is x?
-2/7, 4
Let n(f) = -f**2 + 8. Let g(m) = 2*m**3 - 25*m**2 + 22*m + 8. Let s(p) = -2*g(p) + 2*n(p). What is t in s(t) = 0?
0, 1, 11
Suppose -24*x - 78005 - 3*x**3 + 78005 + 3*x**4 - 30*x**2 = 0. Calculate x.
-2, -1, 0, 4
Suppose 0 = 4*a - f - 12, -16 = -5*a + 291*f - 290*f. Determine h so that -24/5*h**2 - 57/5*h**3 - 21/5*h**a + 0 + 12/5*h = 0.
-2, -1, 0, 2/7
Factor 12/5*x**2 - 4/5*x**5 + 4*x**3 + 0 + 4/5*x**4 + 0*x.
-4*x**2*(x - 3)*(x + 1)**2/5
Let d(c) be the second derivative of 3/20*c**5 - 4*c - 3/4*c**4 + c**3 + 0 + 0*c**2. Solve d(x) = 0 for x.
0, 1, 2
Suppose -33*x + 18 = -48. Suppose 7/4*h**x - 5/2*h + 3/4 = 0. What is h?
3/7, 1
Let q(i) be the first derivative of 15/2*i**2 + 6 + 5/3*i**3 + 0*i. Suppose q(r) = 0. What is r?
-3, 0
Let v(p) be the second derivative of 1/5*p**4 + 0*p**2 + 4/25*p**5 + 0*p**3 + 0 + 2/75*p**6 - 15*p. Factor v(c).
4*c**2*(c + 1)*(c + 3)/5
Let q be 560/770 - 4/11. Let -q + 2/11*k**2 - 2/11*k = 0. Calculate k.
-1, 2
Let n(b) be the second derivative of -b**4/114 + 8*b**3/57 + 33*b**2/19 + 360*b. Factor n(h).
-2*(h - 11)*(h + 3)/19
Let c be 1/((40/12)/1 - 3). Let k be (122/(-42) - -3)*1*c. Find f, given that 12/7*f**2 + 8/7*f**3 + 8/7*f + k*f**4 + 2/7 = 0.
-1
Find x, given that -8/13*x**3 + 12/13*x**2 + 0 - 12/13*x**4 + 10/13*x**5 - 2/13*x = 0.
-1, 0, 1/5, 1
Factor -32/11 - 4/11*g**2 + 6*g.
-2*(g - 16)*(2*g - 1)/11
Let u = -118663/2 + 59333. Let z be (-2)/3*1/(-2). Solve -u*i**2 + 0 - z*i = 0 for i.
-2/9, 0
Let n(f) be the third derivative of 0 + 0*f + 4*f**2 + 1/20*f**5 - 1/8*f**4 + 1/360*f**6 + 1/9*f**3 - 1/210*f**7. Let n(p) = 0. What is p?
-2, 1/3, 1
Suppose -33 = -5*w - 3*m, w - 5*m = -7*m + 15. Solve 2/7*n - 2/7*n**2 - 2/7*n**w + 2/7 = 0.
-1, 1
Let i be (-525)/(-60) - 2/(-8). Suppose -14*b + i*b = -10. Factor b*s**3 + 5*s**3 - s**3 - 3*s**3 - 12 + 9*s**2.
3*(s - 1)*(s + 2)**2
Suppose 154*d = -121*d + 550. Factor 2/3*y + 2/3*y**3 + 0 + 4/3*y**d.
2*y*(y + 1)**2/3
Let y(t) be the first derivative of -t**6/2 + 7*t**5/20 - t**4/16 - 35. Factor y(u).
-u**3*(3*u - 1)*(4*u - 1)/4
Let i be 3*3 + 90/1395 + 446/(-186). Suppose 0 + i*x + 4/3*x**2 = 0. What is x?
-5, 0
Let r(n) be the second derivative of -2*n**6 + 71*n**5/5 - 22*n**4 - 88*n**3/3 + 48*n**2 + 6*n + 3. Find g, given that r(g) = 0.
-2/3, 2/5, 2, 3
Let f = -1375 - -1380. Let r(n) be the first derivative of -2/65*n**f + 4/13*n + 5/13*n**2 - 1/26*n**4 - 1 + 2/13*n**3. Solve r(g) = 0.
-1, 2
Let q = -133 + 239. Let u = q - 104. What is p in 32*p + 128/3 + 2/3*p**3 + 8*p**u = 0?
-4
Let l be (-1 - -1) + 4/10. Let v(n) = n**3 - 9*n**2 - n - 88. Let c be v(10). Factor 0 - 1/5*f**3 + l*f**c + 0*f.
-f**2*(f - 2)/5
Let h = -173 + 170. Let z be ((-6)/(-3) + h)*1/(-5). Suppose -z*x**4 + 2/5*x**2 + 1/5*x**3 + 0 + 0*x = 0. Calculate x.
-1, 0, 2
Suppose -5/2*i**4 + 19/2*i**3 - 8*i - 3/2*i**5 - 6 + 17/2*i**2 = 0. What is i?
-3, -1, -2/3, 1, 2
Let k(f) be the second derivative of -f**5/5 + 62*f**3/3 + 60*f**2 + 167*f. Factor k(b).
-4*(b - 6)*(b + 1)*(b + 5)
Let o(k) be the second derivative of 0*k**2 - 39/20*k**5 + 0 - 11/8*k**4 - 3/8*k**3 - 9/56*k**7 - 21/20*k**6 + 18*k. Find y such that o(y) = 0.
-3, -1, -1/3, 0
Let x(t) = 4*t**3 - 1. Let y be 3*1 - (-5 + 7). Let o be x(y). Let 29*a**2 - 29*a**2 + 6*a - o*a**4 + 3 - 6*a**3 = 0. What is a?
-1, 1
Suppose 7*m - 11*m = -28. Let p be m*(3 + 19/(-7)). Factor -20*d**4 - 4*d**3 + 160*d + 36*d**3 + p*d**5 - 160*d**2 - 64 + 48*d**3.
2*(d - 2)**5
Let c = -240 + 244. Let r(v) be the third derivative of -1/20*v