*q**2 - 15*q + 0 - 1/5*q**5. Factor o(v).
-4*v*(v - 1)*(v + 3)
Let k = -50956/9 + 5662. Factor -2/9*z + k*z**2 + 0.
2*z*(z - 1)/9
Let q(f) = 418*f**3 - 2*f**2 - 2*f**5 + 5*f**4 - f - 418*f**3. Let v(b) = 3*b**5 - 9*b**4 + 4*b**2 + 2*b. Let o(p) = 5*q(p) + 3*v(p). Factor o(g).
-g*(g - 1)*(g + 1)**3
Let i(o) = 7*o**2 + 3*o - 5. Let g be (-15)/(-6)*6*2. Suppose 3*v + g = -2*v. Let h(p) = 8*p**2 + 4*p - 6. Let d(c) = v*i(c) + 5*h(c). What is r in d(r) = 0?
0, 1
Let k(f) be the second derivative of -f**5/60 - f**4/4 - 29*f**2/2 - 10*f. Let i(a) be the first derivative of k(a). What is r in i(r) = 0?
-6, 0
Let t be (-2)/6 + 112/336. Suppose 6/5*j**3 - 2/5*j**4 + t*j + 0 - 4/5*j**2 = 0. What is j?
0, 1, 2
Let u(h) be the first derivative of h**6/30 - 3*h**5/25 + h**4/10 - 136. Factor u(s).
s**3*(s - 2)*(s - 1)/5
Let d = 3720769/351015 + -2/70203. Find y, given that -4/5 - 24/5*y**4 + 53/5*y**3 + 24/5*y - d*y**2 + 4/5*y**5 = 0.
1/2, 1, 2
Let c(a) be the first derivative of -2*a**3/57 - 176*a**2/19 - 15488*a/19 - 151. Factor c(b).
-2*(b + 88)**2/19
Let x(b) = b**3 - b**2 + b. Let s(i) = 3*i**3 - 8*i**2 + 7*i. Let n(q) = s(q) - 6*x(q). Let n(a) = 0. Calculate a.
-1, 0, 1/3
Let d(o) = 4*o**5 + o**4 - 3*o**3 + 5*o**2 - o - 6. Let i(g) = 7*g**5 + 3*g**4 - 7*g**3 + 10*g**2 - 2*g - 11. Let v(h) = 11*d(h) - 6*i(h). Factor v(t).
t*(t - 1)**3*(2*t - 1)
Determine l so that -45*l - 4*l**2 - 2*l**4 + 12*l**3 - 9*l**3 - l**5 + 41*l + 4*l**4 = 0.
-1, 0, 2
Let r(l) be the first derivative of 1/21*l**3 + 3/7*l**2 - 25 + 9/7*l. Factor r(a).
(a + 3)**2/7
Suppose -3*b = -2*r - 17, 3*b - 3*r - 21 = -0*b. Suppose -4*q + b*v = 15, v + 15 = 4*v. Find a, given that -2/5*a**4 + 2/5*a**3 + q - 2/5*a + 2/5*a**2 = 0.
-1, 0, 1
Factor 13/3*h**2 - 35/3*h - 1/3*h**3 - 49/3.
-(h - 7)**2*(h + 1)/3
Let f(o) be the second derivative of 0 + 1/4*o**3 + 9/8*o**2 + 1/48*o**4 + 5*o. Factor f(k).
(k + 3)**2/4
Factor 48*o - o**2 - 244 - 105 - 227.
-(o - 24)**2
Let q(c) be the third derivative of 0 + 0*c - 16*c**2 + 1/120*c**6 - 1/24*c**4 - 1/3*c**3 + 1/30*c**5. Factor q(s).
(s - 1)*(s + 1)*(s + 2)
Let k(v) be the third derivative of -v**5/80 + 13*v**4/32 - 11*v**3/4 + 8*v**2 - 10*v. Factor k(d).
-3*(d - 11)*(d - 2)/4
Let 68/3*b - 7*b**3 + 160/3*b**2 - 32/3 = 0. Calculate b.
-2/3, 2/7, 8
Let c(s) be the third derivative of -16/3*s**3 + 0 - 7/3*s**4 - 1/5*s**5 + 0*s - 26*s**2. Factor c(f).
-4*(f + 4)*(3*f + 2)
Factor -2*z**3 - 90212*z**2 + 89960*z**2 + 6*z**3.
4*z**2*(z - 63)
Let x be (-8)/(-12) + (-12)/18. Let f(i) be the third derivative of -1/80*i**5 + x*i - 2*i**2 + 0*i**4 + 0 + 1/8*i**3. Determine k so that f(k) = 0.
