 2/3*k + 1/3*k**2.
k*(k - 2)/3
Let i = -8 - -17/2. Let -1/2*m**2 - m - i = 0. Calculate m.
-1
Let u(z) be the first derivative of -12*z**5/5 + 51*z**4/4 - 24*z**3 + 39*z**2/2 - 6*z + 72. Let u(k) = 0. Calculate k.
1/4, 1, 2
Let u(b) be the first derivative of -55*b**3/18 - 65*b**2/12 - 5*b/3 + 14. Factor u(r).
-5*(r + 1)*(11*r + 2)/6
Let y = 23 + -19. Let o(z) be the first derivative of 0*z + 0*z**3 - 1 + 0*z**5 + 0*z**2 + 1/16*z**y - 1/24*z**6. Solve o(p) = 0.
-1, 0, 1
Let x(g) be the first derivative of -2/27*g**3 + g - 1/9*g**2 - 2 - 1/54*g**4. Let z(j) be the first derivative of x(j). Factor z(y).
-2*(y + 1)**2/9
Find w, given that -w**2 - 1/2*w**3 + 0 + 0*w = 0.
-2, 0
Determine n, given that 0*n + 0 - 1/4*n**3 - 1/2*n**2 = 0.
-2, 0
Let h(x) be the third derivative of 0*x + 0*x**6 + 7*x**2 + 0*x**4 + 0 + 1/90*x**5 - 1/315*x**7 + 0*x**3. Factor h(k).
-2*k**2*(k - 1)*(k + 1)/3
Let q be (-4)/14*(-860)/(-360). Let o = -1/63 - q. Find y, given that 1/3*y**2 - o*y + 1/3 = 0.
1
Let k(g) be the second derivative of 5*g**4/12 - 9*g. Determine x so that k(x) = 0.
0
Let r(j) be the third derivative of -j**8/13440 - j**7/2016 - j**6/720 - j**5/30 + 2*j**2. Let p(v) be the third derivative of r(v). Factor p(s).
-(s + 1)*(3*s + 2)/2
Factor -2*v**4 + 0 + 4/5*v - 14/5*v**2 + 18/5*v**3 + 2/5*v**5.
2*v*(v - 2)*(v - 1)**3/5
Let i(f) be the third derivative of -f**8/26880 + f**6/2880 + f**4/8 + 7*f**2. Let o(u) be the second derivative of i(u). Factor o(k).
-k*(k - 1)*(k + 1)/4
Let v(u) be the second derivative of u**4/12 + u**3/3 - 13*u**2/2 + 7*u. Let t be v(-5). Suppose 0 - 1/4*x + 1/4*x**t = 0. What is x?
0, 1
Let s be (-2 + -1)/(9/(-6)). Determine u, given that -2/5*u**s + 8/5 + 0*u = 0.
-2, 2
Let r = 2 + -5. Let t = r + 5. Factor 0 + 1/3*v + 1/3*v**t - 1/3*v**3 - 1/3*v**4.
-v*(v - 1)*(v + 1)**2/3
Let u(i) = -4*i**5 + 20*i**4 - 36*i**3 + 19*i**2 + i. Let v(b) = -b**5 + 5*b**4 - 9*b**3 + 5*b**2. Let x(w) = -4*u(w) + 18*v(w). Suppose x(f) = 0. What is f?
0, 1, 2
Let q(n) be the third derivative of n**6/40 - 3*n**5/20 + 3*n**4/8 - n**3/2 + n**2. Factor q(k).
3*(k - 1)**3
Factor 94 + 15*t + 90 - 10*t**3 - 15*t**2 - 174.
-5*(t - 1)*(t + 2)*(2*t + 1)
Solve -98/5*d**4 + 106/5*d**3 - 8/5 - 8/5*d - 98/5*d**5 + 106/5*d**2 = 0.
-1, -2/7, 2/7, 1
Let c(y) be the third derivative of -5*y**8/336 + 4*y**7/21 - y**6/2 - y**5/6 + 65*y**4/24 - 5*y**3 + y**2 + 25*y. Factor c(w).
-5*(w - 6)*(w - 1)**3*(w + 1)
Let v = -7806 - -30779/4. Let x = 112 + v. Find i such that 0 - 3/4*i**3 - x*i**4 - 1/4*i**2 - 1/4*i**5 + 0*i = 0.
-1, 0
Let j(c) be the first derivative of -c**8/84 + 2*c**7/35 - c**6/10 + c**5/15 + 5*c**2/2 - 3. Let a(o) be the second derivative of j(o). Let a(p) = 0. What is p?
0, 1
Let y = -10903/273 + -36/91. Let t = -40 - y. Factor 0 + 0*s**2 + t*s - 1/3*s**3.
