0, 1
Factor 2/11 + 6/11*t**2 - 6/11*t - 2/11*t**3.
-2*(t - 1)**3/11
Factor 52 - 400*d + 50*d**4 - 200*d**3 + 129*d**2 + 271*d**2 - 5*d**5 + 108.
-5*(d - 2)**5
Let b be (78/(-27))/13 + 40/18. Factor 0 + 0*k**b + 0*k - 2/7*k**3.
-2*k**3/7
Let p(j) be the second derivative of j**8/4200 - j**7/1050 + j**6/900 - j**3/6 - j. Let k(h) be the second derivative of p(h). Let k(u) = 0. Calculate u.
0, 1
Factor -36/5*v**2 - 96*v + 192/5 + 84*v**3 + 147/5*v**4.
3*(v + 2)**2*(7*v - 4)**2/5
Find y such that 0*y**3 + 4*y**3 + 4*y**5 - 7*y**2 - 8*y + 12*y**4 - 5*y**2 + 0*y**5 = 0.
-2, -1, 0, 1
Let g(j) be the first derivative of j**3/9 + j**2/6 - 2*j/3 - 10. What is l in g(l) = 0?
-2, 1
Suppose -3*r + 5 = -o - 7, -2*o - 12 = -3*r. Solve 2/3*y + 8*y**5 + 0*y**2 + 0 - 8/3*y**r - 6*y**3 = 0 for y.
-1/2, 0, 1/3, 1
Let u(f) be the second derivative of -f**6/255 + f**5/170 + 26*f. Suppose u(b) = 0. Calculate b.
0, 1
Let w(p) be the first derivative of p**3/9 - p**2/3 + p/3 + 4. Factor w(x).
(x - 1)**2/3
Let b(z) = 7*z**4 - 7*z**3 - 4*z - 4. Let p(y) = -y**4 + y**3 + y + 1. Let s be 7/(105/12)*5. Let r(x) = s*p(x) + b(x). Factor r(c).
3*c**3*(c - 1)
Suppose 5*k = -2*i - 16, -i - k + 2 = 2*i. Find o, given that -4/9*o + 2/9*o**i + 0 = 0.
0, 2
Let f(t) = 3*t**2 + 18*t + 31. Let l(w) = 24*w**2 + 144*w + 249. Let m(v) = -33*f(v) + 4*l(v). Suppose m(i) = 0. Calculate i.
-3
Let s = 99/34 - 24/17. Let k(m) be the first derivative of -2 - s*m + 1/4*m**3 + 3/8*m**2. Factor k(f).
3*(f - 1)*(f + 2)/4
Let p(k) = k - 5. Let n be p(5). Let g(s) be the second derivative of n + 0*s**3 + 1/6*s**2 - 1/36*s**4 + 2*s. Factor g(c).
-(c - 1)*(c + 1)/3
Let t(k) be the second derivative of k**6/60 - k**4/4 - 2*k**3/3 - 3*k**2/2 + 2*k. Let h(j) be the first derivative of t(j). Factor h(o).
2*(o - 2)*(o + 1)**2
Suppose -12 = -14*r + 10*r. Determine n so that -1/4*n + 0 - 1/4*n**r - 1/2*n**2 = 0.
-1, 0
Let c be (2 - 4) + (-28)/(-9). Let o = 49/36 - c. Factor -1/4*i**2 + 1/4*i**3 - o*i + 1/4.
(i - 1)**2*(i + 1)/4
Let d(a) be the first derivative of -a**6/180 + a**5/60 + 2*a**3/3 - 5. Let s(l) be the third derivative of d(l). Suppose s(k) = 0. Calculate k.
0, 1
Let u(j) = -3*j**3 - 43*j**2 - 223*j - 373. Let y(a) = -9*a**3 - 128*a**2 - 668*a - 1118. Let w(d) = -7*u(d) + 2*y(d). Factor w(x).
3*(x + 5)**3
Let o(y) be the second derivative of 0 + 2*y**2 - 4*y - 4/9*y**3 - 1/30*y**5 - 2/9*y**4. Let v(l) be the first derivative of o(l). Factor v(n).
-2*(n + 2)*(3*n + 2)/3
Let s = -491 + 1474/3. Factor 0*b + 0*b**2 + 0 + 1/3*b**3 - s*b**4.
-b**3*(b - 1)/3
Let u(z) be the first derivative of z**4 + 20*z**3/3 + 8*z**2 + 10. Let u(x) = 0. What is x?
-4, -1, 0
Let j = -1 - -1. Let i(c) = -c**3 + c + 2. Let m be i(j). Find a such that 9*a**2 - 10*a**4 + 4*a**5 - 14*a - 4*a**4 + 10*a**3 + 4 + a**m = 0.
