*g*(g + 1)**3/9
Suppose 0*u + 1/3*u**4 - 2/3*u**3 + 0 + 1/3*u**2 = 0. Calculate u.
0, 1
Find z, given that 1/5 + 1/5*z**4 + 1/5*z**5 - 2/5*z**3 - 2/5*z**2 + 1/5*z = 0.
-1, 1
Suppose -5*m = 5*o - 80, 0 = -m - m + 2*o + 24. Suppose -9*x**2 - m*x**3 - 29*x**2 + 8 + x - 17*x = 0. What is x?
-2, -1, 2/7
Let y be 0 + (2 - 0) - -2. Factor 2*u**4 - 3*u**y + 5 - 12*u + 7 + 12*u**3 - 9*u**2 - 2*u**4.
-3*(u - 2)**2*(u - 1)*(u + 1)
Let v(k) = 8 + 2*k**3 + 6*k - 18*k**2 + 24*k**3 + 0*k + 6. Let r(w) = -9*w**3 + 6*w**2 - 2*w - 5. Let a(c) = 14*r(c) + 5*v(c). Factor a(l).
2*l*(l - 1)*(2*l - 1)
Let h(m) be the second derivative of m**4/3 + 2*m**3/3 - 13*m. Factor h(r).
4*r*(r + 1)
Let m(p) be the second derivative of 1/2*p**2 - 1/66*p**4 - p + 0 - 1/330*p**5 - 1/33*p**3. Let r(t) be the first derivative of m(t). Factor r(j).
-2*(j + 1)**2/11
Let q(n) be the second derivative of n**5/70 + n**4/14 + 2*n**3/21 + 7*n. Factor q(t).
2*t*(t + 1)*(t + 2)/7
Suppose 5/2*m**3 - m**4 - 2 + 1/2*m + 6*m**2 = 0. Calculate m.
-1, 1/2, 4
Let d(j) = j**3 - j**4 - 7*j**3 - 9*j**4 + 11 + 2*j**4 - 9*j**2. Let p(l) = -4*l**4 - 3*l**3 - 5*l**2 + 6. Let f(u) = 6*d(u) - 11*p(u). Factor f(t).
-t**2*(t + 1)*(4*t - 1)
Let z(i) be the second derivative of -3*i**5/5 + i**4/4 - 28*i. Suppose z(x) = 0. Calculate x.
0, 1/4
Find b, given that 6*b**3 + 16*b**4 - 2*b**3 - 8*b**4 - 4*b**4 = 0.
-1, 0
Let w = 10 - 5. Factor 1 - 6*j - w - j**2 + 2*j.
-(j + 2)**2
Let w be (2/21)/(2 + (-33)/21). Determine s, given that 4/9*s - 4/9*s**3 - 2/9 + w*s**2 = 0.
-1, 1/2, 1
Let n(k) be the second derivative of -k**6/135 - 2*k**5/45 - k**4/9 - 4*k**3/27 - k**2/9 - 4*k. Factor n(t).
-2*(t + 1)**4/9
Let a(h) be the first derivative of -5/11*h**4 - 1/33*h**6 + 2/11*h**5 + 20/33*h**3 + 1 - 5/11*h**2 + 2/11*h. Let a(v) = 0. What is v?
1
Suppose q = -5*d - 17, 5*d + 31 = 11. Suppose 2*o = -4*v - 4, -o - 10 = q*v + 4*o. Suppose v*x - 1/4*x**2 + 1/4 = 0. Calculate x.
-1, 1
Let m(s) be the third derivative of s**6/840 + s**5/140 + s**4/56 + s**3/42 - 9*s**2. Solve m(a) = 0 for a.
-1
Let y(q) be the first derivative of q**4/24 - 13*q**3/18 + 23*q**2/12 - 11*q/6 - 62. Solve y(k) = 0.
1, 11
Let p = 3 + -6. Let c = 6 + p. Determine v so that 1/3*v**2 - 1/3 - 1/3*v + 1/3*v**c = 0.
-1, 1
Let a(x) = x**3 + 1. Let u(b) = -2*b**4 - 2*b**3 + 2*b**2 - 2*b - 4. Let m(k) = 4*a(k) + u(k). Solve m(s) = 0.
-1, 0, 1
Let a be (-5)/50 - 2/(-4). Factor 0*k**3 + 0*k**2 - a*k**5 + 0 + 2/5*k**4 + 0*k.
-2*k**4*(k - 1)/5
Let y(d) be the first derivative of 0*d - 2*d**3 - 1 + 1/2*d**4 - d**2 + 6/5*d**5. Factor y(t).
2*t*(t - 1)*(t + 1)*(3*t + 1)
Let v(r) be the third derivative of r**7/840 - r**6/96 + 3*r**5/80 - 7*r**4/96 + r**3/12 - 4*r**2. Factor v(q).