-s*(s - 1)*(s + 1)/3
Let o(d) = -3*d**5 + 11*d**4 - 11*d**3 + 5*d**2 + 2*d + 2. Let p(f) = -f**4 + f**3 - f**2 - f - 1. Let m(v) = o(v) + 2*p(v). Factor m(l).
-3*l**2*(l - 1)**3
Let j(q) be the second derivative of -q - 1/45*q**6 + 0*q**2 + 1/18*q**4 + 0*q**5 + 0 + 0*q**3. Find c such that j(c) = 0.
-1, 0, 1
Let c(s) = -s**3 + 11*s**2 + 12*s + 2. Let u be c(12). Let y be -4*2/(-12) + (-36)/54. Let -2/5*h**u + y - 1/5*h = 0. Calculate h.
-1/2, 0
Let b(h) be the second derivative of h**5/90 - 4*h**3/27 - 15*h. Factor b(u).
2*u*(u - 2)*(u + 2)/9
Let a(y) = y**3 - 7*y**2 + 4*y + 8. Let f be a(6). Let x be 9/12 + f/8. Factor -1/4 - 1/2*m + 1/2*m**3 + x*m**2.
(m - 1)*(m + 1)*(2*m + 1)/4
Let z(s) be the third derivative of -s**6/280 + s**5/70 - s**4/56 - s**2. Factor z(d).
-3*d*(d - 1)**2/7
Suppose 0 = -5*a - 3*y + 7*y + 10, -4*y = a - 2. Let d(s) be the first derivative of 1/14*s**4 - 2/35*s**5 - 1/7*s**a + 0*s + 2/21*s**3 - 1. Factor d(o).
-2*o*(o - 1)**2*(o + 1)/7
Suppose -1/2*g**2 + 1/2*g**4 + 0 - g**3 + g = 0. Calculate g.
-1, 0, 1, 2
Let d(n) = n**3 - 8*n**2 + 9*n - 12. Let r be d(7). Factor -2/5*l**3 + 2/5*l + 2/5*l**r - 2/5.
-2*(l - 1)**2*(l + 1)/5
Let o = 0 + -3. Let a be -1*6/9*o. Factor -4/7*l - 2/7 - 2/7*l**a.
-2*(l + 1)**2/7
Factor -1/2*h**2 + 1 + 1/2*h.
-(h - 2)*(h + 1)/2
Factor -2*b - 1/5*b**2 - 5.
-(b + 5)**2/5
Let t(j) be the third derivative of -1/1344*j**8 - 1/160*j**6 + 3*j**2 + 0 - 1/240*j**5 + 0*j**4 + 0*j + 0*j**3 - 1/280*j**7. Factor t(x).
-x**2*(x + 1)**3/4
Let i = 86 + -170. Let l be ((-8)/i)/((-1)/(-3)). Factor l - 4/7*y + 2/7*y**2.
2*(y - 1)**2/7
Suppose -3*y = 4*g - 9, -2 = -2*y - g + 4. Let a(q) be the first derivative of -2/3*q**y - q**2 + 2/5*q**5 + 2 + 1/2*q**4 + 0*q. Factor a(z).
2*z*(z - 1)*(z + 1)**2
Solve -4*x - 3 - 5 + 24*x**3 + 8*x**2 - 20*x**3 = 0 for x.
-2, -1, 1
Let w be ((-568)/(-6))/(22/27). Let z = -116 + w. Determine l so that 0 + z*l**2 - 2/11*l + 2/11*l**3 - 2/11*l**4 = 0.
-1, 0, 1
Let q = -4 + 6. Let u be 3/(q/(2 - 0)). Solve -2*o**2 - 4*o**2 + 8 + 16*o + 0*o**2 + 9*o**u - 27*o**3 = 0.
-2/3, 1
Let j(x) be the third derivative of -x**5/120 + 5*x**4/96 + x**3/8 + 6*x**2. Find c, given that j(c) = 0.
-1/2, 3
Let j(y) be the second derivative of 5*y**7/42 + y**6/3 - 2*y**5 + 5*y**4/6 + 35*y**3/6 - 10*y**2 - 20*y. Factor j(i).
5*(i - 1)**3*(i + 1)*(i + 4)
Let d be (2/1 - 2) + -4. Let n = -2 - d. Factor -w**n + 2*w**2 - 2*w + 4*w - w**3.
-w*(w - 2)*(w + 1)
Let c(j) be the first derivative of j**6/12 - 3*j**5/10 + j**4/8 + j**3/2 - j**2/2 + 9. Solve c(i) = 0 for i.
-1, 0, 1, 2
Suppose l + 0*l - 3 = -j, 4*j - 3*l = -9. Let o(r) be the second derivative of 2/3*r**2 + j - r + 1/9*r**3 - 1/18*r**4. Suppose o(f) = 0. What is f?
