 - 17*i. Factor r(m).
2*m*(m + 1)*(m + 2)/3
Let l(f) be the first derivative of 4*f**5/5 + f**4 - 4*f**3 - 2*f**2 + 8*f + 4. Factor l(t).
4*(t - 1)**2*(t + 1)*(t + 2)
Suppose 6*d**2 - 8*d**5 + 1368 - 2*d - 6*d**4 + 10*d**3 - 1368 = 0. Calculate d.
-1, 0, 1/4, 1
Let q(p) be the first derivative of 0*p + 0*p**3 + 0*p**2 + 2 - 1/20*p**5 + 0*p**4. Let q(u) = 0. Calculate u.
0
Let p(o) be the third derivative of -49*o**7/180 + 49*o**6/720 + 7*o**5/12 + 19*o**4/36 + 2*o**3/9 - 2*o**2. What is y in p(y) = 0?
-2/7, 1
Let l(o) be the first derivative of o**6/35 + o**5/14 + o**4/42 - o**3/21 - o + 3. Let f(h) be the first derivative of l(h). Factor f(z).
2*z*(z + 1)**2*(3*z - 1)/7
Let k = -306/5 + 62. Factor 0 - 2/5*f**3 - 2/5*f - k*f**2.
-2*f*(f + 1)**2/5
Let 32/9*s + 544/9*s**3 + 50/3*s**5 - 224/9*s**2 + 0 - 520/9*s**4 = 0. What is s?
0, 2/5, 2/3, 2
Let y(l) be the third derivative of l**6/360 + l**5/120 + l**3/3 + 2*l**2. Let c(h) be the first derivative of y(h). Suppose c(v) = 0. Calculate v.
-1, 0
Let c(q) be the first derivative of q**3/15 + q**2/10 - 6*q/5 - 22. Factor c(d).
(d - 2)*(d + 3)/5
Let a(c) be the first derivative of 1/12*c**2 + 1/30*c**5 - 1/24*c**4 + 4 + 1/3*c - 1/6*c**3. Factor a(n).
(n - 2)*(n - 1)*(n + 1)**2/6
Let t(x) = x**3 + 4*x**2 + x - 2. Let y(f) = 2*f**3 + 9*f**2 + 2*f - 5. Let m(p) = -5*t(p) + 2*y(p). Suppose m(q) = 0. What is q?
-1, 0
Suppose 0*w = 3*u - w - 14, 2*w = 2. Let 64 - 4*z - 8*z**4 + 8*z**2 + 4*z**u - 64 = 0. What is z?
-1, 0, 1
Factor 0*h**2 + 0 + h**4 - 7/3*h**3 + 4/3*h.
h*(h - 2)*(h - 1)*(3*h + 2)/3
Factor 2*l + 1/2*l**2 + 2.
(l + 2)**2/2
Let h(d) be the second derivative of d**5/360 - d**4/72 + d**3/36 + d**2 - 3*d. Let i(r) be the first derivative of h(r). Factor i(j).
(j - 1)**2/6
Let n = 9 + -7. Find o such that o**2 - n + 5*o**3 - 4*o**3 + 2 = 0.
-1, 0
Factor 6*r**3 - 141 + 2*r**4 + 141 + 4*r**2.
2*r**2*(r + 1)*(r + 2)
Factor -5*j**2 - 3*j**4 - 15*j**5 + 27*j**4 - j**2 - 5*j**3 + 2*j**3.
-3*j**2*(j - 1)**2*(5*j + 2)
Let a(f) = -2*f - 2. Let m be a(-3). Let i(n) be the first derivative of -5/12*n**3 + 1 + 0*n - 1/4*n**2 - 3/16*n**m. Find o, given that i(o) = 0.
-1, -2/3, 0
Let t(c) be the second derivative of c**6/720 + c**3/3 + 4*c. Let s(z) be the second derivative of t(z). Find x, given that s(x) = 0.
0
Let p(t) be the second derivative of -1/6*t**4 + 3*t - 4*t**2 + 4/3*t**3 + 0. Let p(g) = 0. Calculate g.
2
Let g(u) = u**3 - 5*u**2 - 9*u - 9. Let z be g(7). Solve -18*c + 8*c**2 - 4 - c**3 + 0*c**3 + 3*c**3 - z*c**2 + 6*c**4 = 0.
-1, -1/3, 2
Factor -14/3*k**3 + 8/3*k + 0 + 8*k**2.
-2*k*(k - 2)*(7*k + 2)/3
Suppose -3*q - 12 = -3*m, -4*q - m + 0 + 4 = 0. What is p in 0*p**2 - 2/3*p**4 + 0*p**3 + 0*p + q + 2/3*p**5 = 0?
0, 1
Let l be (0 + 2)/(4/22). Let z be 1 - (2 - l/7). Factor 2/7*v**2 - z - 2/7*v.
