 k(g).
-3*g**2*(g - 2)*(g + 1)**2
Suppose 0 = 4*o - 3*r + 45, -2*o + 0*o + 2*r - 22 = 0. Let x be (-4)/o*(1 + 0). Factor x*a**2 - 1/3*a + 0.
a*(a - 1)/3
Factor 1/9*v**4 + 0 - 1/9*v**3 - 1/9*v**2 + 1/9*v.
v*(v - 1)**2*(v + 1)/9
Let i(l) be the second derivative of 0 + 3/4*l**2 + 8*l - 7/8*l**3 + 5/16*l**4. Suppose i(q) = 0. Calculate q.
2/5, 1
Let l(t) be the second derivative of -t**5/110 + t**4/66 + t**3/33 - t**2/11 + 2*t. Determine j so that l(j) = 0.
-1, 1
Let a(o) be the second derivative of o**5/60 + o**4/6 + o**3/2 - o**2/2 + 3*o. Let t(k) be the first derivative of a(k). Find m such that t(m) = 0.
-3, -1
Let b(g) be the first derivative of -4*g**5/5 - 6*g**4 - 52*g**3/3 - 24*g**2 - 16*g - 6. Solve b(r) = 0.
-2, -1
Let f(o) = -5*o**4 + o**3 - 5*o**2 + 3*o. Let j(p) = 4*p**4 - 2*p**3 + 4*p**2 - 2*p. Let i(w) = -2*f(w) - 3*j(w). Factor i(n).
-2*n**2*(n - 1)**2
Let p be (-2)/(-13) + 195/(-169). Let v be p*(-3 + (4 - 1)). Factor v + 2/9*r**3 + 2/9*r + 4/9*r**2.
2*r*(r + 1)**2/9
Let w(t) = -t**2 + 4*t + 3. Let s be w(4). Let k be (0 + 14)/2 - s. What is v in 3 + 2*v**2 - 2*v**3 + 4*v**2 - 2*v - 1 - k*v = 0?
1
Let t(x) be the first derivative of 0*x + 1/5*x**3 + 1/25*x**5 + 1/10*x**2 - 1 + 3/20*x**4. Factor t(j).
j*(j + 1)**3/5
Suppose 8*o - 4*o - 8 = 0. Find d such that 5 + 11*d + 3 + 3*d - 6*d + o*d**2 = 0.
-2
Suppose -2*p - 1 = -o, 2*p - 5*p + 21 = 3*o. Let d(g) = -g**3 + 10*g**2 + g - 8. Let h be d(10). Factor p*w**2 - 4*w**2 - 2 + 4*w**h.
2*(w - 1)*(w + 1)
Factor -8/7 - 2*c**4 - 32/7*c - 38/7*c**3 - 2/7*c**5 - 50/7*c**2.
-2*(c + 1)**3*(c + 2)**2/7
Factor 0 - q**3 - 3/2*q**2 + 0*q + 1/2*q**4.
q**2*(q - 3)*(q + 1)/2
Let z be 84/(-2)*2/(-6). Suppose z + 1 = 5*u. Let -2/5*x**4 + 0 + 0*x + 2/5*x**2 - 2/5*x**5 + 2/5*x**u = 0. Calculate x.
-1, 0, 1
Let o(g) be the second derivative of -g**5/50 + 4*g**3/15 + 24*g. Suppose o(s) = 0. What is s?
-2, 0, 2
Let f = -1 - -5. Solve -4*g**5 - g**5 - 2*g**f + 2*g**5 + g**3 = 0 for g.
-1, 0, 1/3
Let m(n) be the second derivative of n**7/42 - n**6/40 - n**5/16 + n**4/16 + n**3/24 + 2*n. Determine r, given that m(r) = 0.
-1, -1/4, 0, 1
Let r(o) = -o**3 - o**2 - o + 4. Let t be r(0). Suppose t*u - 8 = -0*u. Suppose 4/3*j + 0 - 14/3*j**u = 0. What is j?
0, 2/7
Let z = 3 - 2. Let v = 0 + z. Factor -v + 1 - o**3 + o.
-o*(o - 1)*(o + 1)
Let o(y) be the third derivative of -2*y**7/105 + 2*y**6/15 - 2*y**5/5 + 2*y**4/3 - 2*y**3/3 - 20*y**2. Let o(a) = 0. What is a?
1
Solve 0*g + 0*g**2 + 0 + 2/9*g**4 + 4/9*g**3 = 0.
-2, 0
Let a = 5 + 0. Let l(o) = 117*o**3 - 297*o**2 + 120*o + 48. Let r(q) = -47*q**3 + 119*q**2 - 48*q - 19. Let y(v) = a*l(v) + 12*r(v). Find d such that y(d) = 0.
-2/7, 1, 2
Let j = -60 - -63. Suppose 4/11 - 82/11*u**j + 74/11*u**2 - 8/11*u**5 + 42/11*u**4 - 30/11*u = 0. Calculate u.