(q - 2)*(q - 1)**3/4
Let t be 23/5 + (-18)/30. Let a = t - 1. Factor -4*s**2 + 5*s**2 + a*s**3 - s**3 - 3*s**2.
2*s**2*(s - 1)
Let m(r) be the first derivative of -3*r**4/20 + 2*r**3/5 - 13. Suppose m(a) = 0. Calculate a.
0, 2
Let u be -3 - ((-4)/(-2))/((-18)/45). Solve 2/3*r**2 - 4/3*r - u = 0.
-1, 3
Let k = 3 + 1. Factor 0*f**2 - 3*f**2 - 2*f + f**3 + k*f**2 + 0*f**3.
f*(f - 1)*(f + 2)
Let l(v) be the third derivative of 0*v**7 + 0*v**5 + 1/168*v**8 - 1/30*v**6 + 0*v**3 + 0 - 10*v**2 + 0*v + 1/12*v**4. Factor l(j).
2*j*(j - 1)**2*(j + 1)**2
Suppose -x = -5*w - 22, -5*x + 2*w = -2*w - 26. Suppose g**3 - g**2 + 2*g**2 + 1 - x*g**2 - g = 0. What is g?
-1, 1
Let w(o) = o**3 + 3*o**2 + 2*o - 7. Let g(t) = -1. Suppose l = 3*p - 0*l + 4, -32 = 4*p + 4*l. Let n(k) = p*w(k) + 21*g(k). What is x in n(x) = 0?
-2, -1, 0
Let v(m) = -4*m**3 - 8*m**2 + 4*m + 11. Let n(a) = 69*a**2 - 8 - 61*a**2 - 4*a - 2 + 4*a**3. Let p(o) = 3*n(o) + 2*v(o). Factor p(h).
4*(h - 1)*(h + 1)*(h + 2)
Let z = 92/9 - 89/9. Factor z*b**4 + 0 + 0*b**2 - 1/6*b**5 + 0*b - 1/6*b**3.
-b**3*(b - 1)**2/6
Let p(u) be the third derivative of u**7/1050 - u**6/200 - u**5/300 + u**4/40 - 25*u**2. Determine y, given that p(y) = 0.
-1, 0, 1, 3
Determine s so that 1/4*s**3 + 0*s + 1 - 3/4*s**2 = 0.
-1, 2
Factor 1/4*l**3 + 0 - l + 1/4*l**4 - l**2.
l*(l - 2)*(l + 1)*(l + 2)/4
Suppose 2*z + 15 = 5*z. Find g such that -g**5 - 4*g + 15*g**3 + z*g**5 + g**2 - 14*g**4 - 3*g**3 + g**2 = 0.
-1/2, 0, 1, 2
Suppose -20*q + 17*q = -60. Suppose 2*u + 2*u - 5*n = 20, u + 5*n = -q. Factor u - 2/9*j**3 + 0*j + 2/9*j**2.
-2*j**2*(j - 1)/9
Let m(d) = -d**3 + 12*d**2 + 6. Let b be m(12). Let f = 6 - b. Factor -2/5*p**2 + f - 2/5*p.
-2*p*(p + 1)/5
Let w be (8/10)/((-4)/(-10)). Suppose -w*f + 2*d + 6 = -0*f, 7 = f + d. Solve -3*s**5 + s**5 + 3*s**f + 2*s**4 + s**3 = 0.
-1, 0
What is p in -p + 2*p - 3*p - 2*p + 4*p**2 = 0?
0, 1
Let u be 108/(-16)*32/(-420). Let p = -4/35 + u. Factor -2/5*s**4 + p*s**2 - 2/5*s + 0 + 2/5*s**3.
-2*s*(s - 1)**2*(s + 1)/5
Let q(d) be the second derivative of d**9/6048 + d**8/3360 + d**3/3 - 2*d. Let t(r) be the second derivative of q(r). Find n, given that t(n) = 0.
-1, 0
Let a(x) be the third derivative of -x**6/1020 + x**5/102 - 7*x**4/204 + x**3/17 + 21*x**2. Find p, given that a(p) = 0.
1, 3
Let f(k) be the first derivative of 0*k + 2 + 0*k**3 + 3/22*k**4 - 2/55*k**5 - 4/11*k**2. Suppose f(z) = 0. What is z?
-1, 0, 2
Factor -8/3 + 20/3*m**3 + 52/3*m - 64/3*m**2.
4*(m - 2)*(m - 1)*(5*m - 1)/3
Let g = -12 - -17. Let q(x) be the second derivative of 0*x**3 - x + 1/12*x**4 + 0*x**g - 1/4*x**2 + 0 - 1/60*x**6. Factor q(h).
-(h - 1)**2*(h + 1)**2/2
Suppose 0 + 5 = -5*l. Let r(t) = -t**3 - 1. Let o be r(l). Find h, given that 0 - 2/7*h**2 + o*h = 0.
