- 2*a(v). Solve c(n) = 0 for n.
-2, 0
Let l(a) be the third derivative of -a**5/36 + 5*a**4/36 - 5*a**3/18 + 47*a**2. Factor l(z).
-5*(z - 1)**2/3
Let z(g) = -2*g**2 + 30*g + 8. Let k(n) = n**2 + n + 1. Let l(v) = -12*k(v) + z(v). Determine h so that l(h) = 0.
2/7, 1
Let m(w) = 11*w**2 - 5*w. Let f(j) = -7*j**2 + 3*j. Let l(p) = -8*f(p) - 5*m(p). Let s be l(-2). Factor -4*g**s - 2*g**2 + 8*g**2.
2*g**2
Suppose 6*a - a = z - 11, 0 = -5*z + 4*a + 13. Let r = 4 + z. Factor -6*d**4 + 4*d + 2 - r*d**3 + d**3 + 4*d**4.
-2*(d - 1)*(d + 1)**3
Let v(r) be the third derivative of r**5/15 - r**4/2 + 4*r**3/3 + 12*r**2. Factor v(g).
4*(g - 2)*(g - 1)
Suppose 22*t = -3*k + 17*t - 10, t = 4*k - 2. Factor 1/2*j**3 + 0*j**2 + 0*j + j**4 + 1/2*j**5 + k.
j**3*(j + 1)**2/2
Suppose 0 = -2*m + 2*n - 2, -3*m = -m - 4*n + 8. Let y = 11 + -5. Factor -m*o**2 + 4*o + 3 - y + 3.
-2*o*(o - 2)
Let a(c) be the third derivative of c**6/24 - 7*c**5/4 + 245*c**4/8 - 1715*c**3/6 - 4*c**2. Solve a(b) = 0.
7
Let 7*j + j - 4*j**2 + 4*j**4 + 3*j**2 - 3*j**2 - 8*j**3 = 0. Calculate j.
-1, 0, 1, 2
Let d = 10942/1599 + -310/41. Let q = -5/13 - d. Let -2/3*o - 1/3 - q*o**2 = 0. What is o?
-1
Let h = 77 - 22. Let n be ((-6)/(-20))/(66/h). Factor -n*o + 1/4*o**3 - 1/4*o**2 + 1/4*o**4 + 0.
o*(o - 1)*(o + 1)**2/4
Let f = -8 + 8. Suppose f = 3*d + 21 - 69. Find y, given that 6*y**4 - 6*y**4 - d*y**4 - 20*y**4 - 12*y**3 - 27*y**5 = 0.
-2/3, 0
Let t(i) be the third derivative of 0*i - 1/60*i**5 - 2/3*i**3 + 3*i**2 + 1/6*i**4 + 0. Factor t(u).
-(u - 2)**2
Let y(q) be the first derivative of q**5/5 - q**4/4 - 1. Solve y(f) = 0 for f.
0, 1
Let z(x) = -x**3 + 6*x**2 - 10*x + 27. Let w be z(5). Let 2/3*a - 1/6*a**w - 2/3 = 0. Calculate a.
2
Suppose -2*t + 3 = -1. Find p, given that -3*p**2 + 4*p**2 - p**t - 3*p**2 - 3*p = 0.
-1, 0
Let n = -26 + 30. Let q(s) be the third derivative of -s**2 - 1/300*s**6 - 1/150*s**5 + 1/15*s**3 + 1/60*s**n + 0 + 0*s. Factor q(g).
-2*(g - 1)*(g + 1)**2/5
Suppose -4/9 - 2/9*w**2 - 2/3*w = 0. Calculate w.
-2, -1
Let u(k) = k**2 + 3*k + 3. Let g be u(-4). Let j be 84/24*4/g. Solve -j*x**3 - 3/2*x**2 + 2 + 2*x - 1/2*x**4 = 0 for x.
-2, -1, 1
Let s(b) be the first derivative of -b**6/2 - 12*b**5/5 - 9*b**4/2 - 4*b**3 - 3*b**2/2 - 6. Factor s(a).
-3*a*(a + 1)**4
Let l(d) be the first derivative of -2*d**3/3 + 3*d**2/2 - d - 34. Factor l(v).
-(v - 1)*(2*v - 1)
Let t(o) be the second derivative of -32*o**6/15 - 8*o**5/5 + 5*o**4 + 16*o**3/3 + 2*o**2 - 15*o. Solve t(b) = 0 for b.
-1, -1/4, 1
Factor 0 - 1/3*h**2 - 5/3*h.
-h*(h + 5)/3
Let v = -24 + 73/3. Find w, given that 1/3*w**2 - v + 0*w = 0.
-1, 1
Factor 3/2*z + 0 - 9/4*z**2 + 3/4*z**3.