2*(v - 2)*(v + 1)/7
Let g(y) = -y + 9. Let d be g(4). Let l be (-3)/d - 21/(-10). Factor -3*r**3 + r**4 - l*r + 13/4*r**2 + 1/4.
(r - 1)**2*(2*r - 1)**2/4
Suppose 3*c = -14 + 2. Let m = c + 4. Determine v so that m + 0*v + 1/4*v**2 + 3/4*v**3 = 0.
-1/3, 0
Let n = -11 - -17. Factor -1 + 12*x**2 + 1 + n*x - 4 - 2*x**2.
2*(x + 1)*(5*x - 2)
Let w(b) be the first derivative of -4*b + 10/3*b**3 + 1 - 3*b**2. Factor w(t).
2*(t - 1)*(5*t + 2)
Let y be 0/(-6 + 3) + 2. Let h(p) be the first derivative of 15/2*p**4 + 34/3*p**3 + 8/5*p + 32/5*p**y + 3. Factor h(c).
2*(3*c + 1)*(5*c + 2)**2/5
Determine v, given that -4*v**2 + 0*v + v + 5*v**3 - v**2 - 11*v = 0.
-1, 0, 2
Suppose 0 = -2*p + 3*h + 2*h - 21, -p = -3*h + 13. Let 4*i**2 - p*i - 3*i**2 + 0*i = 0. Calculate i.
0, 2
Suppose 2*b + 4 = 4*b. Suppose -b*d - 20 = -7*d. What is k in 4*k**2 + 0*k**d - 2*k**4 - 2*k**2 = 0?
-1, 0, 1
Suppose 4*y = -0*c - 5*c - 5, 5 = c + 2*y. Let n be (-18)/45 - 6/c. Factor -n*v**3 + 2/5*v**2 + 4/5*v - 2/5.
-2*(v - 1)*(v + 1)*(2*v - 1)/5
Let b(a) be the third derivative of a**8/5040 + a**7/1260 + a**6/1080 + a**3/3 + 4*a**2. Let u(d) be the first derivative of b(d). Factor u(t).
t**2*(t + 1)**2/3
Let i(q) = 2*q**3 - 5*q**2 - 4*q. Let z(b) = -10*b**3 + 24*b**2 + 20*b. Let c(p) = -14*i(p) - 3*z(p). Factor c(x).
2*x*(x - 2)*(x + 1)
Factor -7*v**3 - 5*v**4 + 11*v**3 - 18*v**2 + 2*v**4 + 12*v - 3 + 8*v**3.
-3*(v - 1)**4
Let w be 7 + -1*(0 - -2). Let j = 1 + w. Factor j*l**3 - 14*l**4 + 0*l + 6*l**5 + 6*l**2 - 2*l - 2*l.
2*l*(l - 1)**3*(3*l + 2)
Let u(t) = -t**2 - 7*t + 18. Let n = 28 - 37. Let x be u(n). Solve 2/9*d**3 + x - 2/9*d + 0*d**2 = 0 for d.
-1, 0, 1
Factor 0 + 7/2*t**4 - 1/2*t**5 + 0*t - 3*t**3 + 0*t**2.
-t**3*(t - 6)*(t - 1)/2
Factor 0*p + 7/6*p**3 - 5/6*p**4 - 1/2*p**2 + 0 + 1/6*p**5.
p**2*(p - 3)*(p - 1)**2/6
Let d(c) = 7*c**2 - 5*c + 1. Let q(h) = -h**2 - h + 1. Let s(t) = -d(t) - 3*q(t). Suppose s(f) = 0. Calculate f.
1
Let a(z) be the second derivative of 0*z**2 - 2*z + 0*z**3 + 2/21*z**4 + 1/105*z**6 + 0 - 2/35*z**5. Factor a(k).
2*k**2*(k - 2)**2/7
Let l(u) = -u**2 - 8*u - 5. Let x be l(-7). Factor y**2 - 3*y**3 + 3*y**2 + 2*y**4 - 3*y**x.
y**2*(y - 1)*(2*y - 1)
Let d(r) be the second derivative of 0*r**2 + 0 + 1/12*r**3 - 1/16*r**4 + 1/80*r**5 - 3*r. Find u, given that d(u) = 0.
0, 1, 2
Let c(u) = -2*u**3 - 5*u**2 - 9*u. Let l(q) = q**3 + 3*q**2 + 5*q. Let r(k) = -3*c(k) - 5*l(k). Let i(n) = -n. Let s(w) = -3*i(w) - r(w). Factor s(o).
-o*(o - 1)*(o + 1)
Let d(c) be the second derivative of c**7/126 + c**6/30 + c**5/30 - 12*c. Factor d(f).
f**3*(f + 1)*(f + 2)/3
Let f(k) be the third derivative of k**5/12 - 5*k**4/24 + 23*k**2. Find h, given that f(h) = 0.
