i*x + 0 + 1/5*x**2 + 1/5*x**3.
x**2*(x + 1)/5
Let k = -336 - -336. Let u = 36 - 26. Suppose u*g**4 + 8/7*g - 78/7*g**3 + 0*g**2 + k = 0. What is g?
-2/7, 0, 2/5, 1
Let x(m) be the first derivative of m**6/36 + 2*m**5/15 + m**4/4 + 2*m**3/9 + m**2/12 - 16. Factor x(j).
j*(j + 1)**4/6
Let y = -10 + 15. Let q(h) be the third derivative of 1/490*h**7 + 0 + 0*h**4 + 0*h**y + 1/140*h**6 - 1/784*h**8 + 0*h + 0*h**3 - 2*h**2. Factor q(o).
-3*o**3*(o - 2)*(o + 1)/7
Let t(z) be the second derivative of z**7/11340 - z**6/3240 - z**4/4 + z. Let y(g) be the third derivative of t(g). Factor y(v).
2*v*(v - 1)/9
Let c(k) be the third derivative of k**8/120 + 71*k**7/1575 + 13*k**6/900 - 31*k**5/450 + k**4/30 + 10*k**2. Suppose c(t) = 0. What is t?
-3, -1, 0, 2/7, 1/3
Let m(f) be the third derivative of f**6/840 + f**5/420 - 5*f**4/168 + f**3/14 + f**2. Factor m(g).
(g - 1)**2*(g + 3)/7
Let w(h) be the first derivative of -h**7/210 + h**5/50 - h**3/30 - 5*h - 7. Let u(f) be the first derivative of w(f). Factor u(n).
-n*(n - 1)**2*(n + 1)**2/5
Determine w so that 0 + 110*w**3 + 0*w - 20*w**2 - 735/2*w**5 - 35*w**4 = 0.
-2/3, 0, 2/7
Determine c, given that 720/7*c**2 - 800/7*c**3 + 250/7*c**4 - 256/7*c + 32/7 = 0.
2/5, 2
Let s(j) = -22*j**3 + 22*j**2 - 34. Let y(v) = 2*v**3 - 2*v**2 + 3. Let l(d) = -6*s(d) - 68*y(d). Factor l(t).
-4*t**2*(t - 1)
Let r be 3*(-2 + 6/9 + 2). Factor -1/5*t**r + 0 - 1/5*t.
-t*(t + 1)/5
Let q be (5/15)/(2/12). Factor -2*b + 3*b - q*b - b + 2*b**3.
2*b*(b - 1)*(b + 1)
Let a(k) = 5*k**2 - 3*k + 6. Let b = -21 - -15. Let s(q) be the first derivative of -2*q**3/3 + q**2/2 - 3*q + 17. Let v(y) = b*a(y) - 14*s(y). Solve v(m) = 0.
-1, 3
Let b(u) be the second derivative of u**5/20 + u**4/4 + u**3/3 + 11*u. Determine i so that b(i) = 0.
-2, -1, 0
Let u = -525 + 2103/4. Factor 0*x + 0*x**2 - u*x**4 + 1/4*x**5 + 0 + 1/2*x**3.
x**3*(x - 2)*(x - 1)/4
Let b(i) be the third derivative of -2*i**2 + 1/20*i**5 + 3/2*i**3 - 1/2*i**4 + 0*i + 0. Factor b(r).
3*(r - 3)*(r - 1)
Let b(a) be the third derivative of a**6/960 - a**5/120 - a**4/192 + a**3/12 + a**2 + 5*a. Suppose b(s) = 0. Calculate s.
-1, 1, 4
Factor -1/5*j**4 + 0 + j**2 + 1/5*j**3 + 3/5*j.
-j*(j - 3)*(j + 1)**2/5
Let v be ((-12)/(-16)*-1)/(3/(-8)). Let a(g) be the second derivative of -1/18*g**4 - 1/3*g**v + 2*g + 0 - 2/9*g**3. Factor a(z).
-2*(z + 1)**2/3
Let a(p) = -6*p**3 + 6*p. Let b(r) = -17*r**3 + 17*r. Let l(x) = -8*a(x) + 3*b(x). Factor l(g).
-3*g*(g - 1)*(g + 1)
Let o(w) be the second derivative of -1/5*w**2 + 3*w - 1/10*w**4 + 0 - 1/50*w**5 - 1/5*w**3. Find d such that o(d) = 0.
-1
Let y(g) be the second derivative of -3*g**6/20 - g**5/15 + 3*g**4/4 + 2*g**3/3 + 3*g**2/2 + 5*g. Let f(o) be the first derivative of y(o). Factor f(m).
