. Suppose 7 + 1 = o*d. Factor -d*t**2 + 0*t**2 + 4*t**4 - 2*t**4 + 0*t**2.
2*t**2*(t - 1)*(t + 1)
Let t(k) be the second derivative of -k**7/14 + 7*k**6/10 - 9*k**5/10 + 2*k + 9. Factor t(f).
-3*f**3*(f - 6)*(f - 1)
Suppose 2*z + 5*g - 21 = 0, 4*z + g + 2*g = 21. Let v be -5 + 15/((-1)/((-2)/z)). Factor 0 - 24/5*q**3 - 16/5*q**2 + 36/5*q**4 - 2*q**v + 0*q.
-2*q**2*(q - 2)**2*(5*q + 2)/5
Let g(j) be the second derivative of 1/30*j**5 + 0*j**4 + 0*j**3 - 1/45*j**6 + 2*j + 0 + 0*j**2. Factor g(o).
-2*o**3*(o - 1)/3
Let k(z) be the first derivative of -2*z**3/27 - 59*z**2/9 - 116*z/9 + 41. Factor k(c).
-2*(c + 1)*(c + 58)/9
Factor 3/2*f**3 + 0*f + 0 - 3*f**2.
3*f**2*(f - 2)/2
Let i(x) be the third derivative of 0*x**5 - 2*x**2 + 0 - 1/24*x**6 + 0*x - 5/3*x**3 + 5/8*x**4. Factor i(k).
-5*(k - 1)**2*(k + 2)
Factor 0 - 1/8*g**2 - 5/4*g.
-g*(g + 10)/8
Let d = -551/100 + 144/25. Factor -3/4 + 1/4*w**3 + 3/4*w**2 - d*w.
(w - 1)*(w + 1)*(w + 3)/4
Suppose 4*j = j + 3. Suppose -3 = -w - j. Find o such that 1/2 + 1/4*o + 13/4*o**3 - 19/4*o**w + 17/4*o**4 - 7/2*o**5 = 0.
-1, -2/7, 1/2, 1
Suppose 7 = 6*u + 43. Let d(h) = 3*h**4 + 5*h**3 + 11*h**2 + h + 4. Let p(x) = -x**4 - x**3 - x**2 - 1. Let w(i) = u*p(i) - d(i). Factor w(b).
(b - 1)*(b + 1)**2*(3*b - 2)
Suppose -2*q + 0*q + 6 = 0, 3*v = -5*q - 51. Let s = 112/5 + v. Suppose -7/5*d**5 + 7/5*d**3 - 2/5*d**4 + 0 + 0*d + s*d**2 = 0. Calculate d.
-1, -2/7, 0, 1
Let z(l) be the first derivative of 5 + 0*l - 816/5*l**5 - 32*l**6 + 17*l**3 - 45*l**4 + 6*l**2. Find b, given that z(b) = 0.
-4, -1/4, 0, 1/4
Let c(b) = -6*b**4 - 133*b**3 - 114*b**2 - 13*b. Let g(s) = 3*s**4 + 66*s**3 + 57*s**2 + 6*s. Let o(t) = 6*c(t) + 13*g(t). Factor o(m).
3*m**2*(m + 1)*(m + 19)
Let s be 12/9 + (-330)/315. Factor 0 + s*l + 2/7*l**2.
2*l*(l + 1)/7
Factor -427*w - 34*w**2 + 226*w**2 + 2*w**4 + 683*w + 36*w**3.
2*w*(w + 2)*(w + 8)**2
Suppose j = 2*j - 11. Let c = j - 9. Determine t so that -7*t**2 + t - 2 + 2 - 4*t**3 + 4*t**c = 0.
-1, 0, 1/4
Let g = -742/99 - -74/9. Let d(s) be the first derivative of 20/11*s**2 - g*s + 2 - 50/33*s**3. Let d(v) = 0. Calculate v.
2/5
Let j(i) = -730*i - 10. Let b(l) = l**2 + 366*l + 6. Let o(r) = 5*b(r) + 3*j(r). Factor o(x).
5*x*(x - 72)
Let i = 27801 - 27801. What is j in 0 + 2/9*j**3 - 2/3*j**2 + i*j = 0?
0, 3
Factor -4/3*s**4 - 5/3*s**2 - 2/3*s + 11/3*s**3 + 0.
-s*(s - 2)*(s - 1)*(4*s + 1)/3
Let a be (-2 + 2)/(((-16)/(-4))/(-4)). Factor 2*g**2 + 2 + a - 4*g + g**3 - 10.
(g - 2)*(g + 2)**2
Let w(t) be the second derivative of t**7/2520 + t**6/240 - t**4/3 + 19*t. Let y(c) be the third derivative of w(c). Factor y(f).
f*(f + 3)
Let h(r) = -r**2 - 20*r - 36. Let z be h(-18). Let c be 1 - 5/(-5 + z). Suppose -2/3 - 1/6*l**c + 2/3*l = 0. What is l?
