e -4*c + n*c = -8. Factor 0 + 2/7*d**3 + 2/7*d - 4/7*d**c.
2*d*(d - 1)**2/7
Let f = -5 + 7. Suppose -2 = -5*u + 3. Solve 3 + 0*x**2 + u - f - 2*x**2 = 0.
-1, 1
Let x = -107/12 - -49/4. Let 5/3*z + 1/3*z**5 - 10/3*z**2 - 1/3 - 5/3*z**4 + x*z**3 = 0. Calculate z.
1
Let m(i) be the first derivative of i**6/6 - i**5/5 - i**4/2 + 2*i**3/3 + i**2/2 - i + 18. Factor m(n).
(n - 1)**3*(n + 1)**2
Let x(r) be the first derivative of r**7/840 + r**6/360 + r**3/3 + 4. Let w(h) be the third derivative of x(h). Factor w(y).
y**2*(y + 1)
Let o(a) be the second derivative of a**3/2 - 7*a**2/2 - 2*a. Let v be o(8). Suppose -v*h + h**5 + 7*h**2 - 9*h**3 + 15*h - 2*h**5 + 5*h**4 = 0. What is h?
0, 1, 2
Let i(f) be the first derivative of -f**7/280 + f**6/40 - f**4/2 + 4*f**3/3 - 3. Let p(n) be the third derivative of i(n). What is b in p(b) = 0?
-1, 2
Let i = -1103/165 - -75/11. Let g(t) be the first derivative of i*t**3 - 3 + 0*t + 1/5*t**2. Factor g(z).
2*z*(z + 1)/5
Let i be 4/20 + (-181)/5. Let y = i - -109/3. Solve 1/3*z**4 + z**2 - y*z + 0 - z**3 = 0 for z.
0, 1
Let o be 16/(-120) + 1/30*4. Let d(j) be the second derivative of 0*j**2 + o*j**3 + j + 0 + 3/5*j**5 + 1/4*j**4. Determine b, given that d(b) = 0.
-1/4, 0
Let q(m) = -6*m**4 + 3*m**3 + 17*m**2 - 9*m + 10. Let v(p) = -p**4 + p**3 + p**2 + p + 1. Let d(z) = 2*q(z) - 10*v(z). Find g such that d(g) = 0.
-5, 1
Let j be 3 - (2/3)/((-6)/9). Let t(i) be the second derivative of 7/60*i**6 - 3/8*i**j - 5/12*i**3 + 1/8*i**5 + 3*i + 0 + 1/2*i**2. Factor t(k).
(k - 1)*(k + 1)**2*(7*k - 2)/2
Let h = 4 + 1. Let k(p) = 5*p. Let m be k(1). Factor -l**2 + l**4 + 0*l + l**5 + 3*l**h - m*l**3 - l**5 + 2*l.
l*(l - 1)*(l + 1)**2*(3*l - 2)
Factor -2*y**2 + 62*y**2 - 75*y**3 + 10*y**3 - 5*y + 30*y**4 - 5*y**5 - 15*y.
-5*y*(y - 2)**2*(y - 1)**2
Let k be 60/(-2)*8/(-12). Let w be (6/8)/(5/k). Let q**2 + 2*q + 0*q**4 - q - 5*q**3 + w*q**4 = 0. What is q?
-1/3, 0, 1
Let w(c) be the first derivative of 0*c + 0*c**2 + 1/6*c**4 - 2 + 4/9*c**3. Factor w(y).
2*y**2*(y + 2)/3
Let z be 28/36 - 2/(-9). Suppose 0 = 3*n - 4*h + 9 + 5, 3*n - h = z. Solve 2/3*r**n + 2/3*r - 4/3 = 0 for r.
-2, 1
Suppose 2*c - 4*f - 2 = 0, 2*c + 7*f - 18 = 3*f. Suppose -3*n + 5*t - 14 = -0, c*t = 2*n + 16. Let -2*p**4 + 0*p**5 - n*p**5 + 0*p**4 = 0. What is p?
-1, 0
Let p(g) be the first derivative of -g**5/10 + 7*g**4/4 - 10*g**3 + 25*g**2/2 + 125*g/2 - 1. Factor p(j).
-(j - 5)**3*(j + 1)/2
Let o(u) be the second derivative of -u**7/2520 - u**6/360 - u**4/12 - 2*u. Let a(m) be the third derivative of o(m). Factor a(r).
-r*(r + 2)
Let w(n) = n**2 - n + 1. Let q(j) = -j**2 - 12*j + 47. Let y(x) = q(x) + 2*w(x). Determine r, given that y(r) = 0.
7
Let u(a) = -a**2 - a + 1. Let w(o) = -10*o**2 + 2*o + 3. Let q(x) = 15*u(x) - 3*w(x). Solve q(d) = 0 for d.
