r b(x).
2*(x - 3)**2*(x + 4)**2/17
Suppose -2*d + 1 = -9. Let q(i) be the second derivative of 0 + d*i + 2/5*i**2 + 1/50*i**5 + 1/3*i**3 + 2/15*i**4. Factor q(f).
2*(f + 1)**2*(f + 2)/5
Suppose 14*x - 48 + 6 = 0. Let k(z) be the third derivative of 0*z**5 + 9*z**2 + 0*z**4 + 0*z**x - 1/210*z**7 - 1/60*z**6 + 0 + 0*z. Solve k(v) = 0.
-2, 0
Let o be (-3)/(-9) - (-28)/6. Let f(z) be the first derivative of -3/4*z**4 + 2/5*z**o - 1/4*z**2 - 1/12*z**6 + 0*z - 4 + 2/3*z**3. Find h such that f(h) = 0.
0, 1
Find w such that 2/3*w + 0 - 2*w**3 + 1/3*w**5 + 5/6*w**4 + 1/6*w**2 = 0.
-4, -1/2, 0, 1
Let n = 30 - 19. Suppose n*v - 3 = 10*v. Factor -3/4*b**v + 0*b - 3/4*b**2 + 0.
-3*b**2*(b + 1)/4
Let v(b) = -84*b**3 + 180*b**2 - 112*b + 16. Let q(w) = 84*w**3 - 181*w**2 + 111*w - 14. Let l(g) = 4*q(g) + 5*v(g). Factor l(d).
-4*(d - 1)*(3*d - 2)*(7*d - 3)
Let v(j) be the third derivative of -j**8/224 + j**7/30 - 13*j**6/120 + j**5/5 - 11*j**4/48 + j**3/6 - 92*j**2. Factor v(h).
-(h - 1)**4*(3*h - 2)/2
Suppose -11 = -117*w + 106*w. Let x = -27 + 55/2. Let -1/2*p + x*p**3 + w - p**2 = 0. What is p?
-1, 1, 2
Let y = 4187/264 + -174/11. Let c(m) be the third derivative of 0*m + 1/140*m**7 + 7/120*m**5 + 0*m**3 + 4*m**2 + 0 - 1/30*m**6 - y*m**4. Factor c(a).
a*(a - 1)**2*(3*a - 2)/2
Let w be ((-1)/30)/(150/(-250))*4. Factor 2/9*m**3 + w*m**4 - 2/3*m**2 - 2/9*m + 4/9.
2*(m - 1)**2*(m + 1)*(m + 2)/9
Suppose -14 + 14 = 3*b. Suppose 33 - 71 - 4*q**2 - 32*q + b*q**2 - 26 = 0. What is q?
-4
Suppose -5 = -w - 1. Factor -81*x**4 + 83*x**4 - w*x**2 + 2*x**2.
2*x**2*(x - 1)*(x + 1)
Let f(n) = 25*n**3 + 33*n**2 + 12*n + 15. Let u(m) = 3*m**3 + 4*m**2 + m + 2. Let y(t) = 6*f(t) - 51*u(t). Factor y(i).
-3*(i - 1)**2*(i + 4)
Let f be 4/(-34) + (8 - 2595/340). Let t(n) be the first derivative of 1/8*n**4 - f*n**2 + 7 + 1/10*n**5 - 1/6*n**3 + 0*n. Factor t(o).
o*(o - 1)*(o + 1)**2/2
Let a(g) = g + 1. Let h(d) be the second derivative of d**4/12 + d**3/2 + d**2 - 33*d. Let y(q) = 5*a(q) - 5*h(q). Factor y(r).
-5*(r + 1)**2
Find u such that 16/5*u**3 + 32/5 - 6*u**2 - 2/5*u**4 - 16/5*u = 0.
-1, 1, 4
Let g be (3 - 3)/(3 - 2). Suppose 7*w + 5*x = 2*w, g = 3*w - 2*x - 10. Solve -8/11*p**w + 6/11*p**4 + 0*p**3 + 0 + 0*p + 2/11*p**5 = 0.
-2, 0, 1
Let j(p) be the second derivative of -p**4/6 - 100*p**3 - 22500*p**2 + 252*p. Let j(z) = 0. What is z?
-150
Let f(w) be the second derivative of 1/2*w**2 - 1/40*w**6 - 1/10*w**5 + 6*w - 1/48*w**4 + 1/3*w**3 + 0. Suppose f(b) = 0. Calculate b.
-2, -1, -2/3, 1
Let t(g) be the second derivative of g**6/50 + 9*g**5/25 - 13*g**4/20 - 113*g. Solve t(z) = 0.
-13, 0, 1
Factor 42*i**2 + 36*i - 64 + 5*i**3 - 96 - 24*i**2 + 67*i**2 + 34*i.