2
Let f be (2 + -20)*(-4)/6. Suppose 7*d - f*d = -175. Factor -2 - 7*u**2 + 2*u**3 + 2 - d*u**4 - 2*u + 42*u**4.
u*(u - 1)*(u + 1)*(7*u + 2)
Suppose -3*b + 9 = -0*b. Factor -42*g**2 + 4 + 75*g**b - 18*g**2 - 4 + 12*g.
3*g*(5*g - 2)**2
Let a(p) be the third derivative of -p**5/390 + 53*p**4/156 - 4*p**3/3 + 35*p**2 - 3. Factor a(x).
-2*(x - 52)*(x - 1)/13
Let d(m) = -10*m + 60. Let x be d(6). Let z(c) be the first derivative of -2 + 0*c - 2/27*c**3 + x*c**2. Factor z(a).
-2*a**2/9
Let q = 55 - 43. Factor 10*s + q + 2*s**2 + 6*s**2 + 2*s**3 + 0 - 8.
2*(s + 1)**2*(s + 2)
Let u = 136 + -129. Let l(b) be the third derivative of 1/270*b**5 + 0 + 0*b + 1/540*b**6 + 0*b**3 + 6*b**2 - 1/945*b**u - 1/108*b**4. Factor l(m).
-2*m*(m - 1)**2*(m + 1)/9
Suppose -6 = -4*t + 9*a - 12*a, -3*a - 3 = t. Factor 8/7*p + 6/7*p**2 - 4/7*p**t - 2/7*p**4 - 8/7.
-2*(p - 1)**2*(p + 2)**2/7
Determine u so that -1/3*u**2 - 136/3*u - 4624/3 = 0.
-68
Let p be 2062/(-1792) - ((14 - 6) + -10). Let s = p - -1/128. Factor -4/7 - 2/7*w**2 + s*w.
-2*(w - 2)*(w - 1)/7
Let n(q) be the first derivative of q**9/756 + q**8/84 + 3*q**7/70 + 7*q**6/90 + q**5/15 + 10*q**3/3 - 6. Let l(s) be the third derivative of n(s). Factor l(d).
4*d*(d + 1)**3*(d + 2)
Let z(l) be the third derivative of 0*l + 1/18*l**3 + 7/144*l**4 - 1/630*l**7 - 2*l**2 - 1/2016*l**8 + 1/45*l**5 + 1/360*l**6 + 0. Factor z(f).
-(f - 2)*(f + 1)**4/6
Let r(g) = -13*g**4 - 7*g**3 + 29*g**2 + 153*g + 144. Let y(u) = 6*u**4 + 4*u**3 - 14*u**2 - 76*u - 72. Let a(m) = 4*r(m) + 9*y(m). Factor a(x).
2*(x - 3)*(x + 2)**2*(x + 3)
Let n(k) be the second derivative of 0*k**2 + 1/66*k**4 + 34*k + 0*k**3 - 1/110*k**5 + 0. Solve n(b) = 0 for b.
0, 1
Find h, given that 3/2*h**2 - 12*h - 27/2 = 0.
-1, 9
Let v(s) be the third derivative of -s**9/756 - s**8/105 - 2*s**7/105 - s**3/6 - 6*s**2. Let y(f) be the first derivative of v(f). Factor y(x).
-4*x**3*(x + 2)**2
Let r(t) = 3*t**3 - t**3 + 3*t**2 - 2*t - 4*t**3 + 3*t**3. Let i be r(-2). Factor y - i*y**2 + 5*y + 2*y**3 + 0*y**3.
2*y*(y - 3)*(y - 1)
Let r = 2545 - 17788/7. Factor -87/7*i**2 + r*i**3 - 12/7 + 72/7*i.
3*(i - 2)*(i - 1)*(9*i - 2)/7
Let b be 2*3*13/39. Suppose 3*h - 7 = 2*c + 8, 5*h = b*c + 21. Solve 3/2*s**2 + 0 + h*s = 0 for s.
-2, 0
Suppose 4*q + 332 = -u, -3*q - 3*u - 25 - 215 = 0. Let x be 15/q - 12/(-28). Factor -1/4*l**3 + 0 - x*l**2 + 1/2*l.
-l*(l - 1)*(l + 2)/4
Let k(l) be the second derivative of l**4/54 + 34*l**3/27 + 289*l**2/9 - l + 32. Factor k(p).
2*(p + 17)**2/9
Let z(q) be the first derivative of 5*q**4/12 + 4*q**3/3 + 8*q**2/5 - 30*q + 4. Let d(c) be the first derivative of z(c). Factor d(i).