2/5, 1
Factor 4 + t**2 - 11*t - 6*t + 13*t.
(t - 2)**2
Let g(r) be the second derivative of r**6/60 - r**5/15 - r**4/12 + 2*r**3/3 + 7*r**2/2 - 6*r. Let p(c) be the first derivative of g(c). Factor p(z).
2*(z - 2)*(z - 1)*(z + 1)
Let x(j) be the second derivative of -j**4/12 - 7*j**3/6 - 3*j. Let l be x(-7). Suppose 2/7*s**5 + l*s - 6/7*s**4 - 2/7*s**2 + 6/7*s**3 + 0 = 0. Calculate s.
0, 1
Suppose -5*w + 40 = 30. Determine c so that -2/7*c - 4/7 + 2/7*c**w = 0.
-1, 2
Let t(f) be the first derivative of -7 + 0*f - 2/21*f**3 + 2/7*f**2. Solve t(z) = 0.
0, 2
Let j = 40 - 25. Suppose 3*g = 2*u - j, u - 5*g - 20 = -g. Factor u + 5/3*f**5 - 8/3*f**4 + 1/3*f**3 + 2/3*f**2 + 0*f.
f**2*(f - 1)**2*(5*f + 2)/3
Suppose -3*b + 6*y - 2*y = -2, 1 = b - y. Let h = 4 - b. Factor 0*t**3 - 2*t**4 + 0 + 2/3*t**h + 4/3*t**5 + 0*t.
2*t**2*(t - 1)**2*(2*t + 1)/3
Let f(x) be the third derivative of 1/2*x**3 + 0 + 0*x**5 + x**2 + 0*x - 1/70*x**7 - 1/20*x**6 + 1/4*x**4. Determine l so that f(l) = 0.
-1, 1
Let s(m) = m**3 - m**2 - 3*m - 2. Let f be s(-1). Let j be f/((-14)/32) - 2. Factor j*u**2 + 0 - 2/7*u**3 + 4/7*u.
-2*u*(u - 2)*(u + 1)/7
Let j(f) = f**2 - 2*f - 4. Let w be j(4). Solve -2*x + 0*x**2 + 0*x**2 + 0*x - w*x**2 = 0 for x.
-1/2, 0
Let r(w) be the first derivative of -2/21*w**3 + 0*w + 4/35*w**5 - 1/14*w**4 - 3 + 0*w**2. Factor r(g).
2*g**2*(g - 1)*(2*g + 1)/7
Let b be (3 + -3)/(3 - 1). Suppose b*a - 4*a + 8 = 0. Factor -3*h**2 + 2*h + 3*h**a + h**2.
h*(h + 2)
Let b = -1/3458 - 1493851/17290. Let q = -86 - b. Determine k so that 0*k - 2/5 + q*k**2 = 0.
-1, 1
Let q(l) = 15*l**4 - 72*l**3 + 115*l**2 - 82*l + 20. Let i(u) = -45*u**4 + 217*u**3 - 345*u**2 + 247*u - 60. Let m(x) = 2*i(x) + 7*q(x). Factor m(k).
5*(k - 2)*(k - 1)**2*(3*k - 2)
Let w(o) be the second derivative of -10*o**7/21 + 2*o**6/3 + 11*o**5/4 - 5*o**4/6 - 35*o**3/6 - 5*o**2 + 6*o. Determine z, given that w(z) = 0.
-1, -1/2, 1, 2
Let g(i) = 4 - 6*i + 3*i**3 - 2 + 1. Let h(a) = -3*a**3 - a**2 + 7*a - 3. Let y(u) = -4*g(u) - 3*h(u). Factor y(o).
-3*(o - 1)**2*(o + 1)
Suppose 0 = 4*n - 98 + 86. Determine t so that 0 - 4/3*t**2 + 5*t**n - 4/3*t = 0.
-2/5, 0, 2/3
Suppose -7 - 1 = -k. Suppose -5*c + 16 = -3*n, 0*c - k = c + 5*n. Factor 2/9*q**c + 0 - 2/9*q.
2*q*(q - 1)/9
Let l(v) be the second derivative of v + 1/2*v**2 - 1/3*v**3 + 1/12*v**4 + 0. Solve l(z) = 0 for z.
1
Factor 1/6*p**3 + 0*p + 0 - 1/3*p**2.
p**2*(p - 2)/6
Let c(z) be the third derivative of -z**7/105 - 11*z**6/240 - 3*z**5/40 - z**4/48 + z**3/12 + 18*z**2. Find w such that c(w) = 0.