5*(i - 1)*(i + 2)*(i + 16)
Factor 20/11*j**2 + 38/11*j**3 + 16/11*j**4 - 2/11*j**5 + 0*j + 0.
-2*j**2*(j - 10)*(j + 1)**2/11
Suppose 12*h - 8*h - 4*b + 16 = 0, h = 3*b - 4. Let c be (-110)/(-21) + h/7. Solve 16/3 + 20*y**2 - 24*y - c*y**3 = 0.
2/7, 2
Let b(o) = o + 8. Let c be b(-9). Let t be (((-2)/(-27))/c)/(7/(-21)). Factor -2/9*k**3 + t*k - 2/9*k**2 + 2/9.
-2*(k - 1)*(k + 1)**2/9
Let s(u) be the second derivative of u**6/2700 - u**5/300 - 35*u**3/6 - 31*u. Let a(l) be the second derivative of s(l). Find k, given that a(k) = 0.
0, 3
Let n(z) be the first derivative of -8/27*z**3 + 0*z - 23 + 1/3*z**4 - 4/45*z**5 + 0*z**2. What is j in n(j) = 0?
0, 1, 2
Let b(r) be the third derivative of -32*r**7/105 - 52*r**6/15 - 49*r**5/15 - r**4 - 42*r**2. Let b(j) = 0. What is j?
-6, -1/4, 0
Let h(u) be the second derivative of 0*u**3 + 0*u**2 - 8*u - 5/12*u**4 + 0 + 1/4*u**5. Factor h(g).
5*g**2*(g - 1)
Let x = 133 + -138. Let k be (-10)/(-100)*x/(-2). Solve -k*j - 1/4*j**2 + 0 = 0.
-1, 0
Let h(x) = -5*x - 27. Let g be h(-6). Let w be (-2 - -4)/(g/2). Solve -4/3*a**3 + 0 - w*a - 14/3*a**2 + 2*a**4 = 0.
-1, -1/3, 0, 2
Let k be 13/(-156) - ((-3)/18 - 0). Let n(m) be the first derivative of 0*m**2 + 1/18*m**6 + 2/15*m**5 - 4 + 0*m**3 + k*m**4 + 0*m. Solve n(f) = 0.
-1, 0
Let v(d) be the second derivative of -1/6*d**3 + 0 + 6*d + 2*d**2 - 1/24*d**4 + 1/60*d**5 + 1/120*d**6. Let o(g) be the first derivative of v(g). Factor o(z).
(z - 1)*(z + 1)**2
Let b(u) be the third derivative of -u**7/70 + u**6/30 + 4*u**5/15 - 2*u**4/3 - 8*u**3/3 - 34*u**2 + 1. Factor b(i).
-(i - 2)**2*(i + 2)*(3*i + 2)
Let r be (-67755)/(-680) - (-1)/8. Let g = 100 - r. Factor -2/17*v**2 - g*v - 2/17.
-2*(v + 1)**2/17
Suppose -5*f + 851 - 836 = 0. Let b(l) be the first derivative of 2/5*l**5 - 1/12*l**6 + f - 1/3*l**3 - l - 1/2*l**4 + 5/4*l**2. Factor b(o).
-(o - 2)*(o - 1)**3*(o + 1)/2
Let c be -15 + 20 + (-20)/6. Let v(k) be the first derivative of 2*k + 8 - 7/2*k**2 - c*k**3 + k**4. Factor v(f).
(f - 2)*(f + 1)*(4*f - 1)
Solve 8/9 - 2/9*r**2 - 2/3*r = 0.
-4, 1
Let z = 6 - 7. Let j(a) = 12*a**3 + 3*a**2 - 27*a + 8. Let i(d) = -d**3 + d**2 + d + 1. Let t(r) = z*j(r) - 2*i(r). Find v, given that t(v) = 0.
-2, 1/2, 1
Let t(o) be the third derivative of -o**7/1470 + o**5/210 - o**3/42 - 16*o**2. Let t(g) = 0. Calculate g.
-1, 1
Let q = -127/35 + 21/5. Find u, given that 0*u + q*u**3 + 0 + 20/7*u**2 = 0.
-5, 0
Let m be 10/(-4)*(11/(-110))/((-4)/(-32)). Factor 0*g + 88/5*g**3 - 8/5*g**m + 0 - 242/5*g**4.
-2*g**2*(11*g - 2)**2/5
Let k(f) be the second derivative of f**7/189 - 4*f**6/45 + 28*f**5/45 - 64*f**4/27 + 16*f**3/3 - 64*f**2/9 + 122*f. Factor k(r).
2*(r - 4)*(r - 2)**4/9
Find n, given that 10/7*n - 6/7 + 36/7*n**2 - 62/7*n**4 - 12/7*n**3 - 30/7*n**5 = 0.
