*4 - 5*s**4 - 36*s**3 + 12 + 13*s**4 - 33*s**h + 36*s + 4*s**4 = 0.
-1, -2/7, 1, 2
Let n(l) be the second derivative of -11*l**4/4 - 13*l**3/2 - 3*l**2 - 19*l. Suppose n(m) = 0. Calculate m.
-1, -2/11
Let m(d) be the second derivative of -1/60*d**4 + 1/150*d**6 - 2*d + 0*d**3 + 1/210*d**7 + 0 - 1/100*d**5 + 0*d**2. Factor m(u).
u**2*(u - 1)*(u + 1)**2/5
Let l(j) be the second derivative of 0 + 1/42*j**4 - 1/7*j**2 + 0*j**3 - 2*j. Suppose l(d) = 0. What is d?
-1, 1
Factor 1/5*c**5 - 8/5 - 38/5*c**2 + 28/5*c + 5*c**3 - 8/5*c**4.
(c - 2)**3*(c - 1)**2/5
Let c(z) be the second derivative of z**7/189 + 2*z**6/135 - z**5/10 - 11*z**4/27 + 4*z**3/27 + 8*z**2/3 + 36*z. Find m, given that c(m) = 0.
-2, 1, 3
Let t = 14 + -7. Suppose 0 = -5*f + t*f. Solve -1/4*c**2 - 1/2*c + f = 0.
-2, 0
Let b = -277 - -279. Factor 0*o - 1/3*o**b - 2/3*o**3 - 1/3*o**4 + 0.
-o**2*(o + 1)**2/3
Let h(r) be the third derivative of r**6/30 + 7*r**5/60 - 7*r**4/12 + r**3/2 - 19*r**2. Find x, given that h(x) = 0.
-3, 1/4, 1
Let n = 2/17403 - -2244979/69612. Let r = n + -32. Factor 0 + r*h**4 - 1/2*h**3 + 0*h + 1/4*h**2.
h**2*(h - 1)**2/4
Let y = 2 - -2. Suppose 8 = 2*i, 2*a + 3*i = -7 + 23. Factor 0*z**y + 4/9*z**3 + 0*z**a - 2/9*z - 2/9*z**5 + 0.
-2*z*(z - 1)**2*(z + 1)**2/9
Determine q, given that -8*q**3 + 15*q**3 - 9*q**3 + 0*q**2 - 22*q**2 = 0.
-11, 0
Suppose m = -4*m. Let t be -2 + (m/(-1) - -2). Factor t*p**5 - p**5 + p**3 - 17*p**2 + 16*p**2 + p**4.
-p**2*(p - 1)**2*(p + 1)
Let l = -122 - -125. Factor -2 - 21/2*i**2 + 9/2*i**l + 8*i.
(i - 1)*(3*i - 2)**2/2
Let g be (-5)/(-2)*(-8)/(-30). Suppose 3*i + i - 12 = 0. Determine v so that 0*v - 1/3*v**4 - 1/3*v**2 + 0 + g*v**i = 0.
0, 1
Suppose 3*a = -2*a + 25, -4*a + 18 = -i. Let d(w) be the third derivative of 0*w + 0 + 1/96*w**4 - 1/12*w**3 + 3*w**i + 1/240*w**5. Let d(u) = 0. What is u?
-2, 1
Factor -1/3*q**3 - 4/3 + 4/3*q + 1/3*q**2.
-(q - 2)*(q - 1)*(q + 2)/3
Let l(z) = 5*z**4 + 12*z**3 + 7*z**2 - 3*z + 3. Let f(j) = 10*j**4 + 23*j**3 + 13*j**2 - 7*j + 7. Let p(v) = 3*f(v) - 7*l(v). Factor p(r).
-5*r**2*(r + 1)*(r + 2)
Let x(t) be the second derivative of -1/3*t**2 + 0 + 1/18*t**4 + 1/15*t**5 + 0*t**6 - 1/126*t**7 - 1/6*t**3 - t. Determine d, given that x(d) = 0.
-1, 1, 2
Find f, given that -3*f + 12*f + 6 - 9*f**3 - 3*f**4 + 0*f - 3*f**2 = 0.
-2, -1, 1
Let w(a) be the second derivative of -1/30*a**5 + 0 + 0*a**2 + 0*a**4 + 0*a**3 - 2*a. Factor w(o).
-2*o**3/3
Let a(w) be the third derivative of 1/15*w**5 + 0 - w**2 + 1/3*w**3 - 1/120*w**6 - 5/24*w**4 + 0*w. Factor a(k).
-(k - 2)*(k - 1)**2
Let j(h) = -23*h**3 - 37*h**2 - 10*h - 1. Let z(a) = -3 - 34*a**3 - 55*a**2 - 7*a - 8*a + 2. Let t(w) = 7*j(w) - 5*z(w). Factor t(v).
