2/13*z**2.
-2*z*(z + 1)/13
Suppose -41*k = -45*k + 188. Let w = -47 + k. Determine m so that -2/7*m**4 - 2/7*m**2 + w + 0*m + 4/7*m**3 = 0.
0, 1
Let z(f) be the third derivative of f**5/4 + 65*f**4/24 - 40*f**3/3 - 2*f**2 - 257*f. Suppose z(l) = 0. What is l?
-16/3, 1
Let b be ((-2)/(-4))/(1/(-2)). Let r be (-4)/(b*(1 - 0/(-1))). Suppose -4/5*c + 0 + 16/5*c**3 - 2/5*c**2 - 2*c**r = 0. What is c?
-2/5, 0, 1
Factor -1/2*p**3 + 147/2*p - 37 - 36*p**2.
-(p - 1)**2*(p + 74)/2
Let g be ((-176)/33 - -6)*(-12)/(-20). Let -4/5*a**3 - 1/5*a**4 - g*a + 0 - a**2 = 0. Calculate a.
-2, -1, 0
Let t(w) be the third derivative of -w**8/784 - 3*w**7/245 + w**6/280 + 19*w**5/70 - 16*w**3/7 + 122*w**2. Find r such that t(r) = 0.
-4, -1, 1, 2
Factor -18/7 + 1/7*b**2 + 17/7*b.
(b - 1)*(b + 18)/7
Factor -x**2 - 762*x - 282 + 113 + 736*x.
-(x + 13)**2
Let y(p) be the first derivative of -1/5*p**5 - 10 + 2*p - 3/4*p**4 - 1/3*p**3 + 3/2*p**2. What is g in y(g) = 0?
-2, -1, 1
Let y = 10 - 10. Suppose 0 = -y*q - 5*q + 15. Factor 3 - c**2 + 5*c - c**3 - q - 3.
-(c - 1)**2*(c + 3)
Let n(i) = -7*i**4 - 2*i + 0 - 1 - 2*i**3 + 3 - 4. Let r(z) = 85*z**4 + 25*z**3 + 25*z + 25. Let q(g) = 25*n(g) + 2*r(g). Factor q(o).
-5*o**4
Let f(c) = -23*c**2 + 29*c - 1. Let x(t) = 5*t**2 - 36*t + 6*t**2 + 22*t + 1. Let h(a) = -2*f(a) - 5*x(a). Let h(l) = 0. What is l?
1/3, 1
Let x(z) = z**2 - 4*z - 10. Let w be x(6). Factor -3*n + 3*n**3 + 5*n**2 - 4*n**2 - n**w.
3*n*(n - 1)*(n + 1)
Solve 1/7*y**2 - 57/7 - 8*y = 0 for y.
-1, 57
Suppose 5*c - 14 = 2*v, 8 = -c - 0*c - 5*v. Let f be -3 + (-11)/7 - (-18)/(-3 - -6). Factor -f*z**3 - c*z + 2/7*z**4 + 18/7*z**2 + 4/7.
2*(z - 2)*(z - 1)**3/7
Let -14*f**3 - 8*f**3 - 58*f**2 + 39*f + 18*f - 2*f**4 + 300 + 13*f = 0. Calculate f.
-5, -3, 2
Find w, given that -3*w**3 - 31*w**4 + 13*w**4 - 4*w**2 + 16*w**4 - 3*w**3 = 0.
-2, -1, 0
Let w(q) be the second derivative of 0 + 4*q**2 - 3*q - 1/3*q**3 - 1/12*q**4. Let w(y) = 0. Calculate y.
-4, 2
Let j(m) = -2*m**3 - 2*m**2 - 38*m + 40. Let b(h) = -6*h**3 - 3*h**2 - 76*h + 80. Let a(v) = -2*b(v) + 5*j(v). Factor a(g).
2*(g - 5)*(g - 1)*(g + 4)
Let d(r) be the second derivative of 1/10*r**5 - 4/3*r**3 - 1/30*r**6 - 12*r + 0 + 2*r**2 + 1/4*r**4. Factor d(s).
-(s - 2)*(s - 1)**2*(s + 2)
Suppose -55*p + 51*p + 4*b = 0, -p + 2*b = 3. Solve 0 - 5/6*z**2 + 2/3*z + 1/6*z**p = 0 for z.
0, 1, 4
Solve 0 + 12*q - 3/2*q**3 - 21/2*q**2 = 0 for q.
-8, 0, 1
Let b(m) = -m**2 + 5. Let a be b(-2). Let n be a - -7*25/15. Suppose -16/3*g - 14/3*g**3 + 8/3 - n*g**2 = 0. Calculate g.
-2, -1, 2/7
Let p(r) be the second derivative of 3*r + 1/450*r**6 + 0 - 1/3*r**3 + 1/75*r**5 + 0*r**2 + 1/30*r**4. Let a(d) be the second derivative of p(d). Factor a(t).
