*r**3 + 22/5*r**2.
-2*(r - 5)**2*(r - 1)/5
Let t(y) be the first derivative of y**8/420 + y**7/105 - y**6/30 - 2*y**5/15 + 2*y**4/3 - 2*y**3/3 - 20. Let k(f) be the third derivative of t(f). Factor k(m).
4*(m - 1)**2*(m + 2)**2
Suppose 28*t**5 - 55*t**3 - 13*t**4 - 29*t**5 + 69*t**3 = 0. What is t?
-14, 0, 1
Suppose -355 + 289 = -33*y. Factor y - 8/9*s**3 + 2/9*s**4 - 4/9*s**2 + 8/3*s.
2*(s - 3)**2*(s + 1)**2/9
Let y be (-1)/2 - (-2)/4. Suppose y = -3*h - 15, -l = h + 2*h - 3. Factor -12*a**2 - 12*a**4 - 3*a - 4*a**5 - l*a**3 + 4*a**5 - 3*a**5.
-3*a*(a + 1)**4
Suppose -15 = -6*z - 87. Let p be 4/(-35) - z/30. Factor 0*l + p*l**3 - 2/7*l**2 + 0.
2*l**2*(l - 1)/7
Let c(f) = f - 1. Let j = -121 + 123. Let b(u) = -u**2 + 10*u - 34. Let v(h) = j*c(h) + b(h). Factor v(r).
-(r - 6)**2
Let u = -9 - -9. Suppose -4*r - 8 = -4*z, u*r - r - 4*z + 18 = 0. Factor -2*t**5 + 0*t**5 - t**2 - r*t**4 + 5*t**4.
-t**2*(t - 1)**2*(2*t + 1)
Let h(r) = -3*r**2 - 18*r - 6. Let z(s) = 7*s**2 + 37*s + 13. Let l(k) = 13*h(k) + 6*z(k). Factor l(a).
3*a*(a - 4)
Find i, given that 120*i**2 + 1600*i - 70*i**3 + 56*i**3 + 6*i**4 - 66*i**3 + 2000 - 2*i**4 + i**4 = 0.
-2, 10
Let k = -1780 + 1788. Let p(f) be the first derivative of 2/27*f**3 + k - 1/3*f**2 + 4/9*f. Factor p(i).
2*(i - 2)*(i - 1)/9
Let v(d) = -19*d**2. Let s be v(1). Let m = s + 23. Solve 30*q**3 + 14*q**2 + 15*q + 11*q**5 + 16*q**2 + 15*q**m - 4*q**5 - 4*q**5 + 3 = 0 for q.
-1
Let p(o) = 56*o**3 - 311*o**2 + 383*o - 139. Let n(y) = -11*y**3 + 62*y**2 - 77*y + 28. Let r(v) = -11*n(v) - 2*p(v). Solve r(i) = 0 for i.
2/3, 1, 5
Let l be (-5)/(-5)*(4 - 4)/(-5). Let t be 38/20 + (-14)/35. Factor 3/2*r**4 + 0*r**2 + l + 0*r - t*r**3.
3*r**3*(r - 1)/2
Let r(i) = 8*i**2 + i - 4. Let f be r(1). Suppose -f*n = -5*l - 0*n, 0 = 4*l - n - 15. Factor 0*b + 0 + 0*b**4 - 2/13*b**l + 0*b**2 + 2/13*b**3.
-2*b**3*(b - 1)*(b + 1)/13
Let g(f) be the third derivative of -f**5/180 + 5*f**4/72 + f**3/3 + 23*f**2. Factor g(y).
-(y - 6)*(y + 1)/3
Suppose -8*j + 4*j = -4, 0 = 3*y - 2*j - 4. Suppose -6*h - h = -56. Let 14*m - h*m + 7*m**2 - 4*m**y = 0. What is m?
-2, 0
Let g be 1 - -2 - -4*2/4. Let v(j) be the second derivative of 0 + 4/21*j**3 + 1/42*j**4 + g*j + 3/7*j**2. Factor v(y).
2*(y + 1)*(y + 3)/7
Suppose 137 = -3*z + 2*z + 4*d, 5*d = -5*z - 585. Let j = z - -123. Factor 3/2*l**j + 12*l - 18 - 3/2*l**3.
-3*(l - 2)**2*(l + 3)/2
Let u(r) = -2*r**2 + 15*r - 28. Let m be u(16). Let t be -1*16/(-6)*(-225)/m. Factor -16/9 - 16/9*x - 4/9*x**t.
-4*(x + 2)**2/9
Let u = 8773/5 + -1753. Suppose -8/5*l + 0 + 6*l**3 - 2*l**5 + 4/5*l**4 + u*l**2 = 0. What is l?