(v + 1)**2*(9*v - 2)
Let i(s) = -s + 1. Let a be i(4). Let w = -1 - a. Solve -4*z**2 + 4*z**3 + 0*z**3 - 2*z**5 + 3*z - 5*z + 2 + w*z**4 = 0.
-1, 1
Let i(p) be the third derivative of p**8/42 + 2*p**7/35 - p**5/15 - 25*p**2. Determine l, given that i(l) = 0.
-1, 0, 1/2
Let o(d) be the first derivative of 3*d**5/5 - 9*d**4/4 + 2*d**3 - 1. Find a such that o(a) = 0.
0, 1, 2
Suppose -1/2*u**2 - 1/2*u**4 + 0*u + 0 + u**3 = 0. Calculate u.
0, 1
What is v in 3/2*v**3 - 3/2*v + 9/8 - 3/8*v**4 - 3/4*v**2 = 0?
-1, 1, 3
Let l(n) be the first derivative of -n**3/3 - n**2/2 + 2*n - 4. Solve l(s) = 0 for s.
-2, 1
Let p(o) be the third derivative of o**6/60 + o**5/30 - o**4/12 - o**3/3 + 15*o**2. Factor p(m).
2*(m - 1)*(m + 1)**2
Let i(r) be the first derivative of r**4/7 - 4*r**3/7 + 4*r**2/7 + 5. Let i(c) = 0. Calculate c.
0, 1, 2
Suppose 0 + 2/15*g**2 + 4/15*g = 0. What is g?
-2, 0
Let h(y) = -y**2 - y + 1. Let g(t) = -6*t**2 - 9*t + 2. Let l(p) = -g(p) + 5*h(p). Factor l(f).
(f + 1)*(f + 3)
Let n(s) be the first derivative of s**8/2520 - s**7/1260 - s**6/270 + 5*s**3/3 - 2. Let y(q) be the third derivative of n(q). Factor y(c).
2*c**2*(c - 2)*(c + 1)/3
Find g such that -2*g**3 + g - 4*g**3 - 2*g**2 + 5*g**3 + 2*g**3 = 0.
0, 1
Let y(g) = -3*g**2 + g + 9. Let k(n) = n**2 - 5*n - 1. Let w be k(6). Let q(o) = 5*o**2 - o - 14. Let i(z) = w*q(z) + 8*y(z). Suppose i(a) = 0. What is a?
-2, -1
Let n(v) be the first derivative of -v**2 + 0*v - 1/2*v**4 - 4/3*v**3 + 6. Factor n(s).
-2*s*(s + 1)**2
Let 3/4*c**2 - 1/2*c + 3/4*c**3 - 1/2*c**4 + 0 = 0. Calculate c.
-1, 0, 1/2, 2
Let f(g) be the first derivative of -g**6/1080 + g**5/90 - g**4/18 + 2*g**3/3 + 4. Let h(n) be the third derivative of f(n). What is t in h(t) = 0?
2
Let s = -16 - -16. Suppose 0*c - 5*c = s. Determine z, given that c + 2/7*z + 2/7*z**2 = 0.
-1, 0
Let z(f) = f**2 - 16 - 10*f - 7*f + f + 0*f. Let n(q) = q**2 - 8*q - 8. Let k(r) = -5*n(r) + 3*z(r). Factor k(l).
-2*(l + 2)**2
Let o be ((-2)/6)/(2/(-6)). Let a = 3 - o. Solve 2/7*v**4 - 2/7*v**3 - 2/7*v**a + 2/7*v + 0 = 0.
-1, 0, 1
Let o = 9 + -7. Suppose 0*b = o*b. Factor b + 0*y**3 + 4/7*y**2 - 2/7*y**5 + 2/7*y - 4/7*y**4.
-2*y*(y - 1)*(y + 1)**3/7
Let a be (-10)/2 + 2 + 9. Let v be 10/a + (-1)/3. Factor -v*f**4 - 4/3*f**2 - 2*f**3 - 1/3*f - 1/3*f**5 + 0.
-f*(f + 1)**4/3
Let r(w) be the third derivative of -w**9/756 + w**7/210 + 7*w**3/6 + 6*w**2. Let x(o) be the first derivative of r(o). Factor x(c).
-4*c**3*(c - 1)*(c + 1)
Let u(i) = -i**2 - 4*i - 1. Let o be u(-3). Suppose -2 + o - 7*j**2 + 6*j**2 + j = 0. What is j?
0, 1
Let i be (((-140)/21)/5)/((-20)/6). Factor 4/5 - 2*t - i*t**4 + 6/5*t**2 + 2/5*t**3.
-2*(t - 1)**3*(t + 2)/5
Let f be 4/(-6) + (-64)/(-6). What is a in -f*a**3 - 8*a + 6 + 32*a**2 - 6 + 0*a - 50*a**4 = 0?
