w(c) be the second derivative of c**6/180 - c**5/45 + c**4/36 + 13*c**2/2 + 35*c. Let b(y) be the first derivative of w(y). Factor b(x).
2*x*(x - 1)**2/3
Let t(m) = 46*m**2 + 2 + m**3 - 2*m - 2*m - 43*m**2. Let y be t(-4). Factor 2*u**2 + 2*u**3 + 0*u**y + u - 3*u**3 - 2*u.
-u*(u - 1)**2
Let f = -64 + 76. Let a be 1*(4 + 4 + (-92)/f). Factor 2/3 - a*p**2 + 1/3*p.
-(p - 2)*(p + 1)/3
Let x(r) = -131*r**2 - 125*r + 1. Let k(i) = 394*i**2 + 374*i - 4. Let d(v) = 5*k(v) + 16*x(v). Factor d(h).
-2*(h + 1)*(63*h + 2)
Let k(z) be the second derivative of -z**6/80 + z**5/20 + z**4/16 - z**3/2 + 22*z**2 - 19*z. Let l(i) be the first derivative of k(i). Let l(a) = 0. What is a?
-1, 1, 2
Suppose g - 30 = -27. Determine l so that 144 + g*l**2 - 23*l - 124 + l**2 - l = 0.
1, 5
Suppose -3*x + 42 = -0*x. Let l be (2 + (-27)/15)/(x/10). Factor 0*a + 0 + 1/7*a**2 + l*a**4 + 2/7*a**3.
a**2*(a + 1)**2/7
Suppose -11*o + 18 = 7. Suppose a + o = 3. Factor 0*r + 4/3*r**2 + a*r**3 + 0.
2*r**2*(3*r + 2)/3
Let k = 29701/118756 - 3/29689. Factor 0 + k*f**2 + 0*f + 3/4*f**4 - 3/4*f**3 - 1/4*f**5.
-f**2*(f - 1)**3/4
Let d(g) = -18*g**2 + 76*g + 79. Let j(v) = 15*v**2 - 77*v - 80. Let u(s) = -4*d(s) - 5*j(s). Solve u(l) = 0 for l.
-1, 28
Let b be 2/236*((-87)/(-15) - 5). Let r = 303/1180 - b. Suppose -1/4*t**4 + r*t**5 - 1/4*t**3 + 1/4*t**2 + 0 + 0*t = 0. Calculate t.
-1, 0, 1
Let j = 4 + 2. Let s = 0 + j. Solve 3*a**2 - a + 7*a - s + 6 = 0.
-2, 0
Let o(a) = 2*a**4 - 10*a**3 + 38*a**2 + 154*a - 8. Let r(g) = -g**4 + 3*g**3 - 12*g**2 - 51*g + 3. Let w(v) = 3*o(v) + 8*r(v). Factor w(s).
-2*s*(s - 3)*(s + 3)**2
Let a(i) be the third derivative of 13*i**5/105 + i**4/21 + i**2 + 40*i. Factor a(o).
4*o*(13*o + 2)/7
Let y be (-1140)/72 - 1/6. Let h be (9/2 - 4)/((-14)/y). Find t, given that -h*t**3 + 0*t + 0 - 2/7*t**4 - 2/7*t**2 = 0.
-1, 0
Let g(p) be the third derivative of 1/120*p**5 + 0 + 1/32*p**4 + 0*p + 1/1440*p**6 - 5*p**2 + 1/3*p**3. Let y(i) be the first derivative of g(i). Factor y(x).
(x + 1)*(x + 3)/4
Factor -2*g**5 - 6 - 8*g**2 + 16*g - 12*g**3 - 15*g**4 + 25*g**4 + 6.
-2*g*(g - 2)**3*(g + 1)
Let n(a) be the third derivative of -a**8/1848 + a**7/231 - 7*a**6/660 + a**5/110 - a**2 + 72*a. Find k such that n(k) = 0.
0, 1, 3
Let x(a) be the third derivative of -1/36*a**4 - 1/18*a**3 - 1/180*a**5 + 0*a - 3*a**2 + 0. Suppose x(g) = 0. Calculate g.
-1
Let v = 1 + 12. Let u = v + -10. Factor -j**2 + 3*j**2 + j**4 - 3*j**2 + j**u + 0*j - j.
j*(j - 1)*(j + 1)**2
Let s = 1002 + -1000. Let d(j) be the second derivative of 0 + 0*j**3 - 3/10*j**6 + 0*j**s - 1/4*j**4 - 3/5*j**5 - 8*j. Suppose d(n) = 0. Calculate n.
-1, -1/3, 0
Let n be (-1)/3 + (-150)/(-18). Let k = n + -2. Factor k + a + a**3 - 7*a**2 + 2*a**3 - 4*a + a**2.