3*z*(z - 2)*(z - 1)/4
Let n(m) = m**2 - m. Let b be n(1). What is i in 0*i**4 + 2*i**4 + 8*i**3 + 8*i**2 + b*i**4 + 0*i**4 = 0?
-2, 0
Let t(j) = 2*j**2 + 8*j - 3. Let d be t(-5). Let f be (-21)/d + (-58)/(-18). Factor -f*p**2 + 0 - 2/9*p**3 + 0*p.
-2*p**2*(p + 1)/9
Let w = 14 + -1. Suppose -w*i + 10*i**2 - 2*i + i + 4 = 0. Calculate i.
2/5, 1
Let i(w) be the second derivative of -w**6/720 - w**5/240 + w**4/24 - 2*w**3/3 + 4*w. Let c(q) be the second derivative of i(q). Factor c(o).
-(o - 1)*(o + 2)/2
Let x be 1/3 - (602/294 - 3). Factor -6/7 - 3/7*q**2 - x*q.
-3*(q + 1)*(q + 2)/7
Let l(k) be the first derivative of -k**9/9072 + k**7/630 - k**6/540 - k**5/120 + k**4/36 + 5*k**3/3 + 2. Let d(f) be the third derivative of l(f). Factor d(j).
-(j - 1)**3*(j + 1)*(j + 2)/3
Let w(f) = -2*f**2 + 1. Let j(t) = -7*t**2 + 24*t - 141. Let b(r) = j(r) - 3*w(r). Factor b(l).
-(l - 12)**2
Factor 12/7 + 21*u**3 + 33*u**2 + 96/7*u.
3*(u + 1)*(7*u + 2)**2/7
Let a(x) be the second derivative of x**6/56 - 3*x**5/140 - x**4/28 - x**2 + 6*x. Let g(q) be the first derivative of a(q). Factor g(y).
3*y*(y - 1)*(5*y + 2)/7
Let b(m) be the first derivative of m**6/120 - 2*m**3/3 + 4. Let n(v) be the third derivative of b(v). Let n(h) = 0. What is h?
0
Suppose 9*k + 450 = 4*k. Let z be (-3)/k*4*5. Factor 4/3*f**4 - z*f**3 - 2/3*f**5 + 0*f + 0 + 0*f**2.
-2*f**3*(f - 1)**2/3
Suppose -5*m = -2*m + 4*m. Determine n so that 1/2*n**2 + 1/4*n**3 + m + 1/4*n = 0.
-1, 0
Let p(d) be the third derivative of 0 - 3*d**2 + 1/90*d**5 + 0*d**3 - 1/18*d**4 + 0*d. Factor p(b).
2*b*(b - 2)/3
Let k(h) be the first derivative of 2/33*h**3 - 5 - 2/11*h**2 - 6/11*h. Suppose k(o) = 0. What is o?
-1, 3
Let f = -43 + 43. Let k(b) be the second derivative of 0*b**3 + 1/30*b**6 + 0 + b + 0*b**2 + f*b**4 + 0*b**5. Factor k(a).
a**4
Let p(b) be the first derivative of 1/20*b**5 + 7/16*b**4 + 2*b + 5/2*b**2 + 3/2*b**3 - 2. Factor p(a).
(a + 1)*(a + 2)**3/4
Let o = 147 + -142. Let y(m) be the third derivative of 4*m**2 + 0*m**4 + 0*m - 1/240*m**6 + 1/120*m**o + 0 + 0*m**3. Find f, given that y(f) = 0.
0, 1
Let x(a) be the first derivative of -5 - 4*a**2 + 4 + 2*a**3 + 4*a - 6*a**3. Suppose x(p) = 0. Calculate p.
-1, 1/3
Let i(o) be the first derivative of -o**6/18 + 2*o**5/15 + o**4/6 - 4*o**3/9 - o**2/6 + 2*o/3 + 13. What is u in i(u) = 0?
-1, 1, 2
Let z(a) be the third derivative of -a**6/60 + a**5/5 - a**4 + 8*a**3/3 - a**2. Suppose z(y) = 0. Calculate y.
2
Suppose n**3 + 39*n**2 + 2197 + 309*n + 151*n - 34*n + 81*n = 0. What is n?
-13
Let u(v) = v**3 - 14*v**2 - v + 17. Let r be (-1 + 8)/((-8)/(-16)). Let o be u(r). Factor 2/3*p + 4/3*p**4 + 0 + 10/3*p**o + 8/3*p**2.
2*p*(p + 1)**2*(2*p + 1)/3
Let d(n) be the second derivative of 0 + 2*n + 1/6*n**2 + 0*n**3 - 1/36*n**4. Factor d(m).
-(m - 1)*(m + 1)/3
Let u be -9 + 6 + 0 + 1029. Let v be 2/17 + u/1683. Determine t so that -v*t**2 + 6/11*t**3 - 2/11*t + 4/11 = 0.
