Let z = -54 - -56. Factor -3/4*u**z - 3/4*u + 0.
-3*u*(u + 1)/4
Let x(k) be the third derivative of 1/315*k**7 + 0*k + 0 - k**2 + 1/30*k**5 + 0*k**3 + 1/60*k**6 + 1/36*k**4. Factor x(o).
2*o*(o + 1)**3/3
Let v(x) be the third derivative of -2*x**2 - 1/2*x**4 + 0*x - 3/5*x**5 - 1/16*x**8 + 0 + 0*x**3 + 6/35*x**7 + 11/40*x**6. Suppose v(u) = 0. What is u?
-1, -2/7, 0, 1, 2
Let s be 187/420 - 12/28. Let d(k) be the second derivative of 0 - 1/24*k**4 - 1/20*k**5 - 2*k + 0*k**3 - s*k**6 + 0*k**2. Determine t so that d(t) = 0.
-1, 0
Suppose 0*u = 2*j + 2*u, -5*u = 3*j + 8. Factor 0*b + 1/6 - 1/3*b**2 + 0*b**3 + 1/6*b**j.
(b - 1)**2*(b + 1)**2/6
Suppose 2*y - 40 = -5*u, 4*y + 3*u - 80 = 4*u. Suppose 3*i + y = 5*q, -2*i + 3*q = -3*i + 12. Factor i - 2/7*l - 6/7*l**2 - 2/7*l**4 - 6/7*l**3.
-2*l*(l + 1)**3/7
Let q(s) be the third derivative of s**6/120 - s**5/90 - s**4/72 + s**2. Find c such that q(c) = 0.
-1/3, 0, 1
Suppose 5*h - 13 = -r, -3*r + 5 = -2*h + 17. Let -24*w**h + 12*w + 2*w + 0 - 14*w**2 + 4 = 0. What is w?
-1, -1/4, 2/3
Determine t, given that 2/5*t**2 + 0 + 0*t - 1/5*t**3 = 0.
0, 2
Let d(i) = -4*i**5 + 14*i**4 + 2*i**3 - 12*i**2 - 2*i - 2. Let x(k) = 4*k**5 - 15*k**4 - k**3 + 12*k**2 + 3*k + 3. Let b(r) = -3*d(r) - 2*x(r). Factor b(p).
4*p**2*(p - 3)*(p - 1)*(p + 1)
Let s be (-10)/30*2/((-10)/3). Let -s*q + 1/5*q**2 + 0 = 0. What is q?
0, 1
Let 22*f + 42*f**3 - 36*f**2 - 16*f**2 - 7*f**4 - 3 - 2*f**4 = 0. What is f?
1/3, 1, 3
Let r = 309 - 15449/50. Let o(l) be the second derivative of r*l**5 - 4/5*l**2 + 0 + 1/10*l**4 - 2*l + 0*l**3. Solve o(f) = 0 for f.
-2, 1
Let v = 740 - 737. Factor 1/3*b + 1/3 - 1/3*b**v - 1/3*b**2.
-(b - 1)*(b + 1)**2/3
Factor -11*n**2 + 16*n**4 - 3*n**2 - 6*n**5 + 11*n - 2 - n**5 - 4*n**3.
-(n - 1)**3*(n + 1)*(7*n - 2)
Let t(a) be the third derivative of 49*a**6/720 - 77*a**5/360 + 2*a**4/9 - a**3/9 + a**2. Determine v so that t(v) = 0.
2/7, 1
Let q be 0/(4/(-8)*2). Solve -n**4 - 10 - 22*n**2 + q*n**3 - 24*n + 1 - 8*n**3 = 0.
-3, -1
Let i = -92 + 278/3. Factor 1/3*p**4 + 1/3 + i*p**3 - 2/3*p**2 - 1/3*p**5 - 1/3*p.
-(p - 1)**3*(p + 1)**2/3
Let k(u) be the second derivative of -u**4/12 - u**3/3 + 9*u. Factor k(o).
-o*(o + 2)
Let h(s) = 5*s**2 - 2. Let g(m) = 5*m**2 - 3. Let f(n) = 3*g(n) - 2*h(n). Factor f(k).
5*(k - 1)*(k + 1)
Solve 6*f**2 - 5*f**2 - 3*f - 3 - 1 = 0.
-1, 4
Let y(g) be the third derivative of -27*g**8/28 - 132*g**7/35 - 157*g**6/30 - 44*g**5/15 - 2*g**4/3 - 9*g**2. Factor y(b).
-4*b*(b + 1)**2*(9*b + 2)**2
Let g(j) = -j + 27. Let q be g(27). Factor -2/5*m**2 + 1/5*m**3 + q*m + 0.
m**2*(m - 2)/5
Let x(t) be the third derivative of -t**6/120 + t**5/30 - t**4/24 - 16*t**2. Determine u so that x(u) = 0.