-1, 0, 2/5, 2
Let q(y) = 22*y + 135. Let w be q(-6). Let f(a) be the first derivative of 13/3*a**w + 1/5*a**5 - 3 - 6*a**2 - 3/2*a**4 + 4*a. Factor f(m).
(m - 2)**2*(m - 1)**2
Let p(a) = -30*a**2 + 455*a - 1920. Let b(m) = -5*m**2 + 76*m - 320. Suppose 4 = o + 4*h + 8, -2*h + 4 = 2*o. Let n(l) = o*p(l) - 25*b(l). Factor n(u).
5*(u - 8)**2
Suppose 2*b + 8*b = -30. Let g be -1*b/(-9) - 69/(-99). Factor g + 2/11*p**2 + 6/11*p.
2*(p + 1)*(p + 2)/11
Let i = 32 - 30. Suppose l + 3*l**i - l**3 - 2 + 9*l**3 - 9*l**3 - l**4 = 0. What is l?
-2, -1, 1
Let m(v) = v**3 + 3*v**2 - 5*v - 3. Let t be m(-4). Let c be 1 - 2 - (t + -2). Factor 0*z**3 + c*z + 0*z**2 + 0*z**4 - 2/3*z**5 + 0.
-2*z**5/3
Suppose c - 15 = -2*c. Suppose 4*a + 2*s + 1 = -s, 22 = c*a - 4*s. Solve t - 4*t**a + 5*t**2 - 2 + 0 = 0 for t.
-2, 1
Let j(i) be the third derivative of -i**8/80640 - i**7/20160 + i**6/1440 + 11*i**5/60 + 5*i**2. Let y(p) be the third derivative of j(p). Factor y(d).
-(d - 1)*(d + 2)/4
Let v(d) = d**3 - 19*d**2 + 20*d - 11. Let r(w) = -27 + 6*w**3 + 2 - 29 + 100*w - 94*w**2. Let h(t) = 3*r(t) - 14*v(t). Factor h(y).
4*(y - 2)*(y - 1)**2
Let y(l) = l**3 + 4*l**2 - 6*l - 6. Let u be y(-3). Factor -u*w**3 + 95*w**2 - 5 - 40*w - 3 - 14*w**3 - 12.
-5*(w - 2)*(w - 1)*(7*w + 2)
Let r(p) = 2*p + 33. Let s be r(-14). Determine b so that 6*b**2 + 17*b**3 + 3*b**s + 0*b**2 + 12*b**4 - 2*b**3 = 0.
-2, -1, 0
Let z(n) = 8*n**5 - 20*n**4 - 31*n**3 - 3*n**2 - 6*n. Let b(j) = -15*j**5 + 40*j**4 + 60*j**3 + 5*j**2 + 10*j. Let o(s) = -3*b(s) - 5*z(s). Factor o(y).
5*y**3*(y - 5)*(y + 1)
Suppose 4*z - 2*b - 20 = -4, -4*z + 3*b = -18. Let n(w) be the first derivative of 5/3*w**z - 20*w - 15/2*w**2 - 7. Find f, given that n(f) = 0.
-1, 4
Find l such that -16*l**2 - 66 - l**3 + 3*l**3 - 32*l + 18*l**2 + 34 = 0.
-4, -1, 4
Factor 80*u**3 + 15*u**2 + 130*u**3 + 5*u**4 - 45*u - 185*u**3.
5*u*(u - 1)*(u + 3)**2
Factor 24/5*z + 4/5*z**2 - 64/5.
4*(z - 2)*(z + 8)/5
Let f be (-146)/(-30) + 144/32*24/810. Find o such that 0 - o - 9/2*o**2 - 3/2*o**4 - f*o**3 = 0.
-2, -1, -1/3, 0
Let j(z) be the first derivative of 7*z**7/60 - 7*z**6/60 + z**5/20 - z**4/84 - 13*z**3/3 - 4. Let s(p) be the third derivative of j(p). Factor s(c).
2*(7*c - 1)**3/7
What is a in -4*a**2 + 2751 - 2747 + 0*a**2 = 0?
-1, 1
Let a(k) = 3. Let o(z) = -z. Let p(g) = -2*a(g) + 4*o(g). Let r be p(-2). Factor x - x - 2*x - x + r + x**3.
(x - 1)**2*(x + 2)
Let z(x) be the third derivative of -x**5/60 + 19*x**4/6 - 722*x**3/3 + 24*x**2. Factor z(v).
-(v - 38)**2
Let l(i) be the third derivative of i**11/831600 - i**9/50400 - i**8/25200 + 23*i**5/60 + 16*i**2. Let f(g) be the third derivative of l(g). Factor f(y).
2*y**2*(y - 2)*(y + 1)**2/5
Let o(a) = -a**3 + 3*a**2 + 4*a + 3. Let l be o(4). Let g = -16 - -22. Factor 8*w**2 - 3*w**3 + g*w**2 - 4*w - w**l - 6*w**3.