0
Let f(j) be the third derivative of j**8/6720 - j**7/1260 + j**6/720 - j**4/8 - 2*j**2. Let l(v) be the second derivative of f(v). Factor l(c).
c*(c - 1)**2
Let x(n) be the first derivative of n**3 - 6*n**2 + 12*n + 1. Factor x(k).
3*(k - 2)**2
Let i(m) = 2*m**4 + 5*m**3 - 5*m**2 + 5*m + 5. Let c(d) = d**4 + 3*d**3 - 3*d**2 + 3*d + 3. Let j(t) = -5*c(t) + 3*i(t). Let j(h) = 0. What is h?
0
Let o(t) be the third derivative of -2*t**7/1575 + 7*t**6/900 - t**5/50 + t**4/36 - t**3/45 - 22*t**2. Find l such that o(l) = 0.
1/2, 1
Let p(h) be the second derivative of 1/30*h**4 + 0*h**2 + 0*h**3 + 0 - 1/100*h**5 - 1/150*h**6 - 7*h. Factor p(l).
-l**2*(l - 1)*(l + 2)/5
Let h(x) be the first derivative of -1/6*x + 1/6*x**3 - 1/6*x**2 + 3. Factor h(u).
(u - 1)*(3*u + 1)/6
Suppose 18*g**4 - 10*g**4 - 6*g**4 + 2*g**3 = 0. Calculate g.
-1, 0
Suppose -2 - 6 = -4*o. Let s be (-40)/50 + ((-48)/(-10) - 2). Factor j**s - 9*j**2 - 5*j + j + 10*j**o.
2*j*(j - 2)
Let v be 4/3*9/(-6). Let j be v/(1 + (-9)/6). Factor m**4 - 3*m**4 + 3*m**4 - 2*m**2 + m**j.
2*m**2*(m - 1)*(m + 1)
Let x(q) = 28*q**2 + 57*q + 23. Let k(h) = -195*h**2 - 400*h - 160. Let l(n) = 2*k(n) + 15*x(n). Factor l(t).
5*(t + 1)*(6*t + 5)
What is q in -70*q**2 + 50*q**2 + 7*q**3 - 2*q**3 = 0?
0, 4
Suppose -s = 4*s - 2*h + 146, 4*s - 3*h + 114 = 0. Let m be 7/6 - 10/s. Determine w so that -3/2*w**3 + 3/2*w**2 - m*w**4 + 0 + 3/2*w = 0.
-1, 0, 1
Let z(a) = -a**2 + a - 1. Let h(d) = -8*d**2 + 4*d - 12. Let t(m) = h(m) - 12*z(m). Suppose t(p) = 0. Calculate p.
0, 2
Let p(a) be the second derivative of -1/6*a**3 + a + a**2 + 1/12*a**4 + 0 - 1/60*a**5. Let f(u) be the first derivative of p(u). Factor f(i).
-(i - 1)**2
Let u(n) = -n**4 - n**3 - 2*n**2 + n + 1. Let k = 13 - 12. Let z(i) = i**3 - i**2 + i + 1. Let m(c) = k*z(c) - u(c). Factor m(p).
p**2*(p + 1)**2
Suppose 3*m + 5*y - 16 - 16 = 0, 0 = 4*m - 2*y - 8. Let c be 2/m + 7/(-14). What is k in k**2 + 26*k**4 - 15*k**4 + 4*k**5 - k + 4*k**3 + c*k**2 + 5*k**3 = 0?
-1, 0, 1/4
Let j(q) = -3*q**4 + 3*q**3 + 6*q**2 - 6*q + 6. Let p(w) = -w**3 - w**2 + w - 1. Let l(f) = j(f) + 6*p(f). Suppose l(a) = 0. Calculate a.
-1, 0
Let t(m) = -m**3 - m**2 - m + 1. Let j(g) = 12*g**5 - 4*g**4 - 32*g**3 - 16*g**2 - 20*g + 20. Let q(v) = -j(v) + 20*t(v). Determine l, given that q(l) = 0.
-1, 0, 1/3, 1
Factor 40/3*b + 4/3*b**2 + 100/3.
4*(b + 5)**2/3
Let o(x) = x - 3. Let v be o(5). Find w, given that v*w**3 + 6*w**5 - 5*w**5 - 2*w**4 - 3*w**5 + 0*w**3 + 2*w**2 = 0.
-1, 0, 1
Solve 2/9*a**5 + 8/9*a**4 + 0 - 22/9*a**3 + 4/3*a**2 + 0*a = 0 for a.
-6, 0, 1
Let q(w) = w**2 + 8*w - 3. Let p be q(-7). Let c be 4/p - (-64)/60. Find o, given that -2/3*o**3 + 2/3*o - c*o**2 + 2/3 = 0.
-1, 1
Let d be (3/4)/((-2)/(-8)). Let n = 4