-2*(m - 1)*(m + 1)*(9*m + 2)
Let 0*d**2 + 0 + 1/6*d**5 + 1/6*d**4 + 0*d - 1/3*d**3 = 0. Calculate d.
-2, 0, 1
Let b(x) be the second derivative of x**9/13608 + x**8/2520 + x**7/1260 + x**6/1620 + x**3/2 + x. Let j(u) be the second derivative of b(u). Factor j(i).
2*i**2*(i + 1)**3/9
Let y(b) be the first derivative of b**6/360 - b**5/60 + b**4/24 - 8*b**3/3 - 4. Let n(k) be the third derivative of y(k). Factor n(g).
(g - 1)**2
Factor 2/7*b**3 + 10/7*b + 4/7 + 8/7*b**2.
2*(b + 1)**2*(b + 2)/7
Factor 1/4*c + 0 + 3/8*c**2.
c*(3*c + 2)/8
Let d(f) be the second derivative of 7*f**6/60 + 27*f**5/20 - 2*f**4/3 + 45*f. Determine l, given that d(l) = 0.
-8, 0, 2/7
Let y(q) be the third derivative of q**7/105 + q**6/30 - q**5/10 - q**4/3 + 4*q**3/3 - 25*q**2. Factor y(o).
2*(o - 1)**2*(o + 2)**2
Suppose 3 + 4 = -s. Let t be s*-2*(-2)/(-4). Factor -t*j**2 - j**3 - j + 2*j**2 - 8*j**3 - 4*j**4 - j**2.
-j*(j + 1)**2*(4*j + 1)
Suppose 0 = 4*f - 2*f + b - 1, 3*f = -4*b - 6. Let 4*v**f - v**3 - 4*v**2 + v = 0. Calculate v.
-1, 0, 1
Let v(s) be the second derivative of s**4/42 - 2*s**3/21 + s**2/7 - 4*s. Determine m, given that v(m) = 0.
1
Factor -3/5*u**2 - 12/5 - 12/5*u.
-3*(u + 2)**2/5
Let s(l) be the first derivative of -l**6/2 - 6*l**5 - 75*l**4/4 + 20*l**3 + 120*l**2 - 192*l + 11. Factor s(a).
-3*(a - 1)**2*(a + 4)**3
Let y(k) be the second derivative of 1/35*k**5 - 1/105*k**6 - 1/7*k**2 - 1/147*k**7 - 1/21*k**3 + 0 + 1/21*k**4 + 3*k. Factor y(a).
-2*(a - 1)**2*(a + 1)**3/7
Let o(n) = -7*n + 10 + 2 - 3*n + n**2 + 4*n**2. Let r(g) = -11*g**2 + 19*g - 24. Let z(c) = -5*o(c) - 2*r(c). Find s such that z(s) = 0.
2
Suppose r + 17 = -3*k + 13, 8 = 3*r - k. Factor 4/7 + 10/7*w + 2/7*w**3 + 8/7*w**r.
2*(w + 1)**2*(w + 2)/7
Let u be -5 + 159/9 + -2. What is y in -6*y + 2/3 + 16*y**2 - u*y**3 = 0?
1/4, 1
What is d in -21*d + 15/2 + 12*d**2 = 0?
1/2, 5/4
Let s = -177/2 + 89. Let r(d) be the second derivative of -d**2 - s*d**3 - 1/12*d**4 + 0 + 2*d. Factor r(p).
-(p + 1)*(p + 2)
Let l(p) = 3*p**5 - 7*p**4 - 7*p**3 + 3*p**2 - 2*p. Let t(j) = -11*j**5 + 29*j**4 + 29*j**3 - 11*j**2 + 9*j. Let m(z) = -9*l(z) - 2*t(z). Factor m(g).
-5*g**2*(g - 1)**2*(g + 1)
Let k = -9 + 12. Factor 96*h**5 - k*h**3 + 2*h**2 + 23*h**4 + 25*h**3 + 57*h**4.
2*h**2*(3*h + 1)*(4*h + 1)**2
Let l(c) be the first derivative of -c**3/7 - c**2/14 + 4*c/7 + 24. Factor l(i).
-(i - 1)*(3*i + 4)/7
Let z(s) be the first derivative of -s**6/20 - s**5/15 + s**4/4 + 2*s**3/3 - 5*s**2/2 + 1. Let b(x) be the second derivative of z(x). Solve b(j) = 0.
-1, -2/3, 1
Let d(j) be the first derivative of -9*j**6/10 + 9*j**4/20 + 2*j**3/15 - 1. Solve d(s) = 0 for s.
-1/3, 0, 2/3
Let y(a) be the second derivative of 1/16*a**4 - 3/2*a**2 + 0 + 3/80*a**5 + 5*a - 1/2*a**3. Factor y(w).