-2*w*(w - 1)*(5*w - 2)
Suppose 0 = 6*d - 28 + 16. Solve 12*l**d + 24 - 8*l**2 - 8*l**2 + 3*l - 7*l = 0.
-3, 2
Suppose 11 = -4*b + 23. Suppose -5*l + b*l = -4. Solve -9/4*w**4 - 15/4*w**l + 0 - 21/4*w**3 - 3/4*w = 0.
-1, -1/3, 0
Let y be 1/(-1) - -3*(-1)/1. Let k be 15/y + 16/4. Factor 1/2*p - k - 1/4*p**2.
-(p - 1)**2/4
Let u = -92 + 86. Let j be 2*(0/u - (-2)/8). Suppose 0*n**2 - 1/2*n**3 + j*n**4 + 0*n + 0 = 0. Calculate n.
0, 1
Let 4/3*h**2 + 2/3*h**5 + 26*h**4 + 54*h - 164/3*h**3 - 82/3 = 0. Calculate h.
-41, -1, 1
Let p(h) be the third derivative of -h**8/2856 - h**7/1785 + h**6/1020 + h**5/510 - h**2 + 12*h. Determine q, given that p(q) = 0.
-1, 0, 1
What is t in 1/6*t**2 + 0 + t = 0?
-6, 0
Let o(b) be the first derivative of b**3/9 - 5*b**2/2 - 34*b/3 + 72. Find k, given that o(k) = 0.
-2, 17
Let q be -2 + (45 - 20) + -17. Factor 0 + 3/7*u**3 + q*u**2 + 21*u.
3*u*(u + 7)**2/7
Let m(a) be the third derivative of a**6/48 - 65*a**4/48 + 5*a**3 + 36*a**2. Factor m(d).
5*(d - 3)*(d - 1)*(d + 4)/2
Let m(j) be the second derivative of 7*j**4/96 - 59*j**3/12 - 17*j**2/4 - 210*j. Suppose m(x) = 0. Calculate x.
-2/7, 34
Factor -236*x**2 + 7*x**4 - 46*x**3 + 384*x + 14*x**4 - 23*x**4 + 576.
-2*(x - 2)*(x + 1)*(x + 12)**2
Suppose 12 = -q + 2*l, -5*l = q - 11 - 19. Determine x so that 5/6*x**3 + 5/6*x**2 + q*x + 0 = 0.
-1, 0
Let v(l) be the third derivative of -l**9/18900 + l**8/4200 - l**6/450 + l**5/150 + l**4/6 - 4*l**2. Let z(i) be the second derivative of v(i). Factor z(t).
-4*(t - 1)**3*(t + 1)/5
Suppose 68 = 4*g + 20. Let b = -3 + g. Factor n**3 + b*n**2 - 2 + 2*n**5 + 11*n**2 + 19*n**3 + 4 + 10*n + 10*n**4.
2*(n + 1)**5
Let q = 7 - 4. Suppose -18*c**2 + q + 20*c - 6 - 1 + 2*c**2 = 0. What is c?
1/4, 1
Let w(o) be the second derivative of 2*o**7/21 + 4*o**6/5 + 3*o**5/5 - 10*o**4/3 + 11*o - 19. Factor w(d).
4*d**2*(d - 1)*(d + 2)*(d + 5)
Let n(d) = 196*d**4 - 1087*d**3 + 1263*d**2 + 718*d + 67. Let f(r) = -r**3 + r**2 - 2*r + 1. Let l(u) = -5*f(u) - n(u). Find x, given that l(x) = 0.
-2/7, -1/7, 3
Let c(u) be the first derivative of -u**6/48 + 19*u**5/40 - 31*u**4/8 + 12*u**3 - 54*u + 242. Factor c(m).
-(m - 6)**3*(m - 2)*(m + 1)/8
Let z = -26 - -341. What is a in -15*a + z*a**2 - 7*a**3 + 2*a**3 - 295*a**2 = 0?
0, 1, 3
Suppose x - 24 + 5 = -5*h, -3*x - 3*h + 21 = 0. Let c(l) = -3*l + 12. Let f be c(x). Factor f*a**3 + 0*a + 2/11*a**2 - 2/11*a**4 + 0.
-2*a**2*(a - 1)*(a + 1)/11
Let s be 1 + 13 + (1 - 4). Factor s*m**3 + 2*m + 6 + 2*m**2 + 8*m - 13*m**3.
-2*(m - 3)*(m + 1)**2
What is h in -2/7*h**2 - 88/7 + 90/7*h = 0?
1, 44
Let n(l) be the third derivative of -1/5*l**6 + 2/35*l**7 - 6*l**3 + 0 - 2/3*l**5 + 17*l**2 + 1/84*l**8 + 0*l + 7/2*l**4. Determine p so that n(p) = 0.
-3, 1
Let a(u) be the first derivative