-1, 1
Let f(k) be the third derivative of -1/60*k**5 + 8*k**2 + 0 - 1/6*k**4 - 2/3*k**3 + 0*k. Solve f(i) = 0 for i.
-2
Let y(d) be the second derivative of -d**7/735 + d**5/210 - 5*d**2 - 21*d. Let c(n) be the first derivative of y(n). Determine l so that c(l) = 0.
-1, 0, 1
Let j(v) be the third derivative of -v**6/120 + v**4/24 + 107*v**2 - 2. Let j(h) = 0. What is h?
-1, 0, 1
Let d(a) be the first derivative of -6*a + 8 + 1/54*a**4 + 4/27*a**3 + 1/3*a**2. Let t(x) be the first derivative of d(x). What is v in t(v) = 0?
-3, -1
Let m be -5 + 0/(5 + -9). Let f be (-15)/m - (-52)/(-20). Determine y so that 0*y**2 + 0 - 4/5*y**3 + f*y**4 + 0*y = 0.
0, 2
Factor -2 + 2/7*d**3 - 2/7*d + 2*d**2.
2*(d - 1)*(d + 1)*(d + 7)/7
Let h(i) be the third derivative of 0*i + 0 - 1/10*i**5 - 4/315*i**7 - 4*i**2 + 11/180*i**6 + 1/9*i**3 + 1/36*i**4. Determine u so that h(u) = 0.
-1/4, 1
Suppose 8*z = 2*y + 6*z - 2, -25 = -4*y - 3*z. Suppose -8*l**4 + 6*l + 9*l**4 + 15*l**2 + 2*l**y + 12*l**3 = 0. What is l?
-2, -1, 0
Let o(g) be the third derivative of g**5/210 - g**4/7 + 20*g**3/21 + 13*g**2 + 3. Factor o(s).
2*(s - 10)*(s - 2)/7
Let v(u) be the second derivative of -u**3/6 - 9*u**2/2 - 7*u. Let s be v(-13). Let 4*n + 12*n**2 - 4*n**2 - 14*n**5 + 10*n**5 - 8*n**s = 0. Calculate n.
-1, 0, 1
Let z(s) be the second derivative of -18*s + 1/45*s**6 - 20/9*s**3 + 8/3*s**2 + s**4 - 7/30*s**5 + 0. Factor z(k).
2*(k - 2)**3*(k - 1)/3
Let c be 35 - (9/(-3) - -2). Determine g, given that 604 - 604 + 24*g**2 - 4*g**3 - c*g = 0.
0, 3
Let g(l) be the first derivative of l**5/20 - 7*l**4/16 - 9*l**3/4 - 29*l**2/8 - 5*l/2 - 76. Suppose g(c) = 0. What is c?
-1, 10
Let j(k) = -3*k**3 + 2*k**2 + k. Suppose -i = 2*a + 19, -2*a = 5*i + 51 + 4. Let b(s) = -12*s**3 + 9*s**2 + 3*s. Let x(h) = i*j(h) + 2*b(h). Factor x(p).
3*p*(p - 1)*(p + 1)
Factor 128*p - 8193 + 67*p**2 - 5698 - 72*p**2 + 472*p - 4109.
-5*(p - 60)**2
Let m(o) be the second derivative of o**4/4 - 14*o**3 + 78*o**2 - 648*o. Determine v so that m(v) = 0.
2, 26
Let p(n) be the second derivative of n**9/432 - n**8/840 - n**3/2 - 4*n. Let w(l) be the second derivative of p(l). Determine h, given that w(h) = 0.
0, 2/7
Let t(o) = 8*o + 14*o**2 - 6*o**2 + 14*o**3 - 13*o**3 + 10. Let b be t(-7). Determine u so that -32/5*u**b - 8/5 - 16/5*u**4 + 12/5*u**5 + 24/5*u**2 + 4*u = 0.
-1, 1/3, 1, 2
Let o(n) be the third derivative of -n**7/70 + n**6/5 + 18*n**5/5 + 20*n**4 + 56*n**3 + 16*n**2 + 8. Find s, given that o(s) = 0.
-2, 14
Let i(m) = -m**2 + 4*m - 3. Let v be i(6). Let h be 13/4 + v/60. Suppose h*c**4 + 3*c**4 - 6*c**2 + 3*c + 0*c**5 - 2*c**5 - c**5 = 0. What is c?
-1, 0, 1
Suppose -8 - 1 = -9*z. Let n be 1/(1 + z)*18. Find l, given that -3*l**4 - n*l**5 + 2*l**2 + l**4 + 3*l**5 + 6*l**3 = 0.
-1, -1/3, 0, 1
Let r(v) be the first derivative of -v**4/10 + 8*v**3/15 - 200. Find a such that r(a) = 0.