(5*i + 4)**2/5
Let n(k) be the second derivative of k**9/15120 - k**7/1260 + k**5/120 + 13*k**4/6 + k. Let t(r) be the third derivative of n(r). Factor t(y).
(y - 1)**2*(y + 1)**2
Let s(i) be the third derivative of -i**7/630 - i**6/72 - i**5/30 + i**4/18 + 4*i**3/9 + i**2 + 7*i. Factor s(q).
-(q - 1)*(q + 2)**3/3
Determine t, given that 10*t**4 - 1 + 239*t**2 + 6*t - 267*t**2 - 2*t**5 - 4*t**3 + 19 = 0.
-1, 1, 3
Let z be 2*(-3)/(-2) - (1 + 2). Let d(t) be the third derivative of 0*t + 1/360*t**6 + 1/9*t**3 - 10*t**2 - 1/24*t**4 + z + 0*t**5. Factor d(v).
(v - 1)**2*(v + 2)/3
Let l(u) = -3*u**2 + 8*u + 5. Let q be l(3). Let z(c) be the second derivative of -1/15*c**q - 1/90*c**4 + 0 - 2*c - 2/45*c**3. Suppose z(b) = 0. What is b?
-1
Let f = -1547/2 - -4645/6. Let n(d) be the second derivative of -f*d**3 + 1/5*d**5 - 4*d**2 + 2/3*d**4 + 2*d + 0. Let n(j) = 0. What is j?
-2, -1, 1
Factor 128/5*j + 2/5*j**2 + 0.
2*j*(j + 64)/5
Suppose 9*d + 2*d = 17*d. Suppose 8/7*w**2 - 2/7*w**3 + d + 0*w = 0. What is w?
0, 4
Suppose 0*o + 0*o**2 + 2/7*o**4 + 2/7*o**3 + 0 = 0. What is o?
-1, 0
Let v(g) be the second derivative of 3/2*g**2 + 0*g**3 + 3*g + 0*g**4 + 1/300*g**5 + 0. Let k(i) be the first derivative of v(i). Let k(s) = 0. What is s?
0
Suppose a + 4*w + 10 = 3, 0 = 4*w + 12. Let n be (4/a)/((-1)/(-15)). Factor -7*b + n + 3*b**2 - 7*b + 2*b.
3*(b - 2)**2
Let v(o) be the second derivative of -o**7/210 + 3*o**6/25 - 6*o**5/5 + 92*o**4/15 - 88*o**3/5 + 144*o**2/5 - 17*o. Suppose v(u) = 0. What is u?
2, 6
Let u(p) = -2*p**3 + 12*p**2 + 3. Let b be u(6). Let t(m) be the second derivative of 0 + 1/20*m**5 + 1/4*m**4 + 1/2*m**b + 1/2*m**2 + 5*m. Factor t(c).
(c + 1)**3
Let h be 2 + ((-36)/56)/9. Let y = h + -3/7. Factor -s + y - 1/2*s**2.
-(s - 1)*(s + 3)/2
Let x be (1/(-2) + 2)*(-1514)/3. Let f = x + 8333/11. Determine d so that 8/11*d - f - 2/11*d**2 = 0.
1, 3
Suppose o + 21 = 4*o. Suppose -5 = -4*m + o. Find s, given that s**2 - s**m - 343 + 343 = 0.
0, 1
Let h(x) be the first derivative of -5*x**4/4 - 5*x**3/3 + 15*x**2 - 58. Suppose h(p) = 0. What is p?
-3, 0, 2
Let t(g) = -59*g**2 + 319*g + 78. Let l(j) = -12*j**2 + 64*j + 16. Let f(b) = 22*l(b) - 4*t(b). Factor f(d).
-4*(d - 5)*(7*d + 2)
Let l(s) be the third derivative of 1/240*s**6 + 5/6*s**3 - 13/48*s**4 + 0*s - 29*s**2 + 1/60*s**5 + 0. Find r such that l(r) = 0.
-5, 1, 2
Let g(v) be the third derivative of 0 + 1/3*v**4 - 1/15*v**5 + 5*v**2 + 0*v - 2/3*v**3. Factor g(a).
-4*(a - 1)**2
Determine m so that 126 + 2*m**3 - 256 - 2*m + 6*m**2 + 124 = 0.
-3, -1, 1
Let r(m) be the second derivative of 3*m - 5/6*m**4 + m**2 - 3/10*m**5 + m**3 + 0 + 4/15*m**6. Let r(c) = 0. What is c?
-1, -1/4, 1
Factor 69*t + 31*t - 8*t**2 - 2*t**2 - 12*t**3 + 40 - 13*t**3.
-5*(t - 2)*(t + 2)*(5*t + 2)
Let r(p) be the third derivative of p**10/75600 - p**9/