1/4, 1, 2
Let l = 20 + -14. Let t = 8 - l. Factor -2*d**t + 0 + 4/5*d.
-2*d*(5*d - 2)/5
Let q(k) be the second derivative of k**5/16 - 13*k**4/48 - k**3/4 - 3*k. Factor q(u).
u*(u - 3)*(5*u + 2)/4
Let f = 849/7 + -121. Determine c, given that -2/7*c - f*c**3 + 0 + 4/7*c**2 = 0.
0, 1
Suppose 2*t + 7 + 7 = 4*o, -t = -3*o + 11. What is v in -o*v**3 + 0 + v + 5/2*v**4 + 1/2*v**2 = 0?
-2/5, 0, 1
Let m(x) be the first derivative of -x**4 - 12*x**3 - 30*x**2 + 100*x - 5. Let m(w) = 0. Calculate w.
-5, 1
Solve 16*c**2 + 20*c**3 + 41*c + 4*c**4 - 41*c = 0 for c.
-4, -1, 0
Factor -2/13*q + 4/13 - 2/13*q**2.
-2*(q - 1)*(q + 2)/13
Factor -4*a - 5*a**3 - 5*a**2 + 8*a**4 + 9*a - 3*a**4.
5*a*(a - 1)**2*(a + 1)
Let h(p) be the second derivative of -2*p**7/21 + 2*p**6/3 - 6*p**5/5 - 4*p**4/3 + 16*p**3/3 + 32*p. Factor h(v).
-4*v*(v - 2)**3*(v + 1)
Suppose 5 = 5*x - 25. Let k(p) be the first derivative of 6/5*p**5 + 1 - 4/3*p**3 - 2*p - 3*p**2 + p**4 + 1/3*p**x. Factor k(o).
2*(o - 1)*(o + 1)**4
Factor 7 + 2*h + 1/7*h**2.
(h + 7)**2/7
Factor 48*r - 20*r - r**4 + 4*r**2 - 26*r - r**2.
-r*(r - 2)*(r + 1)**2
Let i(w) be the second derivative of w**5/60 + w**4/24 - w**3/3 + w**2 + w. Let z(t) be the first derivative of i(t). What is j in z(j) = 0?
-2, 1
Let s(g) be the third derivative of -2*g**2 + 0*g + 0*g**3 - 1/48*g**4 + 1/120*g**5 + 0. Factor s(b).
b*(b - 1)/2
Let h(w) be the second derivative of -w**6/6 + w**5 - 5*w**4/2 + 10*w**3/3 - 5*w**2/2 + 10*w. Factor h(j).
-5*(j - 1)**4
Let 52/3*v**2 + 0 - 12*v**3 - 52/3*v**4 + 44/3*v**5 - 8/3*v = 0. What is v?
-1, 0, 2/11, 1
Find l such that 0 - 1/2*l**2 + 1/4*l**3 + 0*l = 0.
0, 2
Suppose 0*d = -d + 2. Factor 5*i**5 - 3*i + 4*i**d + i - 3*i**5 - 4*i**4.
2*i*(i - 1)**3*(i + 1)
Let v = -173 + 179. Let s(m) be the second derivative of 0*m**2 - 7/9*m**v - 1/20*m**5 + 7/18*m**7 + 5/9*m**4 + 0 + 2/9*m**3 + m. Suppose s(x) = 0. What is x?
-2/7, 0, 1
Let b be (6/9)/((-6)/(-45)). Let u(s) = -s**2 - 13*s. Let a(k) = 2*k**2 + 20*k. Let v = 5 - -3. Let i(x) = b*a(x) + v*u(x). Suppose i(w) = 0. What is w?
0, 2
Let w be 3/9 + 10/6. Let h = 50 + -48. Factor 4/3 + w*l - 10/3*l**h.
-2*(l - 1)*(5*l + 2)/3
Let l = -6/341 - -353/682. Solve l*k + 1/2 - 6*k**2 = 0.
-1/4, 1/3
Let f(w) = -w - 5. Suppose 4*g + 6 = -14. Let t be f(g). What is h in -2/7*h**3 + 6/7*h + 4/7 + t*h**2 = 0?
-1, 2
Let r(i) be the first derivative of 2*i**4/3 + 10*i**3/3 + 4*i**2 - 8*i/3 + 9. Solve r(o) = 0 for o.
-2, 1/4
Let m(y) be the third derivative of y**5/150 + y**4/60 - 2*y**3/15 + 26*y**2. Factor m(t).
2*(t - 1)*(t + 2)/5
Let d = 193/1995 - 4/133. Let c(u) be the first derivative of -1/9*u**3 + 0*u - d*u**5 + 1 + 1/6*u**4 + 0*u**2. Factor c(h).