3*(a - 2)*(a - 1)*(a + 1)
Let l(d) be the second derivative of 5*d**4/12 - d**3/3 + 13*d. Let z(t) = 5*t**2 - 3*t. Let b(o) = 3*l(o) - 2*z(o). Factor b(p).
5*p**2
Let v(z) be the third derivative of z**5/135 - z**4/3 + 10*z**2 - 2. Find l, given that v(l) = 0.
0, 18
Let q be 0 + (-2349)/24*52/(-39). Find k, given that -63/2*k**5 - 15*k - 123/2*k**4 + 453/2*k**3 + 12 - q*k**2 = 0.
-4, -2/7, 1/3, 1
Let a(u) be the first derivative of -u**4 - 8*u**3/3 - 2*u**2 + 212. Factor a(f).
-4*f*(f + 1)**2
Let v be 13/4 + 2/(-8). Suppose -5*l = 2*l - 14. Determine m so that 7*m + 0*m - v*m + 3*m**l + 2*m = 0.
-2, 0
Let h(r) = -5*r - 27. Let i be h(-5). Let l be ((-14)/(-6))/(-7) + i/(-6). Factor 0 + l*c - 1/2*c**2 + 1/2*c**3.
c**2*(c - 1)/2
Let 23*q**3 - 5*q**4 + 13*q**2 + 30*q**3 - 70*q**3 + 35*q**3 - 8 - 18*q = 0. What is q?
-1, -2/5, 1, 4
Factor 5/3*i**4 - 1 - 8/3*i + 8/3*i**3 - 2/3*i**2.
(i - 1)*(i + 1)**2*(5*i + 3)/3
Let v be 28/(-8)*24/(-14). Suppose -3*h = -v*h. Factor -30*x**2 - 5 + h + 0 - 24*x**3 + 4*x**3 - 20*x - 5*x**4.
-5*(x + 1)**4
Let l be 2*(36/10 - 3)*10/14. Factor l*t**3 + 0 + 4/7*t**2 + 0*t + 2/7*t**4.
2*t**2*(t + 1)*(t + 2)/7
Suppose -2*h + 40 = 5*z, -6*z + 15 = -3*h - z. Let 4/3*g**h - 8/3*g**4 + 0 - 4/3*g + 8/3*g**2 + 0*g**3 = 0. What is g?
-1, 0, 1
Suppose -68*p + 234 = -106. Let g(b) be the second derivative of -7*b + 1/3*b**4 + 1/5*b**p - 8*b**2 + 0 - 8/3*b**3. Factor g(o).
4*(o - 2)*(o + 1)*(o + 2)
Let x be (0 - -1) + -1 + 2. Let s(j) = 6*j - 21. Let b be s(4). Suppose 2*p + p**2 + 2*p**4 - 2*p**3 - 3 + 3 - b*p**x = 0. What is p?
-1, 0, 1
Determine a, given that -20/9*a**4 - 14/9*a**3 + 8/9*a + 0 + 8/9*a**2 - 2/3*a**5 = 0.
-2, -1, 0, 2/3
Let k(d) be the third derivative of 0*d**4 + 0*d + 1/480*d**6 + 0*d**5 + 1/1344*d**8 - 10*d**2 + 0 + 0*d**3 + 1/420*d**7. Let k(c) = 0. Calculate c.
-1, 0
Let u(s) = 8*s**2 + 10*s + 3. Let z(h) = h**2 + 1. Suppose 2*f = 4*l + 10, f - 8 = 2*l + 3*f. Let n(b) = l*z(b) + u(b). Factor n(o).
5*o*(o + 2)
Let d(a) be the first derivative of -a**4/3 + 2*a**3/3 - 44*a - 3. Let g(c) be the first derivative of d(c). Let g(i) = 0. What is i?
0, 1
Let m be ((-10)/((-15)/(-3)))/(-1). Let q(i) be the second derivative of 1/4*i**3 + 2*i - 3/80*i**5 + 0 + 0*i**m - 1/16*i**4. Determine g so that q(g) = 0.
-2, 0, 1
Let a be (1 - 0)*(-13 + 21 + -8). Let c(t) be the third derivative of a*t + 1/4*t**4 + 10*t**2 + 0 + 1/2*t**3 - 1/20*t**6 - 1/20*t**5. Let c(h) = 0. What is h?
-1, -1/2, 1
Factor 1/4*m**2 + 0*m - 9/4.
(m - 3)*(m + 3)/4
Let r = 2714 + -2712. Let -1/3*v**r + 0*v + 1/3 = 0. What is v?
-1, 1
Let k(o) = -9*o**5 + 5*o**4 - 29*o**3 + 45*o**2 + 26*o. Let b(m) = -4*m**5 + 2*m**4 - 14*m**3 + 22*m**2 + 12*m. Let j(x) = -13*b(x) + 6*k(x). Factor j(l).