0, 1
Suppose 2*i + 7 = -5. Let g be (8/16)/((-1)/i). Let 3/5*q**g + 0 + q**2 - 4/5*q**5 + 1/5*q - q**4 = 0. Calculate q.
-1, -1/4, 0, 1
Factor 0 + 1/6*k**3 - 5/6*k**2 + k.
k*(k - 3)*(k - 2)/6
Let z(q) = -6*q**2 + 16*q - 10. Let u(o) = 5*o**2 + 3*o + 4. Let v(i) = 4*i**2 + 3*i + 3. Let b(l) = -5*u(l) + 6*v(l). Let x(g) = 16*b(g) - 3*z(g). Factor x(c).
2*(c - 1)*(c + 1)
Let t be 108/(-8)*(-2)/3. Factor -14*y**4 - 54*y**2 - 7*y**3 - 39*y**3 - t*y - 4 - 2*y - 15*y.
-2*(y + 1)**3*(7*y + 2)
Factor -84*j**2 + 0 - 10*j + 0 + 79*j**2.
-5*j*(j + 2)
Let -15*v**2 - 14 - 16*v + 2 - 30*v + 10*v = 0. What is v?
-2, -2/5
Suppose 5*y = 1 - 16. Let d = -1 - y. Factor b**d - 6*b**4 + 5*b**4 + 0*b + 0*b.
-b**2*(b - 1)*(b + 1)
Let w(a) = 36*a**3 - 27*a**2 + 6*a + 15. Let u(s) = -5*s**3 + 4*s**2 - s - 2. Let i(c) = -15*u(c) - 2*w(c). Factor i(m).
3*m*(m - 1)**2
Let d(i) be the third derivative of -1/15*i**7 + 0*i - 11/96*i**4 - 1/84*i**8 + 0 - 73/480*i**6 - 43/240*i**5 - 1/24*i**3 + 3*i**2. Factor d(t).
-(t + 1)**3*(4*t + 1)**2/4
Let u(r) = r - 1. Let i(f) = -f**2 - 4*f + 7. Let q(h) = -i(h) - 5*u(h). Factor q(v).
(v - 2)*(v + 1)
Let r = 206 + -206. Suppose 0*v**4 - 1/3*v**5 + 1/3*v**3 + r*v**2 + 0*v + 0 = 0. Calculate v.
-1, 0, 1
Let o(z) = z**2 - 4*z + 8. Let m be o(2). Let 0*x + 0*x**2 + 2/7*x**m + 2/7*x**3 + 0 = 0. Calculate x.
-1, 0
Let t(m) = -m**2 + m + 1. Let l(k) = -2*k**2 + 9*k + 10. Let g(n) = l(n) - t(n). Let y(q) = q + 1. Let c(p) = 2*g(p) - 18*y(p). Solve c(h) = 0.
-1, 0
Let r(j) be the second derivative of -5/12*j**4 - 1/21*j**7 - 7/30*j**6 - 4*j + 0 + 0*j**2 - 9/20*j**5 - 1/6*j**3. Find y such that r(y) = 0.
-1, -1/2, 0
Let t(h) = -h**3 + 10*h**2 + 11*h + 3. Let g = -23 + 34. Let f be t(g). Factor 2/9*b**f + 2/9*b**2 + 0*b - 2/9*b**5 + 0 - 2/9*b**4.
-2*b**2*(b - 1)*(b + 1)**2/9
Let b be (-2)/3*(3 + -9). Solve 0*t**b + 0*t**2 + 1/2*t + 0 - t**3 + 1/2*t**5 = 0.
-1, 0, 1
Let s = 17 - 26. Let o be (-21)/s - 1*2. Factor 2/3 + o*d**2 + d.
(d + 1)*(d + 2)/3
Suppose 0 = 5*z, 2*f + f = 5*z. Suppose -b = -3*d + 2, 4*d + f*b = b + 4. Let 0*u**4 + 0 + 1/2*u**3 - 1/2*u**5 + 0*u**d + 0*u = 0. What is u?
-1, 0, 1
Find m, given that -4/9*m**4 + 0 - 2/9*m**5 + 2/9*m + 0*m**3 + 4/9*m**2 = 0.
-1, 0, 1
Let k(s) be the third derivative of -s**8/420 + s**7/210 + s**6/90 - s**5/30 - s**3/6 + 4*s**2. Let c(w) be the first derivative of k(w). Factor c(o).
-4*o*(o - 1)**2*(o + 1)
Let g(y) be the second derivative of 1/3*y**2 + 1/6*y**3 + 5*y - 1/60*y**5 + 0*y**4 + 0. Factor g(w).
-(w - 2)*(w + 1)**2/3
Let s(y) be the third derivative of y**8/9240 - y**6/990 + y**4/132 - y**3/3 - y**2. Let b(n) be the first derivative of s(n). Factor b(a).
2*(a - 1)**2*(a + 1)**2/11
Let g = 0 - -2. Let i(r) = -2*r - 2. Let x be i(-3). Factor 0*y - 2/9*y**g + 2/9*y**x + 2/9*y**3 - 2/9*y**5 + 0.