-h**2*(h - 1)**2/3
Let n(b) be the first derivative of -b**6/360 + b**5/60 - b**4/24 + b**3/3 - 1. Let v(j) be the third derivative of n(j). Factor v(p).
-(p - 1)**2
Let y be -3 + -6 + 4 - 4. Let c be 4/y*39/(-26). Factor -2*g + 4/3*g**3 + 2/3*g**5 - 2*g**4 + c + 4/3*g**2.
2*(g - 1)**4*(g + 1)/3
Suppose 5*s - 9 = -2*b - 32, -5*b - 8 = -4*s. Let w be (-4)/(-3)*(-9)/s. Factor -7*l**5 + w*l**5 + l + 2*l**4 - 2*l**2 + 2*l**5.
-l*(l - 1)**3*(l + 1)
What is f in 2*f - 6 - 2*f**3 + 4 + 3*f**2 + 3*f**4 - 7*f**2 + 3 = 0?
-1, -1/3, 1
Let l = 25 + -22. Suppose 1 - l + 0*v + 2*v**2 + 2*v - 2 = 0. Calculate v.
-2, 1
Let k(z) be the third derivative of z**7/105 - z**5/10 + z**4/6 + z**2. Factor k(h).
2*h*(h - 1)**2*(h + 2)
Let -12*v - 31*v + 6*v**4 - v**4 - 7*v + 15 - 30*v**3 + 60*v**2 = 0. What is v?
1, 3
Suppose -5*f + 5 = -2*o - 1, -5*o = -10. Let n be (4 - 2) + (-3)/f. Factor 3/4*w**2 - n*w**3 + 0 - 1/4*w.
-w*(w - 1)*(2*w - 1)/4
Factor -b**4 + 176*b**3 - 1539*b**2 + 85184*b + 3*b**4 + 468512 + 7347*b**2.
2*(b + 22)**4
Let k = 7 + -75/11. Factor -k*q**5 + 0*q + 0 + 6/11*q**4 + 2/11*q**2 - 6/11*q**3.
-2*q**2*(q - 1)**3/11
Let 705/4*g**2 + 66*g + 435/4*g**4 + 75/4*g**5 + 9 + 837/4*g**3 = 0. Calculate g.
-3, -1, -2/5
Let u = 34 - 32. Factor -10/11*d - 2/11*d**3 + 4/11 + 8/11*d**u.
-2*(d - 2)*(d - 1)**2/11
Factor -1558*r**4 - 6*r**2 - 4*r + 1560*r**4 + r**3 - r**3.
2*r*(r - 2)*(r + 1)**2
Let s = 74/451 - 3/41. Let u(i) be the first derivative of -3 - 2/11*i**3 - s*i**2 + 0*i + 2/11*i**4. Factor u(a).
2*a*(a - 1)*(4*a + 1)/11
Let q(w) = -w - 6. Let c be q(-5). Let a be 0 - c - (4 + -7). Factor 36*z**a - 13*z**2 + z**2 - 5*z + 14*z**3 + 15*z**5 - 2*z**4 + 2.
(z + 1)**3*(3*z - 1)*(5*z - 2)
Let t(s) be the third derivative of s**9/37800 - 17*s**8/50400 + s**7/630 - s**6/450 + s**5/60 + 2*s**2. Let b(r) be the third derivative of t(r). Factor b(h).
2*(h - 2)**2*(4*h - 1)/5
Let d be (6/(-8))/((-24)/8). Let n(a) = 2*a**3 - a**2 + 1. Let c be n(1). Factor -d*v**5 - 3/4*v**3 + 0 + 1/4*v**c + 3/4*v**4 + 0*v.
-v**2*(v - 1)**3/4
Let l(n) = n + 3. Let m be l(0). Suppose -2*j - 13 = -5*c, -m*c - 4*j = -6 - 7. Factor -4/9*p**2 + 10/9*p**c + 4/9 - 10/9*p.
2*(p - 1)*(p + 1)*(5*p - 2)/9
Let s(d) be the first derivative of 1 + 1/6*d**2 - 1/6*d**4 - 1/3*d + 1/18*d**6 + 2/9*d**3 - 1/15*d**5. Find b, given that s(b) = 0.
-1, 1
Solve 0 + 2/3*z**5 - 2*z**4 + 4/3*z**3 + 0*z**2 + 0*z = 0 for z.
0, 1, 2
Let z(q) = 3*q**3 - 42*q**2 + 109*q - 92. Let w(y) = 14*y**3 - 211*y**2 + 547*y - 461. Let f(d) = -2*w(d) + 11*z(d). Factor f(a).
5*(a - 3)**2*(a - 2)
Let n(z) be the first derivative of z**6/69 - 8*z**5/115 + 3*z**4/46 + 56. Factor n(u).
2*u**3*(u - 3)*(u - 1)/23
Let g(k) be the first derivative of -k**3/12 + k/4 + 27. Let g(r) = 0