-2*l**2*(l - 2)**2*(l + 2)
Suppose 55*i - 59*i = -2*c - 8, -c = 4*i - 14. Factor 4/3*q**c + 0*q + 4/3*q**3 + 0.
4*q**2*(q + 1)/3
Solve 292/5 + 204*j - 7/5*j**2 = 0 for j.
-2/7, 146
Let h(i) be the first derivative of 3*i**5/5 + 3*i**4/4 + 7*i**2/2 - 7*i + 31. Let t(u) = -u**4 - u**3 - 2*u + 2. Let d(x) = -2*h(x) - 7*t(x). Factor d(m).
m**3*(m + 1)
Let s = -3578 + 3581. Determine c, given that 0 - 2/3*c**s - 2/3*c**4 + 10/3*c**2 - 2*c = 0.
-3, 0, 1
Let r(i) = -14*i - 65. Let o be r(-5). Let c(s) be the second derivative of 0*s**2 + 0 + s + 1/100*s**o - 1/10*s**3 + 1/30*s**4. Determine k so that c(k) = 0.
-3, 0, 1
Let o be 64/416 + 63/(-2184). Factor 0*t + 0 - t**2 - o*t**3.
-t**2*(t + 8)/8
Let m = -152 - -156. Find n such that -3 - 2*n + 13*n**4 + m + 4*n**4 - 18*n**4 + 2*n**3 = 0.
-1, 1
Let n(x) be the first derivative of -x**5/10 + x**3/2 - x**2/2 + 167. Suppose n(q) = 0. Calculate q.
-2, 0, 1
Let c = 0 - -2. Factor 3*z**c - 4*z**3 - 4*z**2 - 2*z**2 - z**2.
-4*z**2*(z + 1)
Let z(l) be the second derivative of 3*l**5/40 + 17*l**4/8 + 20*l**3 + 48*l**2 - 34*l. Factor z(j).
3*(j + 1)*(j + 8)**2/2
Suppose 0 = -b - 3*j + 5, 13 + 7 = 4*b + 4*j. Let l(v) be the first derivative of 2/7*v**2 + 0*v + 2/21*v**3 - b. What is i in l(i) = 0?
-2, 0
Let v(i) = -8*i**2 + 650*i - 12795. Let c(p) = -12*p**2 + 976*p - 19192. Let z(n) = 5*c(n) - 8*v(n). Factor z(h).
4*(h - 40)**2
Let r(b) be the second derivative of -6*b**6/5 + 3*b**5 + 45*b**4/4 + 5*b**3 - 9*b**2/2 - 40*b + 3. Find v such that r(v) = 0.
-1, -1/2, 1/6, 3
Let c(l) be the third derivative of -l**6/120 - l**5/60 + 5*l**4/24 - l**3/2 - 37*l**2 + l. Let c(r) = 0. What is r?
-3, 1
Let r(j) be the first derivative of 0*j + 8/9*j**3 - 1/2*j**4 + 0*j**2 - 6 - 2/15*j**5. Factor r(v).
-2*v**2*(v - 1)*(v + 4)/3
Let m(n) be the second derivative of -10*n**7/7 - 87*n**6/10 - 51*n**5/20 + 21*n**4/2 - 4*n**3 - 571*n. Find h such that m(h) = 0.
-4, -1, 0, 1/4, 2/5
Let g(a) be the third derivative of a**5/420 + 25*a**4/84 + 625*a**3/42 - 75*a**2. Let g(m) = 0. What is m?
-25
Let d(p) be the second derivative of -35*p - 25/2*p**2 - 1/12*p**4 + 0 + 5/3*p**3. Factor d(s).
-(s - 5)**2
Let h be 4*1/4 - -2. Solve 1095 - 1095 + 5*l**h = 0.
0
Let o(t) = 5*t - 5. Let j = 139 + -138. Let p be o(j). Suppose 2/3*g + p - 2/3*g**2 = 0. Calculate g.
0, 1
Let a(n) be the first derivative of -n**6/10 - n**5/25 + 3*n**4/20 + n**3/15 - 181. What is f in a(f) = 0?
-1, -1/3, 0, 1
Let g(o) be the third derivative of 0 + 6*o**2 + 0*o**3 - 1/60*o**5 - 1/240*o**6 - 1/48*o**4 + 0*o. What is n in g(n) = 0?
-1, 0
Suppose -t + 0*t = 0, -4*v + 12 = 2*t. Suppose 0 = -v*q + 2*a + 4, 12*a = -q + 15*a - 1. Factor 6/5*g + 1/5 + 9/5*g**4 + 16/5*g**3 + 2/5*g**5 + 14/5*g**q.
(g + 1)**4*(2*g