-2/3, 1
Let v = -62 + 110. Factor -93*d**2 - 27*d**2 - 9 + v*d**3 + 8*d - 77*d.
3*(d - 3)*(4*d + 1)**2
Let w = -10 - -16. Suppose 4*r = -w + 30. Factor 6*f**3 + 3*f**4 - 3 - 8*f**2 + 3*f**2 - r*f + 5*f**2.
3*(f - 1)*(f + 1)**3
Let m(q) be the third derivative of -2*q**7/105 + 7*q**2. Solve m(u) = 0.
0
Let y(w) = -2 + 6 + w + 1. Let h be y(-5). Factor h + 0*b + 0*b**2 + 0*b**3 + 1/5*b**4.
b**4/5
Let b = 1656/7 - 236. Let 7*d**5 - b - 16/7*d + 23/7*d**2 - 17*d**4 + 67/7*d**3 = 0. Calculate d.
-2/7, 1
Let k(h) be the first derivative of 1/14*h**5 - 3 - 1/21*h**4 + 0*h**3 + 0*h**2 + 4*h. Let u(f) be the first derivative of k(f). What is w in u(w) = 0?
0, 2/5
Let c(w) be the second derivative of -w**8/504 + w**7/105 - w**6/60 + w**5/90 - 7*w**2/2 - 7*w. Let b(m) be the first derivative of c(m). Solve b(p) = 0.
0, 1
Let b(o) be the second derivative of 3*o**5/5 + 4*o**4/3 - 2*o**3/3 - 4*o**2 - 10*o. Find r such that b(r) = 0.
-1, 2/3
Let y(s) = 14*s**5 + 20*s**4 - 2*s**3 - 8*s. Let g(j) = 5*j**5 + 7*j**4 - j**3 - 3*j. Let n(z) = -8*g(z) + 3*y(z). Determine v so that n(v) = 0.
-1, 0
Let x(h) be the second derivative of 5*h + 0 - 1/40*h**5 + 0*h**3 + 1/30*h**6 - 1/84*h**7 + 0*h**4 + 0*h**2. Find j, given that x(j) = 0.
0, 1
Let d be (-1)/3*(4 - 13). Let h = -2 + 4. Factor 4*c - d + 4 + 2*c**h + 1.
2*(c + 1)**2
Let d(r) be the second derivative of -1/21*r**4 - 4*r + 1/70*r**5 + 0*r**2 + 1/21*r**3 + 0. Factor d(n).
2*n*(n - 1)**2/7
Find r such that 9*r**2 + 231 + 3*r - 3*r**4 - 237 + 0*r - 3*r**3 = 0.
-2, -1, 1
Determine l so that -2/5*l - 4/5 + 2/5*l**2 = 0.
-1, 2
Let n = 0 + 13. Let r = n + -9. Solve 3*v**4 - 3*v**r - v**4 - v**3 + 2*v**5 = 0.
-1/2, 0, 1
Find z, given that -32/3*z**4 + 28/3*z**2 + 8/3*z**3 - 22/3*z + 14/3*z**5 + 4/3 = 0.
-1, 2/7, 1
Factor -16/7 - 1/7*l**2 - 8/7*l.
-(l + 4)**2/7
Let l(r) = r**4 - r**3 + r**2 + 1. Let a(t) = -t**5 + 7*t**4 - 3*t**3 + t**2 + 2*t + 6. Suppose 0 = -3*n + 2 + 1. Let f(d) = n*a(d) - 6*l(d). Factor f(b).
-b*(b - 1)**3*(b + 2)
Factor -i**2 - 98*i + 95*i - 2*i**2.
-3*i*(i + 1)
Let a(w) = -2*w**3 + 33*w**2 + 100*w + 75. Let o(z) = -z**3 - z. Let n(u) = a(u) - 5*o(u). Determine d so that n(d) = 0.
-5, -1
Suppose 0*z + 232 = 3*z + n, 5*n - 224 = -3*z. Let u = z - 388/5. Factor -u*a**4 + 0 + 2/5*a**2 - 1/5*a + 1/5*a**5 + 0*a**3.
a*(a - 1)**3*(a + 1)/5
Let i be 2 + 1 - (1 + (-4)/10). Let 3/5 + 9*o**2 - 21/5*o - 39/5*o**3 + i*o**4 = 0. Calculate o.
1/4, 1
Let z(u) = u**2 - 6*u + 2. Let g be z(6). Let f = 5 - 0. Find y such that 3*y - f*y + y**g - 3*y**2 = 0.
-1, 0
Suppose l - 6*m + m + 9 = 0, -2*l - 11 = -3*m. Let a be (1 + l/6)*15. Factor 1/2*h**4 + 0 +