-1, 2
Suppose -3*y - 2*s = 2*y - 12, -s = -y + 1. Factor 2*t**y - 10 + 2*t**2 - 2 + 8*t.
4*(t - 1)*(t + 3)
Let 0 - 3/5*u**3 - 12/5*u**2 - 12/5*u = 0. Calculate u.
-2, 0
Let z(p) be the second derivative of 3*p**5/20 + p**4/4 + 8*p. Suppose z(t) = 0. What is t?
-1, 0
Determine n, given that 6/7*n**4 + 0 + 0*n**3 + 0*n - 2/7*n**2 - 4/7*n**5 = 0.
-1/2, 0, 1
Factor -12/5 + 148/5*k - 624/5*k**2 + 192*k**3 - 256/5*k**4.
-4*(k - 3)*(4*k - 1)**3/5
Let g(q) = -2*q**2 - 4*q + 1. Let u be g(-3). Let a be (0 - (u + 4))*4. Suppose -6/5*w**3 - 3/5*w**a + 0*w**2 + 6/5*w + 3/5 = 0. Calculate w.
-1, 1
Factor -98/3*s**3 - 16/3 - 84*s**2 - 40*s.
-2*(s + 2)*(7*s + 2)**2/3
Let v(i) be the second derivative of 3*i - 1/15*i**3 + 0 + 1/30*i**4 + 0*i**2. Factor v(j).
2*j*(j - 1)/5
Suppose 10*f = 16*f. Let n(y) be the third derivative of f*y**5 - 1/448*y**8 - 2*y**2 + 1/80*y**6 + 0*y - 1/32*y**4 + 0*y**7 + 0*y**3 + 0. Factor n(p).
-3*p*(p - 1)**2*(p + 1)**2/4
Let o(c) = -c**2 + 1. Let a(q) = 2*q**2 - 2. Suppose -4 = 3*i - 1. Let r(n) = i*a(n) - 5*o(n). Let r(l) = 0. What is l?
-1, 1
Suppose 0 = -21*c + 7*c. Let -2/3*v**3 + 2/3*v**5 - 2/9*v**2 + c*v + 2/9*v**4 + 0 = 0. Calculate v.
-1, -1/3, 0, 1
Let z(g) be the third derivative of -g**8/6720 - g**7/1008 - g**6/360 - g**5/240 - 5*g**4/24 - 3*g**2. Let w(b) be the second derivative of z(b). Factor w(v).
-(v + 1)**2*(2*v + 1)/2
Let u(w) be the third derivative of w**7/210 - w**6/48 - w**5/10 - w**4/48 + w**3/3 + 29*w**2. Solve u(p) = 0.
-1, 1/2, 4
What is h in 0 + 0*h + h**2 + 1/2*h**3 - 1/2*h**4 = 0?
-1, 0, 2
Let j be (178/(-18) + 10)/((-2)/(-64)). Determine q, given that 16/9*q - 2/9*q**2 - j = 0.
4
Let w(a) be the second derivative of a**6/180 - a**5/30 + 2*a**3/3 + 3*a. Let g(v) be the second derivative of w(v). Factor g(f).
2*f*(f - 2)
Suppose -w + 7 = -j, -5*w = 3*j + 7 - 2. Suppose 30*u**3 + 3*u**4 - 123*u**2 + 120*u - 6*u**4 - 48 + 24*u**w = 0. What is u?
1, 4
Let s = 30/11 - 349/132. Let n(g) be the third derivative of g**2 + 0*g**3 - 2/21*g**7 - s*g**4 + 0*g + 0 - 1/5*g**5 - 1/56*g**8 - 1/5*g**6. Factor n(h).
-2*h*(h + 1)**3*(3*h + 1)
Let n = 21 + -14. Suppose o + 3*k - 1 = 2*k, n = o - 5*k. Let -o*a**2 + 5*a + 2*a - 5*a = 0. What is a?
0, 1
Let r(z) be the first derivative of -z**4/4 - z**3/5 + z**2/5 - 5. Factor r(p).
-p*(p + 1)*(5*p - 2)/5
Suppose -21 = -4*p - o - 11, 0 = 5*p + 3*o - 16. Factor -4/5*s + 0 - p*s**2.
-2*s*(5*s + 2)/5
Determine l, given that 3*l + 1/4*l**2 + 9 = 0.
-6
Let b = -4 + 3. Let u be (6/(-2) + -1)*b. Factor 2*a**3 + 0 - 1 - 2*a**u + 0 + 3*a**4 - 2*a.
(a - 1)*(a + 1)**3
Let n = -2 - -5. Suppose -4*z = 4*r, 0*r - z = n*r. Factor 2*u - 2*u + 2*u**5 + 2*u**2 - 2*u**3 + r*u**2 - 2*u**4.
2*u**2*(u -