4*(t + 1)**2/5
Let g(n) be the second derivative of -n**7/315 - 2*n**6/75 + 17*n**5/150 + n**4/15 - 16*n**3/45 - 312*n. Suppose g(t) = 0. What is t?
-8, -1, 0, 1, 2
Let p(w) be the first derivative of -3*w**5/5 - 39*w**4/4 - 57*w**3 - 285*w**2/2 - 150*w - 92. Factor p(t).
-3*(t + 1)*(t + 2)*(t + 5)**2
Let a be 10*(128/40)/16. Factor -17*p - 7/2 + a*p**3 - 23/2*p**2.
(p - 7)*(p + 1)*(4*p + 1)/2
Suppose -d = -4*d - 2*p - 164, -3*p = 12. Let h = -49 - d. Find u such that 3/2*u + 0*u**2 - 1/2*u**h + 1 = 0.
-1, 2
Suppose 2*d - 2*n - 6 = 0, -5*d + 6*n + 11 = 3*n. Suppose -5 + d = -2*c. Factor 3 - j**2 - 4 - c + 4*j**2.
3*(j - 1)*(j + 1)
Factor -b**2 + 6*b**4 + 4*b**4 - 2*b**3 - 11*b**4.
-b**2*(b + 1)**2
Let f(w) be the first derivative of -w**4/12 - 13*w**3/9 - 2*w**2 + 414. Suppose f(v) = 0. Calculate v.
-12, -1, 0
Let u(i) = 2*i - 2*i**2 - 7*i - 1 + 2*i + 0. Let k be u(-1). Determine f so that 0 + 1/4*f**2 - 1/4*f**3 + k*f = 0.
0, 1
Solve 46/5*x**2 + 2/5*x**3 - 98/5*x + 10 = 0.
-25, 1
Let o(v) = -3*v**4 + 88*v**3 - 732*v**2 + 2016*v - 1728. Let l(m) = -m**3. Let x(f) = 4*l(f) + o(f). Factor x(b).
-3*(b - 12)**2*(b - 2)**2
Let m be ((-4)/3)/(14/315*-5). Let u(g) be the second derivative of 1/40*g**5 + 1/80*g**m + 0 - 1/96*g**4 + 0*g**2 - 1/24*g**3 + 9*g. Factor u(h).
h*(h + 1)**2*(3*h - 2)/8
Let z = 1292946/230885 - -2/46177. Solve -64/5*b**2 - 8/5 + z*b**3 + 44/5*b = 0.
2/7, 1
Suppose -2*r - 128 = 3*x - 109, r - 49 = 5*x. Factor 1/9*c**3 - 1/9*c**r + 0 + 0*c**2 + 0*c.
-c**3*(c - 1)/9
Factor -9*s**3 + s - s**4 - 1 + s**5 + 2*s**2 + 2*s**3 + 5*s**3.
(s - 1)**3*(s + 1)**2
Let g(w) be the third derivative of -7*w**8/23040 - w**7/2880 - w**6/5760 - 43*w**5/60 - 4*w**2 + 1. Let i(c) be the third derivative of g(c). Factor i(y).
-(7*y + 1)**2/8
Let x(q) be the second derivative of 4*q**7/945 + q**6/270 + q**5/720 - q**4 + 2*q. Let m(n) be the third derivative of x(n). Factor m(v).
(8*v + 1)**2/6
Let c = -451/12 - -153/4. Let q(g) be the second derivative of -c*g**3 + 2*g**2 - g + 1/12*g**4 + 0. Let q(b) = 0. Calculate b.
2
Let p(v) = 5*v**2 - 355*v + 6845. Let y(o) = 10*o**2 - 715*o + 13690. Let j(s) = 5*p(s) - 3*y(s). Factor j(w).
-5*(w - 37)**2
Find s, given that 40*s**3 + 0*s**2 + 0 + 0*s - 5/2*s**4 = 0.
0, 16
Let i(d) be the first derivative of 1/9*d**2 - 2 + 2/27*d**3 + 0*d. Find b, given that i(b) = 0.
-1, 0
Let u(q) = -11*q**2 + 41*q + 6. Let t(r) = -120*r**2 + 455*r + 65. Let x(j) = 6*t(j) - 65*u(j). Factor x(b).
-5*b*(b - 13)
Let d(a) be the third derivative of 0 - 1/12*a**4 + 24*a**2 + 0*a - 1/120*a**5 - 1/4*a**3. Find u such that d(u) = 0.
-3, -1
Let f(t) be the third derivative of 8*t**6/75 + 4*t**5/15 + 4*t**4/15 + 2*t**3/15 - 17*t**2. Factor f(h).