-2*y**2*(y - 1)**2*(y + 1)/9
Let n be 30/6 - (3 + 5)/4. Let l(i) be the second derivative of 1/3*i**4 + 2*i - 1/3*i**n - 2*i**2 + 1/10*i**5 + 0. Factor l(x).
2*(x - 1)*(x + 1)*(x + 2)
Factor -112*r**2 + 2*r - 3*r + 2 + 111*r**2.
-(r - 1)*(r + 2)
Let k(b) = b**2 - 2. Let x(n) = 6*n**2 + 24*n + 28. Let r(w) = -2*k(w) + x(w). Factor r(p).
4*(p + 2)*(p + 4)
Let w(v) be the first derivative of 3 + 3*v + 1/15*v**3 + 1/15*v**4 + 0*v**2 + 1/50*v**5. Let c(p) be the first derivative of w(p). Factor c(j).
2*j*(j + 1)**2/5
Suppose -2 + b + 3*b - 3*b**2 + 3*b**2 - 2*b**2 = 0. What is b?
1
Let c = -9 - -13. Suppose 0 = 5*g - c*k - 2, 4 = -g + 3*k - 0*k. Solve -1/5*d**3 + 0 + 1/5*d + 0*d**g = 0.
-1, 0, 1
Let c(d) = d**2 + 3*d + 2. Let a(l) = -2*l**2 - 7*l - 4. Let i(h) = -6*a(h) - 13*c(h). Suppose i(z) = 0. What is z?
1, 2
Let c(m) be the first derivative of -m**6/27 + 2*m**5/15 - m**4/6 + 2*m**3/27 + 10. Let c(q) = 0. What is q?
0, 1
Let j(v) be the first derivative of -v**5/66 - 7*v**4/132 - 2*v**3/33 + v**2 + 1. Let o(q) be the second derivative of j(q). Solve o(n) = 0.
-1, -2/5
Factor -8*j**4 + 169*j - j**5 - 12*j**3 + 16*j**2 - 153*j + 5*j**5.
4*j*(j - 2)**2*(j + 1)**2
Suppose 0 = -11*p + 9*p - 4*a - 4, -1 = a. Factor 1/2*y**2 + y**4 + p + 0*y - 3/2*y**3.
y**2*(y - 1)*(2*y - 1)/2
Let o(t) be the third derivative of -t**8/560 - t**7/350 + t**6/100 + t**5/50 - t**4/40 - t**3/10 + 9*t**2. Let o(i) = 0. Calculate i.
-1, 1
Let k(l) be the second derivative of l**4/8 - 5*l**3/4 + 9*l**2/2 + 25*l. Determine q so that k(q) = 0.
2, 3
Factor -12/7 - 6/7*c**3 + 9/7*c**2 - 3/7*c**4 + 12/7*c.
-3*(c - 1)**2*(c + 2)**2/7
Let p(g) = -4*g**3 + 4*g**2 - g + 6. Let a(d) = d**3 - d**2 - 1. Let u(r) = -10*a(r) - 2*p(r). Factor u(y).
-2*(y - 1)**2*(y + 1)
Let w(n) be the second derivative of n**4/12 - n**3/6 - n**2 + n. Factor w(m).
(m - 2)*(m + 1)
Let f(x) be the third derivative of -x**5/450 - x**4/45 - 4*x**2. Suppose f(j) = 0. What is j?
-4, 0
Suppose -5 = -2*a - 3. Solve -3/2*k**4 + a - 7/2*k**3 - 3/2*k**2 + 3/2*k = 0.
-1, 2/3
Solve -3 + 3*v - v**2 + v + 6*v - 22 = 0.
5
Solve -12/5*x**3 - 18/5*x**2 - 3/5 - 12/5*x - 3/5*x**4 = 0.
-1
Factor 5*x**3 + 15*x**4 + 0*x**3 + 87*x - 15*x**2 - 97*x + 5*x**5.
5*x*(x - 1)*(x + 1)**2*(x + 2)
Let k = 407/10 + -81/2. Let -2/5*n + 1/5*n**2 + k*n**3 + 0 = 0. What is n?
-2, 0, 1
Factor 16/7 + 440/7*m + 9386/7*m**3 - 13718/7*m**4 + 3876/7*m**2.
-2*(m - 1)*(19*m + 2)**3/7
Factor 4*d**2 - 3*d - 5*d**2 - 2*d**2.
-3*d*(d + 1)
Suppose 3*i - 20 = -2*i. Let l(j) be the first derivative of 1/22*j**i + 3 - 1/11*j**2 + 0*j**3 + 0*j. Determine c, given that l(c) = 0.
-1, 0, 1
Suppose 0 = -d + 6*d - 30. Suppose s - d = -4. Solve 0 + 1/2*p**4 + 0*p + 0*p**3 + 0*p**s 