-1, 1/2, 1, 2
Let w be (-8)/6*(-1)/20. Let r(f) be the second derivative of 1/10*f**5 + 0*f**4 + 0*f**2 - w*f**6 + 2*f + 0*f**3 + 0. Factor r(m).
-2*m**3*(m - 1)
Let r(t) be the third derivative of -t**8/336 + t**7/30 - 17*t**6/120 + 17*t**5/60 - t**4/4 - 67*t**2. Find o such that r(o) = 0.
0, 1, 2, 3
Let x(g) be the third derivative of -g**8/14 + 11*g**7/105 - g**6/30 + g**2. Determine y, given that x(y) = 0.
0, 1/4, 2/3
Suppose -5*b = -2*p + 50, 0*p + b + 49 = 3*p. Factor 12*c**2 + p*c + 2 - 3 + 8 - 4.
3*(c + 1)*(4*c + 1)
Suppose 1 - 3 = n - 2*j, -5*n - j + 1 = 0. Suppose 4*u - 7 - 9 = n. Factor -q**2 + 6*q**u - q**4 - 4*q**4.
q**2*(q - 1)*(q + 1)
Solve -4*f**4 + f**3 - 3*f**2 - f**3 - 8*f**3 - f**2 = 0 for f.
-1, 0
Let f(q) = q**4 + q**3 + q**2. Let t(v) = -v**4 + 24*v**3 - 21*v**2 + 10*v. Let z(o) = -4*f(o) + t(o). Solve z(k) = 0.
0, 1, 2
Let s be (3 + 2 - 3) + 0. Solve 6*z**4 - 6*z**3 - 5*z**s - z**2 + 9*z**5 - 3*z**3 + 0*z**2 = 0 for z.
-1, -2/3, 0, 1
Let r(m) = m**3 + m**2. Let i(u) = 4*u**4 - 18*u**3 - 54*u**2 - 32*u. Let g(b) = i(b) - 6*r(b). Solve g(a) = 0 for a.
-1, 0, 8
Solve -1/6*t**3 + 1/6*t - 1/6*t**2 + 1/6 = 0.
-1, 1
Determine w, given that 8/3*w - 8/3*w**2 - 14/3*w**3 + 0 + 2*w**5 + 8/3*w**4 = 0.
-2, -1, 0, 2/3, 1
Let y = 4 - 0. Let j be (-3)/((-60)/8)*y. Factor j*f - 16/5*f**2 + 2*f**3 + 0 - 2/5*f**4.
-2*f*(f - 2)**2*(f - 1)/5
Let a(g) = g**3 + 7*g**2 - 8*g + 2. Let f be a(-8). Determine m so that 2*m**3 - 2*m**f - m - m**2 + 3*m**2 - m**5 = 0.
-1, 0, 1
Let h(p) = 7*p**3 + 5*p**2 - 7*p + 5. Suppose m + m = -10. Let c(v) = 4*v**3 + 3*v**2 - 4*v + 3. Let f(b) = m*c(b) + 3*h(b). Factor f(d).
d*(d - 1)*(d + 1)
Let z(p) be the third derivative of p**5/60 + p**4/24 + p**2. Let z(q) = 0. What is q?
-1, 0
Let u = 1042/777 + -2/259. Suppose -3*n - 3*b = 6, -2*n - 4*b = -5 + 13. Solve n + 2/3*z**2 - u*z = 0 for z.
0, 2
Let u(v) = -v**2 + v + 1. Let c(z) = 4*z**3 - 9*z**2 - 15*z - 7. Let d(t) = c(t) - 5*u(t). Factor d(g).
4*(g - 3)*(g + 1)**2
Let a(b) be the third derivative of -b**6/120 + b**5/30 - b**4/24 - 9*b**2. Solve a(t) = 0.
0, 1
Let z = -19 + 115/6. Let s(a) be the third derivative of 0 + 5/48*a**4 - z*a**3 - 2*a**2 + 7/120*a**5 + 0*a. Factor s(n).
(n + 1)*(7*n - 2)/2
Let h(z) be the third derivative of -15/4*z**4 + z**2 - 6*z**3 - 1/105*z**7 + 0*z + 0 - 11/10*z**5 - 29/180*z**6. Let h(r) = 0. Calculate r.
-3, -2/3
Let j(o) be the third derivative of -7*o**5/30 + o**4/12 + 6*o**2. Determine n so that j(n) = 0.
0, 1/7
Let y be 10*10/(-125)*-5. Let q(b) be the second derivative of 1/9*b**y + 2*b + 1/30*b**5 + 0 + 1/9*b**3 + 0*b**2. Factor q(r).
2*r*(r + 1)**2/3
Let w(a) = -2*a**2 + 3. Let q(f) = -5*f**2 + 8. Let k(z) = 3*q(z) - 8*w(z). Suppose k(j) = 0. Calculate j.