4*(2*h + 1)**2*(4*h + 1)/5
Let m(z) be the second derivative of -9*z**5/5 - 23*z**4 - 320*z**3/3 - 200*z**2 - 103*z. Factor m(f).
-4*(f + 1)*(3*f + 10)**2
Let b(q) be the second derivative of 0*q**4 + 0 - 2/3*q**3 + 1/15*q**6 + 21*q - q**2 + 1/5*q**5. Factor b(p).
2*(p - 1)*(p + 1)**3
Let x be (14/77)/(21/(-11) + 2). Let n(f) be the first derivative of -21/10*f**x + 3/25*f**5 + 9/5*f**3 - 1 - 3/4*f**4 + 6/5*f. Factor n(y).
3*(y - 2)*(y - 1)**3/5
Let p(f) be the first derivative of 0*f**2 + 8/3*f - 2/9*f**3 + 6. Factor p(h).
-2*(h - 2)*(h + 2)/3
Let w(v) = -v**3 + v**2 - 1. Let m(l) be the second derivative of l**6/2 + l**5/4 - 5*l**2/2 + 23*l. Let c(s) = m(s) - 5*w(s). Factor c(h).
5*h**2*(h + 1)*(3*h - 1)
Suppose -3*z - 2*p + 4 = -z, -2*z + 2*p + 8 = 0. Suppose 7*k - 4 = -2*h + 4*k, z*h - 6 = 2*k. Determine s so that 0 - 2/17*s + 2/17*s**h = 0.
0, 1
Let a(t) be the first derivative of 6 + 1/27*t**3 - 4/9*t**2 + 16/9*t. Solve a(j) = 0 for j.
4
Let l(o) = -o**3 + 37*o**2 - 102*o + 3. Let g be l(34). What is r in -3/4*r**4 - 5/4*r + 1/4*r**2 + 1/2 + 5/4*r**g = 0?
-1, 2/3, 1
Let u = 74/21 - 286/105. Let q(n) be the second derivative of 6*n + u*n**2 - 1/15*n**4 - 2/15*n**3 + 0. Factor q(k).
-4*(k - 1)*(k + 2)/5
Suppose -7/2*u**3 + 0*u - 13/4*u**2 - 1/4*u**4 + 0 = 0. What is u?
-13, -1, 0
Let t(p) = -3*p**4 + 9*p**3 - 45*p**2 - 51*p + 144. Let o(d) = -2*d**4 - d**3 + d**2 - d. Let q(u) = 3*o(u) - t(u). Factor q(s).
-3*(s - 2)**2*(s + 2)*(s + 6)
Let f(w) be the third derivative of -w**5/20 - 19*w**4/2 - 722*w**3 + w**2 - 123. Suppose f(m) = 0. Calculate m.
-38
Let p(y) = -y**2 + 4*y + 27. Let u be p(7). Let v(o) be the first derivative of 4/33*o**3 + 0*o**2 - u + 0*o + 1/22*o**4. Factor v(k).
2*k**2*(k + 2)/11
Let s(u) be the third derivative of u**6/10 - 26*u**5/15 + 5*u**4/2 + 16*u**3/3 + 121*u**2. Let s(i) = 0. Calculate i.
-1/3, 1, 8
Let r be (-8)/(-3) - 4/6. Let k(o) be the first derivative of o**r + 0*o**2 - o**3 + 3 - 4*o**2. Find i such that k(i) = 0.
-2, 0
Factor 5/2*m**5 + 5*m**2 - 5*m**4 - 5/2*m + 0 + 0*m**3.
5*m*(m - 1)**3*(m + 1)/2
Suppose 2*n = -8*n + 50. Let x = -39 + 39. Factor -1/2*g**n - 3/2*g - g**2 + 1 + x*g**4 + 2*g**3.
-(g - 1)**3*(g + 1)*(g + 2)/2
Let k(q) be the first derivative of 3*q**4/8 - 5*q**3/2 - 9*q**2/2 + 499. Let k(s) = 0. What is s?
-1, 0, 6
Let l = -166 + 235. Factor -3 - 19*a**4 - 2*a**4 + 12*a + l*a**3 - 3 + 27*a - 81*a**2.
-3*(a - 1)**3*(7*a - 2)
Let d(r) be the third derivative of r**5/240 - 9*r**4/32 - 29*r**3/12 + 39*r**2 + 5*r. Factor d(u).
(u - 29)*(u + 2)/4
Let v(i) be the third derivative of i**5/210 + 155*i**4/42 + 24025*i**3/21 - 633*i**2. Let v(y) = 0. Calculate y.
-155
Let i(q) be the second derivative of 0 - 2*q**3 - 1/3*q**4 - 4*q**2 - 8*q. Factor i(k).
-4*(k + 1)*(k + 2)
Let c(x) be the thi