0, 4
Let p be (-25)/(-100)*(-2 + 22/9). Let u(d) be the second derivative of -p*d**3 + 0 - 2/3*d**2 + d + 1/18*d**4. Factor u(o).
2*(o - 2)*(o + 1)/3
Factor 19*y - 1/5*y**2 + 0.
-y*(y - 95)/5
Suppose 0 = 5*v - h - 20, 2*h + 6 = v + 2. Suppose 0 = 2*d + 5*i - 13, -v*d + 0*d - i = -17. Factor 6*m**2 - 4*m**4 + 0*m**4 + m**d - 3.
-3*(m - 1)**2*(m + 1)**2
Let b(w) = -w**3 - 10*w**2 - 6*w + 15. Let t be b(-9). Let r be 0/((-4)/t*0 + 1). Factor 0 + r*c**2 - 2/9*c**5 + 0*c**4 + 0*c + 2/9*c**3.
-2*c**3*(c - 1)*(c + 1)/9
Factor 510*k + 2*k**4 - 1538*k + 40 + 509*k + 511*k - 30*k**2 - 4*k**3.
2*(k - 5)*(k - 1)*(k + 2)**2
Let f(g) be the first derivative of 0*g - 1/5*g**2 + 3/40*g**4 - 1/25*g**5 - 1/60*g**6 + 5 + 2/15*g**3. Factor f(x).
-x*(x - 1)**2*(x + 2)**2/10
Let w(n) be the first derivative of -n**4/10 + 8*n**3/15 - 157. Factor w(b).
-2*b**2*(b - 4)/5
Let a(p) = p**3 + 9*p**2 - 11*p + 2. Let i be a(-10). Let k be (520/i)/10 + 2/6. Suppose 4/3 + 8/3*b**4 - 14/3*b**3 + k*b - 4*b**2 = 0. What is b?
-1, -1/4, 1, 2
Let f = 1327345/108 - 12290. Let x = 1/54 + f. Determine h, given that 0 + 3/4*h**2 - 1/4*h + x*h**4 - 3/4*h**3 = 0.
0, 1
Let f(k) be the first derivative of 3*k**5/40 - 21*k**4/32 + 15*k**3/8 - 27*k**2/16 - 70. Factor f(x).
3*x*(x - 3)**2*(x - 1)/8
Let d(q) be the second derivative of -q**5/100 - 3*q**4/20 + 7*q**3/10 + 31*q**2/2 + 20*q. Let p(g) be the first derivative of d(g). Factor p(w).
-3*(w - 1)*(w + 7)/5
Let f be 8 + -1 + (5 - (-14 + (-4230)/(-165))). Suppose -2/11*c**2 + 0 + f*c = 0. What is c?
0, 2
Let m = -1249 + 1252. Let u(f) be the second derivative of -4*f + 0*f**2 + 0 - 2/3*f**m + 2/3*f**4. Find i, given that u(i) = 0.
0, 1/2
Let f(l) = l - 12. Let j be f(8). Let k(d) = -2*d - 4. Let q be k(j). Factor 1 + 4*a - q - a**2 - 1.
-(a - 2)**2
Let f(x) = -x**2 + 2*x + 2. Let t(o) = -6*o**2 - 224*o + 14175. Let z(g) = -14*f(g) + 2*t(g). Factor z(h).
2*(h - 119)**2
Suppose 5*t + 46 = 136. Suppose t = 5*p + j, -p - 4*p - 5*j = -10. Factor 4 + 17*f**2 + 10*f**2 + 15*f**4 + 36*f**3 + 6*f - p.
3*f*(f + 1)**2*(5*f + 2)
Let t = 56159/4 + -14034. Factor -1/2 - t*q**2 + q**5 - 11/4*q**3 + 5/4*q**4 - 13/4*q.
(q - 2)*(q + 1)**3*(4*q + 1)/4
Solve -3*i**3 - 318*i**4 - i + 5*i**2 + 319*i**4 - 2*i**2 = 0 for i.
0, 1
Let k = -18 - -58/3. Let g(i) be the first derivative of -k*i**3 - 3/2*i**4 + 0*i**2 - 2 + 0*i. Determine b, given that g(b) = 0.
-2/3, 0
Let n(u) be the second derivative of 1/78*u**4 + 6/13*u**3 + 81/13*u**2 + 0 - 37*u. Solve n(d) = 0.
-9
Let g(t) be the first derivative of -t**4/2 - 4*t**3/3 - t**2 + 183. Factor g(w).
-2*w*(w + 1)**2
Let x(l) = -8*l**3 + l**2 - 1. Let r be x(1). Let j be 0/r - (-4)/2. Determine n, given that -8/5*n + 2/5*n**j + 8/5 = 0