/(-9). Determine g so that -2/3 + 2/3*g - 2/3*g**3 + c*g**2 = 0.
-1, 1
Factor -24/13 + 2/13*c**3 - 16/13*c + 2/13*c**2.
2*(c - 3)*(c + 2)**2/13
Find a such that 3/2*a**2 - 3/2*a**5 - 21/2*a**3 + 6 - 15/2*a**4 + 12*a = 0.
-2, -1, 1
Let g(y) be the third derivative of 0*y + 0*y**3 + 0*y**4 - 1/336*y**8 + 1/120*y**6 + 1/60*y**5 - y**2 - 1/210*y**7 + 0. Find z, given that g(z) = 0.
-1, 0, 1
Let k(x) be the third derivative of x**5/240 + x**4/96 + x**2. Factor k(r).
r*(r + 1)/4
Let y(l) be the second derivative of -l**6/6 - l**5/4 + 5*l**4/3 + 10*l**3/3 - 3*l. Factor y(m).
-5*m*(m - 2)*(m + 1)*(m + 2)
Suppose -d - 3*d = -8. Let h(n) be the first derivative of -d*n**2 - 2/3*n**3 + 0*n - 1. Factor h(x).
-2*x*(x + 2)
Let c be (4/(-5))/((-2)/10). Let f = -803/3 + 269. Factor -10*p**2 - 2*p**c - 22/3*p**3 - f - 6*p.
-2*(p + 1)**3*(3*p + 2)/3
Suppose 2 = -4*z - 2*t + 16, -t - 17 = -4*z. Let g be -4*(26/260)/(2/(-15)). Let -2/7*w**g + 0*w + 0 + 2/7*w**z + 0*w**2 = 0. What is w?
0, 1
Let -6/7*r + 2/7*r**4 - 36/7 + 2*r**3 + 26/7*r**2 = 0. Calculate r.
-3, -2, 1
Let w(u) be the first derivative of -1/12*u**6 - 1/3*u**3 - u - 1/2*u**4 - 2 + 5/4*u**2 + 2/5*u**5. Let w(x) = 0. Calculate x.
-1, 1, 2
Let o(m) be the first derivative of 2 - 1/3*m**3 + 0*m - 1/1440*m**6 - 1/96*m**4 + 0*m**2 - 1/240*m**5. Let h(g) be the third derivative of o(g). Factor h(j).
-(j + 1)**2/4
Factor 8*u**2 + 6*u**3 + u - 14*u**3 - 2*u**4 - u + 2*u**5.
2*u**2*(u - 2)*(u - 1)*(u + 2)
Factor -4*d**4 - 68*d**3 - 72*d**3 + 132*d**3 + 32*d + 16 + 12*d**2.
-4*(d - 2)*(d + 1)**2*(d + 2)
Let y be (1 + -2 - -2) + (-117)/162. Let n(b) be the second derivative of 4/27*b**3 + 10/27*b**4 + 0*b**2 - b + 0 + y*b**5. Factor n(h).
2*h*(5*h + 2)**2/9
Let u(n) = -19*n + 3. Let s be u(0). Suppose -4/9*r**s + 2/9*r**2 + 2/9*r**4 + 0 + 0*r = 0. What is r?
0, 1
Let i(n) be the third derivative of 0*n**5 + 2/15*n**6 - 8/105*n**7 - 7*n**2 + 0*n**3 + 0*n**4 + 0 + 0*n + 1/84*n**8. Factor i(o).
4*o**3*(o - 2)**2
Let n(j) be the second derivative of j**7/3780 + j**6/810 + j**5/540 + j**3/2 - 4*j. Let o(q) be the second derivative of n(q). Factor o(z).
2*z*(z + 1)**2/9
Let u be 10/35 - (-26)/7. Suppose -2*o + 5*g = 6, o + 3*g = u*o. Find c, given that 0 + 2/7*c**o + 0*c = 0.
0
Let a = -53 + 56. Determine g so that 2/3*g - 2/3*g**2 + 2/9*g**a - 2/9 = 0.
1
Let a(k) = -k**3 - 2*k**2 + 2*k - 3. Let j be a(-3). Let n = j - -2. Factor -2 - 2*w**4 + 0*w + 4*w**2 + 2*w + 0*w**5 - 4*w**3 + n*w**5.
2*(w - 1)**3*(w + 1)**2
Let r be 2*(-2)/(12/(-27)). Let i = -1 + r. Factor 0 - i*c**2 - 21/2*c**3 - 9/2*c**4 - 2*c.
-c*(c + 1)*(3*c + 2)**2/2
Let l(r) be the second derivative of -r**5/60 + r**4/18 + r**3/18 - r**2/3 - 6*r. Solve l(m) = 0 for m.