3*(w - 2)*(w + 1)*(w + 2)/4
Let n(b) = -b + 2. Let k be n(-2). Let -10*t**k - 4*t**2 + 2*t + 0*t + 14*t**4 - 2*t**5 = 0. Calculate t.
-1, 0, 1
Find n, given that 3 + 9/2*n + 3/2*n**2 = 0.
-2, -1
Suppose 0*x + 0 + 1/8*x**2 - 1/8*x**3 = 0. Calculate x.
0, 1
Let z(h) = h**3 - 2*h**2 + h + 1. Let a(t) = t + 1. Let q(f) = a(f) - z(f). Factor q(i).
-i**2*(i - 2)
Determine n so that -3/7*n**3 + 27/7*n**2 + 81/7 - 81/7*n = 0.
3
Let y be 4/(-6 + 8) - (-4)/(-5). Suppose 4/5 + y*w + 2/5*w**2 = 0. What is w?
-2, -1
Factor 5 + 15/2*j**3 + 5/4*j**4 + 15*j + 65/4*j**2.
5*(j + 1)**2*(j + 2)**2/4
Suppose -4*q + 3*k + 2*k - 5 = 0, -2*q = -2*k + 2. Suppose r - 3 + q = 0. Factor 0*s**2 + 0*s + s**r - 1 + s**2 - s.
(s - 1)*(s + 1)**2
Let s(f) = -2*f + 2. Let x be s(-2). Suppose 2*m + x = -m + 4*b, 5*m - 5*b + 5 = 0. What is z in m*z - 2*z**2 + 0*z - 4*z = 0?
-1, 0
Let g be (-1 + 10/12)*-4. Suppose -3*y - s + 4 = -6*y, 0 = -4*s + 16. Factor 0 - 2/3*l**3 + 2/3*l**5 + y*l - 2/3*l**4 + g*l**2.
2*l**2*(l - 1)**2*(l + 1)/3
Let h(o) = -6*o**2 - 7*o - 5. Let s(c) = 6*c**2 + 6*c + 6. Let x(r) = -3*h(r) - 2*s(r). Determine g so that x(g) = 0.
-1, -1/2
Factor 4/3 + 2/3*h - 2/3*h**2.
-2*(h - 2)*(h + 1)/3
Suppose 20 = 4*y - 4. Suppose -11*x**2 - 10*x**2 + y*x**2 - 4*x - 2*x - 9*x**3 = 0. Calculate x.
-1, -2/3, 0
Suppose -d = -2*d + 6. Let g(v) = -3*v**4 - 6*v**3 + 9*v**2 - 12*v. Let p(j) = 8*j**4 + 19*j**3 - 28*j**2 + 35*j. Let t(o) = d*p(o) + 17*g(o). Factor t(m).
-3*m*(m - 2)*(m - 1)**2
Let n(t) be the first derivative of -t**6/75 + t**5/25 - t**4/30 + 2*t + 1. Let y(x) be the first derivative of n(x). Factor y(j).
-2*j**2*(j - 1)**2/5
Let r(d) be the second derivative of -d**7/14 + d**6/5 - d**4/2 + d**3/2 - 13*d. Solve r(g) = 0 for g.
-1, 0, 1
Let d be ((-6)/(-12))/(1/2). Let o be (4/16*0)/d. Factor o*n + 4/3*n**3 + 2/3*n**4 + 2/3*n**2 + 0.
2*n**2*(n + 1)**2/3
Suppose -27*g + 4 = -26*g. Let k(f) be the third derivative of 0*f - 1/240*f**5 - 1/12*f**3 + 0 + 3*f**2 + 1/32*f**g. Factor k(y).
-(y - 2)*(y - 1)/4
Let u(f) be the third derivative of f**6/120 + f**5/15 - f**4/8 - f**3 + 2*f**2. Let x be u(-4). Solve 2 + x*n + 3*n**2 - n**2 - 2*n = 0 for n.
-1
Factor 0 - 2/3*w - 2/3*w**5 + 4/3*w**3 + 0*w**4 + 0*w**2.
-2*w*(w - 1)**2*(w + 1)**2/3
Let s(a) be the third derivative of -a**6/480 - a**5/240 + a**4/96 + a**3/24 - 2*a**2. Suppose s(g) = 0. Calculate g.
-1, 1
Let s(w) be the first derivative of -1/15*w**3 - 2/5*w - 3/10*w**2 - 5. Suppose s(b) = 0. What is b?
-2, -1
Let r(a) be the second derivative of 0 - 1/6*a**7 - 5*a - a**2 + 1/3*a**4 + 7/10*a**5 - 7/6*a**3 - 1/15*a**6. Determine l, given that r(l) = 0.
-1, -2/7, 1
Let m(p) be the first derivative of -3*p**7/80 - 19*p**6/