-1, 0, 2/5
Let r(h) be the third derivative of -h**8/336 - h**7/105 + h**6/60 + 2*h**5/15 + 7*h**4/24 + h**3/3 - 22*h**2. Solve r(g) = 0.
-1, 2
Suppose 2*g = g + 2. Let q(z) be the first derivative of -g + 1/9*z**2 - 1/18*z**4 + 0*z**3 + 0*z. Find m such that q(m) = 0.
-1, 0, 1
Let d(q) be the first derivative of q**4/42 + 8*q**3/63 + 4*q**2/21 + 4. Determine x so that d(x) = 0.
-2, 0
Let b = -124 - -4465/36. Let v(a) be the third derivative of -b*a**4 + 0*a - 1/6*a**5 + 0 + 2/9*a**3 + 3*a**2. Factor v(f).
-2*(3*f - 1)*(5*f + 2)/3
Solve -3/5*l**2 + 9/5 - 6/5*l = 0.
-3, 1
Let s = 105 + -102. Determine t so that -2/5 - 4/5*t**2 - 1/5*t**s - t = 0.
-2, -1
Let t(z) = -2*z**2 + z + 1. Let l(v) = 17*v**2 - 8*v - 12. Let d(q) = 3*l(q) + 24*t(q). Factor d(s).
3*(s - 2)*(s + 2)
Let p = -25 + 25. Let q(t) be the third derivative of 0 + 0*t**4 + 0*t + 1/120*t**5 - 1/480*t**6 + 3*t**2 + p*t**3. Determine o so that q(o) = 0.
0, 2
Let l = 270 + -268. Solve -2/13*q**l + 0*q + 2/13 = 0 for q.
-1, 1
Let h be (-66)/(-3) + (-4)/(-1). Let u be 2/12*h + -4. Suppose 1/3*f**3 - u*f**2 + 0*f + 0 - 1/3*f**5 + 1/3*f**4 = 0. Calculate f.
-1, 0, 1
Let y = 0 - -5. Suppose y*n = n. Solve 0 + 1/4*c**3 - 1/4*c**2 + n*c = 0.
0, 1
Let s = -11 - -17. Factor 4*w**3 - 11*w**5 + 13*w**5 + 6*w**4 - 1 - 1 - s*w - 4*w**2.
2*(w - 1)*(w + 1)**4
Let n(o) be the third derivative of o**6/160 + o**5/60 - o**4/96 - o**3/12 + 8*o**2. Factor n(m).
(m + 1)**2*(3*m - 2)/4
Let w(k) = 2*k + 15. Let i(s) = 1. Let t(l) = i(l) - w(l). Let x be t(-7). Factor x*j**3 + 0 - 2/5*j**4 + 0*j + 2/5*j**2.
-2*j**2*(j - 1)*(j + 1)/5
Let o(q) be the third derivative of q**8/5880 - q**6/630 + q**4/84 - q**3/3 + q**2. Let r(a) be the first derivative of o(a). Factor r(w).
2*(w - 1)**2*(w + 1)**2/7
Let k(r) = r**2 + r - 1. Let w be k(1). Suppose w = 3*f - 8. Find t such that 3*t**2 - t**f - 1 - 2*t**2 - 4*t**2 - 3*t = 0.
-1
Let a be (8/(-84) + 0)/((-1)/3). Find b, given that -a*b**2 - 2/7*b**4 + 0 - 4/7*b**3 + 0*b = 0.
-1, 0
Let w(a) = a**4 - 12*a**3 + 9*a**2 - a. Let r(c) = 4*c**4 - 60*c**3 + 44*c**2 - 4*c. Let n(l) = -3*r(l) + 16*w(l). Factor n(t).
4*t*(t - 1)**3
Let w(y) be the third derivative of y**8/504 + y**7/105 + y**6/60 + y**5/90 - 5*y**2. Factor w(l).
2*l**2*(l + 1)**3/3
Let q(l) be the first derivative of -l**3/9 + l**2/6 + 9. What is y in q(y) = 0?
0, 1
Let g = -61283/5780 - -3/1156. Let s = -573/55 - g. Let -2/11 + s*c**5 + 4/11*c**3 + 6/11*c**4 - 6/11*c - 4/11*c**2 = 0. What is c?
-1, 1
Factor 2*h**2 + 4*h**2 - 2*h - 3*h**2 + 3*h**3 + 2*h**4 - 6*h**2.
h*(h - 1)*(h + 2)*(2*h + 1)
Factor -18/7*p**3 + 0 - 4/7*p + 22/7*p**2.
-2*p*(p - 1)*(9*p - 2)/7
Factor 1/2*x**4 + x - 3/2*x**2 + 0*x**3 + 0.
x*(x - 1)**2*(x + 2)/2
Suppose 2/11*o**3 - 20/