-1, 1, 2
Let d(v) = v**2 + 4*v. Let l be d(-4). Suppose -m + 4 + l = 0. Find z, given that 0*z**m + z**5 + 5*z**3 + 0*z**3 - 2*z**2 - 4*z**4 = 0.
0, 1, 2
Let g(y) = y**2 + 6*y. Let u be g(-6). Suppose u*c = 2*c - 4. Solve -4/9*o**c - 2/9*o + 0 - 2/9*o**3 = 0.
-1, 0
Suppose 3*g + 3*g = 2*g. Let y(l) be the third derivative of 2*l**2 + 0 + 0*l + g*l**3 + 1/30*l**5 - 1/48*l**4. Solve y(k) = 0.
0, 1/4
Let d(g) be the first derivative of g**3/2 + 9*g**2/8 + 4. Solve d(a) = 0 for a.
-3/2, 0
Let s(b) = -b + 8 + 12 - 20. Let i(n) = n**2 - 2*n + 4. Let j(t) = -i(t) - 2*s(t). Determine m so that j(m) = 0.
2
Factor 6/7*i - 9/7 - 1/7*i**2.
-(i - 3)**2/7
Suppose -2*y + 6 = -2. Suppose y*q = q. Factor q - 2/9*t**3 + 4/9*t**2 - 2/9*t.
-2*t*(t - 1)**2/9
Let o(c) be the first derivative of 7 + 2*c**2 - 2/5*c**5 + 0*c - c**4 + 2/3*c**3. Factor o(s).
-2*s*(s - 1)*(s + 1)*(s + 2)
Let n be (8/(-40) + (-8)/10)*0. Let y(f) be the third derivative of n + 0*f + 3*f**2 - 1/36*f**4 + 1/90*f**5 + 0*f**3. What is q in y(q) = 0?
0, 1
Let f(h) be the first derivative of -5/7*h**3 + 8 + 24/7*h**5 + 3/7*h + 15/14*h**2 - 8/7*h**6 - 75/28*h**4. Factor f(d).
-3*(d - 1)**3*(4*d + 1)**2/7
Let r(l) = -13*l**5 + 13*l**3 + 9*l**2 - 9. Let k(i) = -3*i**5 + 3*i**3 + 2*i**2 - 2. Let b(u) = 9*k(u) - 2*r(u). Factor b(t).
-t**3*(t - 1)*(t + 1)
Let c = -62 - -22. Let n be (-30)/c + (-2)/4. What is q in 0 - 1/4*q - n*q**3 + 1/2*q**2 = 0?
0, 1
Suppose 4*w - 3 = 5. Find z, given that -z + 4*z**2 - 3*z**w + z**2 - z**3 = 0.
0, 1
Suppose 18 = 5*u - s, 2*u = s - 0*s + 9. Let p be u/(0 - 3/(-2)). Factor -18/7*d + 4/7 + p*d**2.
2*(d - 1)*(7*d - 2)/7
Factor 420 - 8*h + 12*h**3 + 20*h**2 - 420.
4*h*(h + 2)*(3*h - 1)
What is v in 2*v**2 + 3*v - 3*v**4 + 5*v**3 - 5*v + v**2 - 3*v**3 = 0?
-1, 0, 2/3, 1
Suppose -3*j + 7 = -2. Suppose 0 = j*h - 0*h - 6. Factor 2*b - 2 - h*b + 2*b**2.
2*(b - 1)*(b + 1)
Let k = -6 - -6. Let l(o) = -o + 15. Let y be l(15). Solve k - 2/5*g**4 - 2/5*g**3 + y*g + 2/5*g**2 + 2/5*g**5 = 0 for g.
-1, 0, 1
Let l(j) be the second derivative of -20/3*j**3 - 1/15*j**6 - 7*j - 3*j**4 - 7/10*j**5 - 8*j**2 + 0. Factor l(a).
-2*(a + 1)*(a + 2)**3
Factor -1/2*i**2 + 0 - 3/2*i**3 + 3/2*i + 1/2*i**4.
i*(i - 3)*(i - 1)*(i + 1)/2
Let g(f) = 3*f**2 + 5 - 5*f**2 - 1 - f. Let h(u) = -u. Let l(n) = -g(n) - h(n). Factor l(r).
2*(r - 1)*(r + 2)
Factor 1 - 1/3*w**2 + 2/3*w.
-(w - 3)*(w + 1)/3
Let b(z) be the second derivative of -z**5/60 + z**3/18 - 2*z. Factor b(n).
-n*(n - 1)*(n + 1)/3
Suppose 0 = -0*k - 3*k + 3. Let k - 2*a**4 - 3 + 6*a**2 - 2*a**2 = 0. What is a?
-1, 1
Let i(x) be the second derivative of -x**3/3 - 3*x**2 - 3*x. Let h be i(-4). Factor -10*j**3 + 9*j**3 - 3*j**h + 2*j**2.
