+ 1)
Let z(l) = 16*l. Let p(h) = h**2 + 49*h. Let u(j) = -2*p(j) + 7*z(j). Factor u(t).
-2*t*(t - 7)
Let q(c) be the third derivative of -1/24*c**6 - 1/10*c**5 + 3*c**2 - 1/12*c**3 + 0 - 1/8*c**4 - 1/140*c**7 + 0*c. Factor q(w).
-(w + 1)**3*(3*w + 1)/2
Let t = -187/4 + 47. Determine k, given that 1/4*k - t*k**3 + 1/2 - 1/2*k**2 = 0.
-2, -1, 1
Solve 21/5*d**2 - 9/5*d + 0 = 0 for d.
0, 3/7
Let i(s) be the first derivative of -2*s**3/3 + 4*s**2 - 8*s - 12. Factor i(l).
-2*(l - 2)**2
Let m(g) = -29*g**3 + 74*g**2 - 39*g - 10. Let v(i) = -320*i**3 + 815*i**2 - 430*i - 110. Let r(z) = -45*m(z) + 4*v(z). Factor r(s).
5*(s - 2)*(s - 1)*(5*s + 1)
Let f(b) be the second derivative of b**5/80 - b**4/48 - b**3/24 + b**2/8 + 2*b - 31. Determine i so that f(i) = 0.
-1, 1
Let x(g) be the second derivative of g**6/120 + g**5/20 - 2*g**3/3 + g**2/2 + g. Let u(p) be the first derivative of x(p). Let u(k) = 0. Calculate k.
-2, 1
Let w(u) = -u**2 + u + 1. Let s be 0 + 1 - (2 + -3). Let t be w(s). Let r(j) = -j. Let z(m) = -m**3 - m**2 - 4*m. Let l(a) = t*z(a) + 4*r(a). Factor l(p).
p**2*(p + 1)
Let k(b) be the second derivative of 1/18*b**4 + 0 + 4*b + 4/27*b**3 + 1/9*b**2. Suppose k(w) = 0. Calculate w.
-1, -1/3
Let o be 4/10 - (-6)/10. Let y be (-1 + 4)*1 + o. Let 18*c**2 - 6*c**3 - 4*c + 10*c**4 + y*c**3 - 22*c**3 = 0. What is c?
0, 2/5, 1
Let v(n) be the first derivative of -3 + 1/6*n**6 - 1/3*n**3 - 1/4*n**4 + 0*n + 0*n**2 + 1/5*n**5. Let v(b) = 0. What is b?
-1, 0, 1
Let u be (20/(-35))/(((-40)/(-28))/(-5)). Factor -2/3*v + 2/3*v**3 - 4/3*v**u + 4/3.
2*(v - 2)*(v - 1)*(v + 1)/3
Let a(x) = x**2 + x - 3. Let u be a(-3). Let w(m) be the second derivative of -3/4*m**4 + 0*m**2 + m - 1/3*m**u + 0. Determine k so that w(k) = 0.
-2/9, 0
Let j be 6/10*13/13. Let v(n) be the first derivative of j*n - 1 - 3/2*n**2 + 4/5*n**3. Let v(h) = 0. What is h?
1/4, 1
Let z(u) be the first derivative of 5 - 3/2*u**2 - 1/3*u**3 - 2*u. Factor z(v).
-(v + 1)*(v + 2)
Suppose 2*b + 2*b - 24 = 0. Factor 4*h**2 - b + 3*h - h**2 + 0*h**2.
3*(h - 1)*(h + 2)
Let o = -1789/42 - -2/21. Let i = 43 + o. Factor -5/4*j + 3/4*j**2 + i.
(j - 1)*(3*j - 2)/4
What is p in 0*p + 2/13*p**4 + 0 - 10/13*p**2 + 8/13*p**3 = 0?
-5, 0, 1
Let n(i) be the second derivative of -i**5/70 + i**4/42 + 2*i**3/21 - 14*i. What is z in n(z) = 0?
-1, 0, 2
Let v(r) = r**2 + 5*r + 3. Let u be v(-5). Suppose -2*p - 41 = -6*p + 5*w, -w - 13 = -2*p. Factor -11*q**4 - 2*q**5 + 4*q**2 + 11*q**p + 6*q**u.
-2*q**2*(q - 2)*(q + 1)**2
Let q(g) be the first derivative of -g**6/105 - g**5/70 + 2*g - 2. Let p(n) be the first derivative of q(n). Factor p(y).
-2*y**3*(y + 1)/7
Let j(z) = 3*z**3 - 5*z**2 - 4*z - 4. Let v = -37 - -26. Let k(m) = 8*m**3 - 15*m**2 - 13*m - 12. Let w(c) = v*j(c) + 4*k(c). Factor w(g).