0, 1
Let p(s) be the second derivative of -s**7/21 - 2*s**6/15 + s**4/3 + s**3/3 - 10*s. Factor p(m).
-2*m*(m - 1)*(m + 1)**3
Let x = -4 - -5. Let v be (-3 - x)/(-2) - -1. Factor -4*o**3 + 3*o + 5*o**3 - 4*o**3 - 3 + v*o**2.
-3*(o - 1)**2*(o + 1)
Let r(x) be the third derivative of 0*x**4 - 4*x**2 + 0 + 0*x**3 + 0*x - 1/150*x**5. Factor r(u).
-2*u**2/5
Suppose -3*c - 2*i = -4, 9*i + 4 = -c + 11*i. Let w(n) be the first derivative of 2/45*n**5 - 1/18*n**4 + c*n + 1/27*n**6 + 1 + 0*n**2 - 2/27*n**3. Factor w(r).
2*r**2*(r - 1)*(r + 1)**2/9
Solve 0*t**3 + 0*t + 0 - 1/7*t**2 + 1/7*t**4 = 0.
-1, 0, 1
Factor 14*w - 49/2*w**2 - 2.
-(7*w - 2)**2/2
Determine w, given that 4*w + 11*w + 3 + 3 + 5*w**3 - 1 + 15*w**2 = 0.
-1
Let k(u) be the second derivative of u**6/45 + u**5/30 - u**4/18 - u**3/9 - 24*u. Suppose k(i) = 0. What is i?
-1, 0, 1
Let n(w) = 5*w - 16*w + 10*w + 1. Let l be n(1). Find t such that 0*t - 1/4*t**5 + l*t**2 + 0 - 1/4*t**4 + 0*t**3 = 0.
-1, 0
Let w(n) = 5*n**3 - 5*n**2 + 7*n - 1. Let s(j) = j**3 - j**2 + j. Let g(r) = -6*s(r) + w(r). Factor g(f).
-(f - 1)**2*(f + 1)
Let f = 3970/7 + -566. Find j, given that 2/7 - 10/7*j + f*j**2 = 0.
1/4, 1
Let n(g) be the third derivative of 0*g**5 - 1/180*g**6 + 0 - 1/18*g**3 + 2*g**2 + 0*g + 1/630*g**7 + 1/36*g**4. Solve n(l) = 0.
-1, 1
Let p(q) be the first derivative of 0*q**3 + 3 + 3/2*q**2 - 3/4*q**4 + 0*q. Factor p(v).
-3*v*(v - 1)*(v + 1)
Let x = 4 + 1. Suppose -x*n + 9 = -1. Factor 80*d**3 + 11*d + 0 - 64*d**4 + 2 - n*d + 14*d + 84*d**2.
-(d - 2)*(4*d + 1)**3
Let u = 9 + -10. Let g be u + (-1 - 100/(-45)). Factor 2/9*y + g*y**2 + 0.
2*y*(y + 1)/9
Let w(i) be the second derivative of 0*i**5 + i + 1/180*i**6 - 1/12*i**4 + 0*i**2 + 0 - 1/3*i**3. Let z(h) be the second derivative of w(h). Factor z(c).
2*(c - 1)*(c + 1)
Let w(a) = a - 2. Let o be w(2). Let u(d) be the second derivative of 1/10*d**5 + d + d**3 - d**2 + o - 1/2*d**4. Factor u(p).
2*(p - 1)**3
Let f(q) = q + 7. Let w be f(-5). Suppose -5*v**3 + 4*v**3 + 4*v**w + 0 - 5*v + 2 = 0. Calculate v.
1, 2
Let p be (-3)/6 - ((-1)/2 + -2). Determine g, given that 1/2*g + 0 - g**p + 1/2*g**3 = 0.
0, 1
Let v(i) = i**3 + i**2 + i. Let k(y) be the first derivative of 3/4*y**4 + 1 + 3/2*y**2 + 4/3*y**3 + 0*y. Let w(l) = -k(l) + 2*v(l). Factor w(d).
-d*(d + 1)**2
Let t be 3 - 75/12 - (-10 - -6). Factor 3*m**3 - 3*m + 3/4*m**2 - t.
3*(m - 1)*(m + 1)*(4*m + 1)/4
Factor 4/11 + 2/11*b - 2/11*b**2.
-2*(b - 2)*(b + 1)/11
Let w(z) = -z**2 - 9*z + 39. Let g be w(-12). Factor 0 + 2*k**2 + 2/3*k**4 + 2*k**g + 2/3*k.
2*k*(k + 1)**3/3
Let v = -4 - -6. Suppose -3*i**3 - 9*i - 6 - 3*i - 12*i**v - 3*i = 0. Calculate i.
-2, -1
Let t(v) be the second derivative of 0*v**2 + 0*v**4 + 0 + 2/45