-1, 1/3, 3/5
Let t(x) be the second derivative of -x**7/1260 + x**6/120 + x**4/3 - 14*x. Let u(s) be the third derivative of t(s). Factor u(d).
-2*d*(d - 3)
Solve i**2 + 2*i**2 - 89 - 27 + 4 + i**2 - 108*i = 0.
-1, 28
Let z(j) be the third derivative of -j**7/7560 + j**6/216 - 5*j**5/72 + 29*j**4/24 + 34*j**2. Let n(o) be the second derivative of z(o). Factor n(l).
-(l - 5)**2/3
Let f(r) be the first derivative of 5/2*r**6 + 0*r - 5/3*r**3 - 31 - 7*r**5 + 0*r**2 + 25/4*r**4. Factor f(h).
5*h**2*(h - 1)**2*(3*h - 1)
Let n be 37/6 - (-1029)/(-882). Solve 0*u - 1/2*u**2 + 0 + 3/4*u**3 + 0*u**4 - 1/4*u**n = 0.
-2, 0, 1
Let o(n) be the first derivative of 4*n**5/5 + 23*n**4 + 120*n**3 - 32. Factor o(i).
4*i**2*(i + 5)*(i + 18)
Let o(g) be the first derivative of -26 + 32/9*g**5 + 0*g + 11/3*g**4 + 40/27*g**3 + 32/27*g**6 + 2/9*g**2. Factor o(t).
4*t*(t + 1)**2*(4*t + 1)**2/9
Suppose -15*a - 15 = -12*a. Let w(b) = 10*b**3 + 2*b**2 - 12*b - 12. Let u(v) = -4*v**3 - v**2 + 5*v + 5. Let c(r) = a*w(r) - 12*u(r). Factor c(m).
-2*m**2*(m - 1)
Let u = 3849 + -3847. Factor -3/2*y**u + 0 + 9/2*y.
-3*y*(y - 3)/2
Let f(x) be the first derivative of x**8/336 - x**7/168 - x**6/72 + x**5/24 - x**3 + 4. Let g(i) be the third derivative of f(i). Determine n so that g(n) = 0.
-1, 0, 1
Let x(z) be the second derivative of 1/14*z**7 - 1/2*z**4 + 1/2*z**6 + 9/10*z**5 - 7/2*z**3 - 9/2*z**2 + 0 + 26*z. Factor x(m).
3*(m - 1)*(m + 1)**3*(m + 3)
Let u(z) be the first derivative of -25*z**6/6 + 8*z**5 + 5*z**4 - 51. Factor u(g).
-5*g**3*(g - 2)*(5*g + 2)
Let u(p) be the first derivative of 8/9*p**3 + 2/3*p + 5/3*p**2 - 17. Solve u(f) = 0 for f.
-1, -1/4
Let o(d) be the third derivative of d**8/448 - 9*d**7/280 + 3*d**6/16 - 23*d**5/40 + 33*d**4/32 - 9*d**3/8 - 2*d**2 - 32*d. Factor o(f).
3*(f - 3)**2*(f - 1)**3/4
Suppose 2*u - 48 = -44. Let x(h) be the third derivative of 6*h**u - 1/4*h**4 + 0*h - 1/20*h**5 + 3/2*h**3 + 0. Find f such that x(f) = 0.
-3, 1
Suppose 0 = 123185*w - 123165*w. Determine y, given that 1/8*y + w - 1/8*y**2 = 0.
0, 1
Let f(l) be the third derivative of l**5/210 - 3*l**4/28 - 44*l**2. Factor f(p).
2*p*(p - 9)/7
Factor 24/11 + 16/11*u - 2/11*u**2 - 2/11*u**3.
-2*(u - 3)*(u + 2)**2/11
Factor 121/2 - 21/2*n**2 - 99/2*n - 1/2*n**3.
-(n - 1)*(n + 11)**2/2
Let v be (-3)/269*-89 + (-76)/95. Let k = v - -2/269. Suppose 0 + 3/5*b**3 + 0*b + k*b**2 + 2/5*b**4 = 0. Calculate b.
-1, -1/2, 0
Let n(z) be the third derivative of -4*z**9/1323 - 2*z**8/245 + z**7/98 - z**6/315 - 4*z**3 - 5*z**2. Let c(s) be the first derivative of n(s). Factor c(q).
-4*q**2*(q + 2)*(4*q - 1)**2/7
Factor 1/4*f**3 - 25/4*f**2 - 23/4 + 47/4*f.
(f - 23)*(f - 1)**2/4
Let v(l) be the third derivative of l**8/1680 + 3*l**7/350 + 17*l**6/600 - 29*l*