-1, 1/4
Let f = -115 - -72451/630. Let l(c) be the third derivative of -1/360*c**6 - 1/180*c**5 + 0*c**3 + 2*c**2 + 0*c + f*c**7 + 1/72*c**4 + 0. Factor l(n).
n*(n - 1)**2*(n + 1)/3
Let o(f) be the third derivative of -f**7/630 - f**6/240 + f**5/120 - f**4/3 - 11*f**2. Let h(g) be the second derivative of o(g). Factor h(c).
-(c + 1)*(4*c - 1)
Let g(f) be the first derivative of -1/42*f**7 - 3 + 0*f**2 + 0*f**6 + 0*f**4 + f + 1/10*f**5 - 1/6*f**3. Let d(l) be the first derivative of g(l). Factor d(t).
-t*(t - 1)**2*(t + 1)**2
Suppose -2*w + 16 = 4*f, 0 = -6*w + 4*w + 4*f. Factor -2*v**2 + w*v**2 + 0 - 2.
2*(v - 1)*(v + 1)
Let h(o) be the second derivative of o**6/10 - 7*o**4/4 - 3*o**3 - 30*o. Factor h(c).
3*c*(c - 3)*(c + 1)*(c + 2)
Let x(p) be the first derivative of -p**6/2520 + p**5/420 - p**4/168 + 3*p**3 + 1. Let b(a) be the third derivative of x(a). Determine k so that b(k) = 0.
1
Let u be (7/14)/(1/6). Factor -3*o**4 + 0*o + 2*o**u + 8*o**4 - 2*o**2 - 2*o - 3*o**4.
2*o*(o - 1)*(o + 1)**2
Let u(t) be the second derivative of -t**7/126 - t**6/90 + t**5/10 - t**4/18 - 5*t**3/18 + t**2/2 + 2*t. Factor u(q).
-(q - 1)**3*(q + 1)*(q + 3)/3
Let k(g) be the third derivative of -5*g**5/12 - 5*g**4/12 - g**3/6 + 10*g**2. Factor k(r).
-(5*r + 1)**2
Let q(f) = -7*f**2 + 13*f + 47. Let l(h) = 4*h**2 - 6*h - 24. Let t(m) = 11*l(m) + 6*q(m). Factor t(b).
2*(b + 3)**2
Suppose 46/7*p**2 - 2*p**3 + 8/7 - 40/7*p = 0. Calculate p.
2/7, 1, 2
Factor -9*d - 3*d**2 - 5*d + 4*d**2 + 8*d.
d*(d - 6)
Let l = -382 - -18337/48. Let c(m) be the second derivative of -1/24*m**3 - 2*m + 0 - l*m**4 + 0*m**2. Factor c(i).
-i*(i + 1)/4
Let v be ((-54)/(-12))/9*(-60)/(-4). Factor 21/2*o**2 + 0 + 3*o + 3/2*o**5 + v*o**4 + 27/2*o**3.
3*o*(o + 1)**3*(o + 2)/2
Let t(p) = -8*p**2 + 6*p + 14. Let i(c) = -3*c**2 + 2*c + 5. Let h(d) = 11*i(d) - 4*t(d). Factor h(z).
-(z + 1)**2
Let m(h) = h**3 + 4*h**2 + 2*h + 2. Let s be m(-3). Let u(w) = w**2 + s*w - w - 5*w**3 - w**2. Let k(q) = 9*q**3 - 7*q. Let y(l) = 4*k(l) + 7*u(l). Factor y(n).
n**3
Let d(r) be the first derivative of -r**4/6 + r**3/3 + r + 3. Let w(t) be the first derivative of d(t). Find b such that w(b) = 0.
0, 1
Let j be ((-6)/(-24) - 0)*11. Find d such that j*d**3 + 0 + 9/4*d**4 + 1/2*d**2 + 0*d = 0.
-1, -2/9, 0
Let u(w) be the third derivative of w**7/315 - w**6/75 + w**5/50 - w**4/90 + 9*w**2 + 2. Determine i, given that u(i) = 0.
0, 2/5, 1
Suppose -4*s = -0 - 16. Suppose u + 0 = 2. Factor -2/7*b**5 + 0*b**s + 0 + 0*b**u + 4/7*b**3 - 2/7*b.
-2*b*(b - 1)**2*(b + 1)**2/7
Let w(j) be the second derivative of 2*j**7/63 - 2*j**5/15 + 2*j**3/9 + 7*j. Determine n so that w(n) = 0.
-1, 0, 1
Let x(w) be the second derivative of -w**6/60 + w**4/12 - w**2 + 3*w. Let h(d) be the first derivative of x(d). Suppose h(o) = 0. Calculate o.
-1, 0, 1
Let w(d) be the first derivative of -3/2*d**2 + 3*d + 3/4*d*