-j**2*(j + 1)
Suppose i = -2*i - 6. Let a be 148/6 - i/(-3). Let h**4 - 9*h + 16 + 8*h**3 + 41*h + a*h**2 + 0*h**4 = 0. What is h?
-2
Let r = -5 - -7. Solve 3*n**3 - 5*n + n - 6*n**2 + 3 + 3*n**r + n = 0.
-1, 1
Let b(j) = j + 10. Let o be b(-8). Solve 6*d**3 + 3*d**4 + 49 + 3*d**o - 49 = 0 for d.
-1, 0
Let d(f) = f**2 + f. Let a(o) = -6*o**2 - 8*o - 11. Let s(z) = -z**2 - z - 1. Let l(t) = -2*a(t) + 18*s(t). Let i(h) = 2*d(h) + l(h). Factor i(r).
-4*(r - 1)*(r + 1)
Let t(u) = -12*u**3 + 25*u**2 + 3*u - 5. Let g(y) = 6*y**3 - 13*y**2 - y + 3. Let w(x) = 5*g(x) + 3*t(x). Find i such that w(i) = 0.
-1/3, 0, 2
Let k(t) = -t**2 + 5*t - 2. Let a be k(3). Suppose 4*r**4 - 5 - 3*r**a + 4 - 2*r + 2*r**3 = 0. What is r?
-1, 1
Let n(z) be the third derivative of z**5/60 + z**3/6 + z**2. Let i(m) = 4*m**4 + 8*m**3 + 5*m**2 + 1. Let o(u) = -i(u) + n(u). Factor o(j).
-4*j**2*(j + 1)**2
Let a(d) = -d**2 - 8*d + 2. Let i be a(-8). Let v(u) = u + 7. Let p be v(-5). Factor 4*h**2 + 2*h**i + 3*h**3 - 4*h**p + 0*h**2.
h**2*(3*h + 2)
Let d = 36 + -11. Let u be (-15)/d - (-4)/2. Solve -2/5*q + u*q**2 + 0 = 0 for q.
0, 2/7
Let p(c) be the third derivative of -c**9/3024 + c**8/840 - c**7/840 - 2*c**3/3 + 5*c**2. Let g(d) be the first derivative of p(d). Factor g(t).
-t**3*(t - 1)**2
Let h(d) be the third derivative of 0*d + 0 - 2/3*d**3 + 1/4*d**4 - 3*d**2 + 1/240*d**6 - 1/20*d**5. Factor h(m).
(m - 2)**3/2
Let n be -27*6/(-36)*4/6. Factor -3/5*l**n - 6/5*l**2 - 3/5*l + 0.
-3*l*(l + 1)**2/5
Let l be (24/(-30))/((-18)/10). Factor -l - 2/3*d**3 - 2/3*d + 16/9*d**2.
-2*(d - 2)*(d - 1)*(3*d + 1)/9
Let h(i) = 9*i**2 - 1. Let a be h(1). Factor 112*f**2 + a - 7*f - 52*f - f.
4*(4*f - 1)*(7*f - 2)
Let n(u) be the second derivative of -u**4/12 + u**2/2 - 5*u. Let k(t) = -t**3 + t**2 - 3*t + 3. Let l(s) = k(s) - 2*n(s). Determine y, given that l(y) = 0.
1
Let f(d) be the second derivative of -d**5/30 + d**4/36 + 2*d**3/9 + d**2 + d. Let a(j) be the first derivative of f(j). Suppose a(r) = 0. Calculate r.
-2/3, 1
Factor 0 - 1/2*n**2 + 1/4*n.
-n*(2*n - 1)/4
Let y(z) be the third derivative of -z**5/60 + 7*z**4/24 + z**3/3 + 16*z**2. Let c be y(7). Factor 0*k**3 + 1/3 + 1/3*k**4 - 2/3*k**c + 0*k.
(k - 1)**2*(k + 1)**2/3
Suppose 7*m = -5*g + 4*m + 12, 2*m - 1 = -g. Factor 0 + 4/11*u**g - 2/11*u + 0*u**4 - 2/11*u**5 + 0*u**2.
-2*u*(u - 1)**2*(u + 1)**2/11
Let a(v) be the second derivative of 16*v**5/5 + 40*v**4/3 - 46*v**3/3 + 6*v**2 + 7*v. Solve a(p) = 0 for p.
-3, 1/4
Let z(d) be the third derivative of -7*d**5/12 + 25*d**4/24 + 5*d**3/3 + 19*d**2. Find i such that z(i) = 0.
-2/7, 1
Let c(o) be the first derivative of o**8/720 - o**7/1260 - 7*o**6/1080 + o**5/180 + 3*o**3 + 8. Let d(k) be the third derivative of c(k). Factor d(w).
w*(w - 1)*(w + 1)*(7*w - 2)/3
Suppose 3*u = 9, -5*u = g - 18 