-(g + 1)*(g + 2)**2
Let a(x) = -4*x**3 - 15*x**2 - 27*x - 7. Let k(n) = -n**3 - 4*n**2 - 7*n - 2. Let t(v) = -2*a(v) + 9*k(v). Factor t(m).
-(m + 1)**2*(m + 4)
Let n(o) be the second derivative of o**9/12096 - o**8/3360 + o**7/3360 - o**3/3 + 3*o. Let z(x) be the second derivative of n(x). Factor z(g).
g**3*(g - 1)**2/4
Let q = -6 + 2. Let k = 19 + q. Suppose k*n - 12*n + 2 + 0 + n**2 = 0. Calculate n.
-2, -1
Let -1/3*v**3 + 1/3*v**2 + 0 + 0*v = 0. What is v?
0, 1
Let u(j) be the second derivative of j**10/166320 + j**9/41580 - j**7/6930 - j**6/3960 + j**4/3 + 6*j. Let i(y) be the third derivative of u(y). Factor i(f).
2*f*(f - 1)*(f + 1)**3/11
Let l(y) = -y**2 + y + 5. Let k = 5 + -5. Let m be l(k). Find p such that 0*p - 16*p**4 - p**2 + 0*p - 3*p**2 + 14*p**3 + 6*p**m = 0.
0, 2/3, 1
Let k(w) be the second derivative of -w**4/20 + 4*w**3/5 - 24*w**2/5 - 3*w. Factor k(x).
-3*(x - 4)**2/5
Let v(q) be the second derivative of -q**9/1512 + q**7/420 + q**3/2 - 5*q. Let c(s) be the second derivative of v(s). Factor c(g).
-2*g**3*(g - 1)*(g + 1)
Let f(r) = -3*r**2 + 3*r + 2. Let w(p) = -4*p**2 + 4*p + 2. Let n(s) = -6*f(s) + 4*w(s). Factor n(m).
2*(m - 2)*(m + 1)
Solve -r**3 - 1/2*r**4 + 1/2*r**5 + r**2 + 1/2*r - 1/2 = 0.
-1, 1
Factor -3*t**3 + 4*t**4 - 6*t**3 - 27*t**3 + 108*t**2 - 108*t.
4*t*(t - 3)**3
Find v such that 2*v**2 - 3/2*v**3 + 2*v - v**4 + 0 + 1/2*v**5 = 0.
-1, 0, 2
Let b be 0/2 + (-1 - 0 - -3). Solve 0 + 1/2*v**4 + 0*v**b + 1/2*v**3 + 0*v = 0 for v.
-1, 0
Factor 4/13*d + 0 + 4/13*d**3 + 10/13*d**2.
2*d*(d + 2)*(2*d + 1)/13
Determine d, given that 3*d - 8*d**3 + 12*d**3 - 7*d**3 = 0.
-1, 0, 1
Let y(v) = 3*v**2 + v. Let j(m) = -13*m**2 - 5*m. Let b(f) = f**3 - 6*f**2 - 7*f - 2. Let c be b(7). Let w(g) = c*j(g) - 9*y(g). Find p, given that w(p) = 0.
0, 1
Suppose p - 28 - 1 = -5*k, 0 = 4*p + 3*k - 31. Suppose 5*o - 2 - 1 = -f, 3*f - 9 = 5*o. Factor o*w - 1/3*w**2 - 1/3*w**5 + 1/3*w**3 + 0 + 1/3*w**p.
-w**2*(w - 1)**2*(w + 1)/3
Let o(x) = -3*x**3 - 6*x**2 + 3*x + 11. Let q(h) = 1. Let a(n) = -o(n) + 5*q(n). Factor a(v).
3*(v - 1)*(v + 1)*(v + 2)
Suppose 2*z + 5*g + 5 = 0, -2*g + 15 = z - 3*g. Let l = 14 - z. Factor 2*t - 4*t**2 - t**2 + l*t**2.
-t*(t - 2)
Find g, given that -21/4*g**3 + 4*g**2 + 0 + 9/4*g**4 - g = 0.
0, 2/3, 1
Let m(c) = -c**3 + 6*c**2 - 6*c + 2. Let q be m(4). Determine f so that -q*f**2 - 4 + 4 - 3*f**3 - 6*f + f**2 = 0.
-2, -1, 0
Let n be (-2)/(-3) - (-31)/3. Let s be n/(44/24) + 2. Factor 0*k + 0 - s*k**4 + 6*k**3 - 4/3*k**2 + 10/3*k**5.
2*k**2*(k - 1)**2*(5*k - 2)/3
Let u(c) be the third derivative of c**5/150 + c**4/30 - c**3/5 - 2*c**2. Factor u(n).
2*(n - 1)*(n + 3)/5
Let h(d) be the third derivative of -1/105*d**7 + 0 - 4*d**2 + 1/20*d**6 - 1/30*d**5 + 0*d + 2/3*d**3 - 1/4*d**4. Factor h(w).