0
Let g(b) = -b**3 - 10*b**2 - 10*b - 3. Let v be g(-9). Let 2*i**3 - 5*i**2 + 2*i + 7*i**2 - v*i**2 = 0. Calculate i.
0, 1
Let o(c) be the second derivative of -c**8/840 + c**7/140 - c**6/60 + c**5/60 + 2*c**3/3 + 8*c. Let d(h) be the second derivative of o(h). Factor d(u).
-2*u*(u - 1)**3
Let v(k) be the first derivative of -k**4/48 + k**3/12 - k/3 + 67. Solve v(a) = 0.
-1, 2
Let s be (0 + 3/(-3))*-3. Let c(v) be the first derivative of 1/2*v**4 + 2 + 0*v + 10/21*v**s - 2/7*v**2. Factor c(i).
2*i*(i + 1)*(7*i - 2)/7
Let m(q) be the third derivative of -q**8/23520 + q**7/4410 - q**6/2520 + q**4/24 + 3*q**2. Let n(x) be the second derivative of m(x). Factor n(v).
-2*v*(v - 1)**2/7
Let o = -32 - -12. Let q be -2*o/16 + -2. Factor 1/4*r**3 + 0 + q*r**2 - 3/4*r**4 + 0*r.
-r**2*(r - 1)*(3*r + 2)/4
Let f(p) = p**2 + 15*p + 4. Suppose -2*c + 6*c = -60. Let y be f(c). Factor 0 + 2*i**2 + 2/3*i**y - 2*i**3 - 2/3*i.
2*i*(i - 1)**3/3
Let t(m) be the second derivative of 3*m**2 - 3*m - 1/6*m**4 - 2/3*m**3 + 0. Suppose t(p) = 0. What is p?
-3, 1
Let f(k) be the third derivative of k**6/300 + k**5/75 - k**4/15 - 8*k**3/15 + 16*k**2. Factor f(b).
2*(b - 2)*(b + 2)**2/5
Let x(l) be the second derivative of -3*l**5/140 + l**4/14 + l**3/14 - 3*l**2/7 - 22*l. Factor x(u).
-3*(u - 2)*(u - 1)*(u + 1)/7
Suppose 16 - 3 = 5*z - 2*d, -3*z - 4*d + 13 = 0. Factor 2/11*m**4 + 2/11*m**z + 0*m**2 + 0 + 0*m.
2*m**3*(m + 1)/11
Suppose -2*m = 3*n, -4*m - n - 5 + 15 = 0. Let h(u) = u. Let l(z) = -2*z**3 + 2*z**2 - 3*z. Let t(d) = m*h(d) + l(d). Suppose t(w) = 0. What is w?
0, 1
Let j(o) be the first derivative of -o**4/2 + 38*o**3/21 + 6*o**2/7 - 3. Find t, given that j(t) = 0.
-2/7, 0, 3
Let l = 26 - 23. Solve 0 + 1/2*i**l - 5/4*i**4 + 5/4*i**2 - 1/2*i = 0 for i.
-1, 0, 2/5, 1
Solve -j**2 + 7*j**2 - 24*j**5 + 27*j**5 - 6*j**4 - 3*j = 0.
-1, 0, 1
Let f(z) be the first derivative of -1/20*z**5 - 4/3*z**3 - 5/12*z**4 + 1 - z - 2*z**2. Let q(o) be the first derivative of f(o). Find t such that q(t) = 0.
-2, -1
Let a = 2 + 0. Let u(t) = -10*t**5 - 31*t**4 + 31*t**2 - t. Let r(d) = -3*d**3 + 2*d**5 + 3*d**3 + 6*d**4 - 6*d**2. Let j(l) = a*u(l) + 11*r(l). Factor j(z).
2*z*(z - 1)*(z + 1)**3
Let h(r) be the second derivative of r**6/30 - 5*r**4/12 + 2*r**2 + 9*r. Suppose h(o) = 0. What is o?
-2, -1, 1, 2
Factor 4*d**2 + 15*d + 9*d**2 - 16*d**2 + 0*d.
-3*d*(d - 5)
Let w be 50/6 - 4/(-6). Suppose -2*f = f - w. Factor 1 - f*s**3 + 8*s**2 + 5*s**3 + 10*s + 3.
2*(s + 1)**2*(s + 2)
Let u(b) be the first derivative of 60*b**4 - 40*b**3/3 - 65*b**2/2 - 10*b + 9. Factor u(k).
5*(3*k - 2)*(4*k + 1)**2
Let j = 19 + -9. Let y(p) = 7*p**2 + p + 1. Let h be y(-1). Factor 2*z + 14*z