-2*(w - 2)*(w - 1)**2*(w + 1)
Let g(x) be the second derivative of -x**6/135 + x**5/45 + 6*x. Solve g(h) = 0.
0, 2
Let n be (14/49)/((-9)/(-105)) + -3. What is u in -1/3*u - n*u**5 + 2/3*u**3 + 1/3*u**4 - 2/3*u**2 + 1/3 = 0?
-1, 1
Let h(w) = -w**5 + w**4 + w**3 + 1. Let i(n) = -n**5 - 15*n**4 - n**3 + 9*n**2 + 2*n - 6. Let j(g) = -6*h(g) - i(g). What is c in j(c) = 0?
-1, -2/7, 0, 1
Let r(f) be the third derivative of f**5/135 - 2*f**4/27 + 8*f**3/27 - 20*f**2 + 2. Solve r(a) = 0 for a.
2
Let x(a) be the third derivative of -5*a**8/336 + a**6/8 - a**5/6 + 9*a**2. Factor x(u).
-5*u**2*(u - 1)**2*(u + 2)
Let m(f) be the first derivative of f + 1/3*f**3 + 1/6*f**4 - 3 + 0*f**2. Let r(i) be the first derivative of m(i). Factor r(j).
2*j*(j + 1)
Let m(a) be the third derivative of -a**8/5880 - a**7/2940 + a**6/1260 + a**5/420 - a**3/6 - 4*a**2. Let l(w) be the first derivative of m(w). Factor l(g).
-2*g*(g - 1)*(g + 1)**2/7
Let s(c) = -c. Let q be s(-1). Let j be (q - 6)*(-20)/25. What is k in -3/2*k**j + k**2 + 1/2 - 1/2*k**5 - k**3 + 3/2*k = 0?
-1, 1
Suppose -214*h = -216*h + 8. Solve 2*d + 24*d**h - 38*d**3 - 64/3*d**2 + 4/3 = 0 for d.
-1/3, 1/4, 2
What is h in 2/7*h**5 + 10/7*h - 12/7*h**3 + 4/7*h**2 + 2/7*h**4 - 6/7 = 0?
-3, -1, 1
Suppose -4 = -c - 3. Let u be 1 - (c + -1 - 1). Solve 3*t**3 + 3*t**u - 2 + 8*t - 15*t**2 - 2*t**4 + 5*t**3 = 0.
1
Let p be (2/4)/((-2)/(-36)). Let f be 2/(-3) - 3/p. Let w(h) = 4*h**2 - 4*h + 2. Let j(b) = b**2 + b - 1. Let x(t) = f*w(t) + 2*j(t). Factor x(m).
-2*(m - 2)*(m - 1)
Let n be 0/(-3 + 2 - -2). Suppose n = -x + 5*r + 27, -4*x - 2*r = -4*r - 18. What is g in -6*g**3 + 3*g**2 + 5*g**4 - 3*g**4 + g**x = 0?
0, 1, 2
Let v(g) be the second derivative of 1/21*g**7 + 1/10*g**5 - 2*g - 2/3*g**3 + 0*g**2 - 1/2*g**4 + 1/5*g**6 + 0. Determine i, given that v(i) = 0.
-2, -1, 0, 1
Let p(h) = -h**3 - 5*h**2 + 4*h + 25. Let o be p(-5). Factor -3/4*k**2 + 0*k + 0 + 3/4*k**4 + 3/4*k**3 - 3/4*k**o.
-3*k**2*(k - 1)**2*(k + 1)/4
Let a be (0 + 2 - -1) + -16 + 16. Factor 0 + 1/3*w**a - 2/3*w**2 + 1/3*w.
w*(w - 1)**2/3
Let o = -5 - -8. Let q = -913/4 + 229. Factor 3/4*j**o + 0 + q*j + 3/2*j**2.
3*j*(j + 1)**2/4
Solve -2/13*y - 2/13*y**3 - 4/13*y**2 + 0 = 0.
-1, 0
Solve 8*h**5 - 54*h + 87*h**4 - 60*h**2 + 27*h - 53*h**5 + 3*h + 42*h**3 = 0.
-2/3, -2/5, 0, 1, 2
Let o(j) be the third derivative of 0*j + 2*j**2 + 1/1440*j**6 - 1/480*j**5 - 1/6*j**3 + 0*j**4 + 0. Let n(k) be the first derivative of o(k). Factor n(x).
x*(x - 1)/4
Let a(h) be the third derivative of -h**8/112 - h**7/35 + h**5/10 + h**4/8 + 51*h**2. Factor a(m).
-3*m*(m - 1)*(m + 1)**3
Let r(j) = -j - 18. Let f be r(-18). Let a(p