- 4/9*f**2 - 2/9*f**4. Factor v(j).
-2*(j + 1)**4/9
Suppose -2/3*n + 0 - 2/3*n**3 - 4/3*n**2 = 0. Calculate n.
-1, 0
Factor -2/3 - 1/3*z**2 - z.
-(z + 1)*(z + 2)/3
Let h(u) be the second derivative of -u**5/10 + u**4/18 + 2*u**3/9 + 3*u. Factor h(t).
-2*t*(t - 1)*(3*t + 2)/3
Suppose 4*w = 5*s - 35, 2 = -s + 2*w + 15. Let -4*y + 2 - 2 + 2*y**2 + 4*y**3 - 2*y**4 + 0*y**s = 0. Calculate y.
-1, 0, 1, 2
Let q(t) be the third derivative of 1/210*t**7 + 1/24*t**4 + t**2 + 0*t**3 + 0 - 1/120*t**6 - 1/60*t**5 + 0*t. Determine n, given that q(n) = 0.
-1, 0, 1
Let y(k) = -k**2 - 5*k - 4. Let v be y(-4). Let i(x) be the second derivative of v + 0*x**3 - 3*x + 1/48*x**4 + 0*x**2. Factor i(l).
l**2/4
Let w(z) be the first derivative of 3*z + 1/24*z**4 + 1/12*z**3 + 0*z**2 + 1. Let c(d) be the first derivative of w(d). Factor c(y).
y*(y + 1)/2
Let g(o) be the first derivative of 32*o**3/5 - 8*o**2/5 + 2*o/15 - 41. Factor g(x).
2*(12*x - 1)**2/15
Factor 0*c + 0 + 4/9*c**3 + 2/9*c**4 + 2/9*c**2.
2*c**2*(c + 1)**2/9
Let o(c) be the first derivative of -c**5/150 + c**4/90 - 2*c - 6. Let s(p) be the first derivative of o(p). Determine z so that s(z) = 0.
0, 1
Let c(h) be the first derivative of h**5/120 - h**3/12 - 3*h**2/2 + 3. Let y(r) be the second derivative of c(r). Factor y(a).
(a - 1)*(a + 1)/2
What is w in 0 + 3/2*w - 3*w**2 = 0?
0, 1/2
Suppose -5*h + u - 4 = -23, -20 = -4*h + 2*u. Suppose -37 + 9 = -14*f. Factor -3*g**h + 7*g**f - 17*g**3 + 10*g**4 - 2*g**5 - 10*g + 13*g**2 + 2.
-2*(g - 1)**5
Suppose m - 12 + 10 = 0. Let t be (m/(-6))/(22/(-33)). Factor 1/2 + t*r**2 - r.
(r - 1)**2/2
Let m(k) be the first derivative of 4*k**4 - 2/5*k**5 + 1 + 32*k**2 - 32*k - 16*k**3. Factor m(b).
-2*(b - 2)**4
Let p(g) be the second derivative of 0 + 2/3*g**3 + 6*g + 3/25*g**5 - 3/5*g**2 - 1/75*g**6 - 2/5*g**4. Let p(t) = 0. Calculate t.
1, 3
Let y(k) = k**5 - k**3 - k**2 + k - 1. Let r(h) = 5*h**5 - 3*h**4 - 7*h**3 - 3*h**2 + 8*h - 6. Let p(w) = r(w) - 6*y(w). Find n such that p(n) = 0.
-2, -1, 0, 1
Let a be (-1)/(1 + 8/(-6)). Find l, given that 9*l**4 + 11*l + 10*l**3 - 9*l**2 - 17*l - 4*l**a = 0.
-1, -2/3, 0, 1
Let i(y) be the third derivative of 1/1344*y**8 + 0*y**4 + 0*y**3 - 3*y**2 + 0*y - 1/840*y**7 - 1/240*y**6 + 0*y**5 + 0. Factor i(t).
t**3*(t - 2)*(t + 1)/4
Let i = 4 + -3. Let g(k) = 2*k**2. Let t be g(i). Factor -4 - 6*f**4 - 20*f**2 + 22*f**3 + 0*f**4 - 10*f**t + 18*f.
-2*(f - 1)**3*(3*f - 2)
Let y(p) be the third derivative of p**8/504 - p**7/63 + p**6/18 - p**5/9 + 5*p**4/36 - p**3/9 - 3*p**2. Solve y(d) = 0.
1
Let f = -86 + 517/6. Let g(j) be the third derivative of -f*j**3 + 0 + 0*j + 0*j**4 + 1/60*j**5 + j**2. Factor g(c).
(c - 1)*(c + 1)
Let u(b) be the second derivative of -13*b**5/25 + 11*b**4/15 + 4*b**3/15 + b. Suppose u(g) = 0. What is g?
-2/13, 0, 1
Factor -12*o + 12*o**3 + 51 - 2*o**2 - 54 + 5*o**2.
3*(o - 1)*(o + 1)*(4*o + 1)
Let z = -5 + 4. Let y = z + 3. Factor 1 + 3*k - 2*k**3 + 1 - k - 2*k**y.
-2*(k - 1)*(k + 1)**2
Let c(f) = -f**3 + 4*f**2 - 4*f + 2. Suppose -2*q - 4*h + 7 = -3*h, 4*q - 2 = 2*h. Let p be c(q). Let 3/2 - 3/2*x**3 - 9/2*x + 9/2*x**p = 0. What is x?
1
Let z(m) be the first derivative of m**6/135 - m**5/18 + m**4/6 - 7*m**3/27 + 2*m**2/9 + m - 2. Let t(p) be the first derivative of z(p). Factor t(o).
2*(o - 2)*(o - 1)**3/9
Let j(i) = -4*i**3 - 38*i**2 - 96*i - 76. Let s(u) = 8*u**3 + 77*u**2 + 192*u + 150. Let v(f) = 5*j(f) + 2*s(f). Solve v(g) = 0 for g.
-5, -2
What is a in 0 - 8/7*a**5 + 12/7*a**3 - 2*a**4 - 4/7*a + 2*a**2 = 0?
-2, -1, 0, 1/4, 1
Factor -1/2*d**2 - 3/4*d - 1/4.
-(d + 1)*(2*d + 1)/4
Factor 2/9*i**3 - 4/9 - 2/3*i + 0*i**2.
2*(i - 2)*(i + 1)**2/9
Let f(s) be the second derivative of -1/12*s**3 + 1/40*s**5 + 0 + s + 1/2*s**2 - 1/12*s**4. Factor f(c).
(c - 2)*(c - 1)*(c + 1)/2
Suppose -8/19*w**2 - 2/19*w**3 - 4/19 - 10/19*w = 0. Calculate w.
-2, -1
Let s(j) = -j**3 + 7*j**2 - 2*j - 38. Let c be s(5). Solve 1/2*h**c - 1/4 + 0*h + 0*h**3 - 1/4*h**4 = 0.
-1, 1
Let r(a) = a**3 - 4*a**2 + 4*a - 1. Let q be r(3). Suppose -24 + 0*m**3 - q*m**2 - 16*m**2 + 3*m**3 + 33*m + 3*m = 0. What is m?
2
Let c(w) be the second derivative of w + 1/3*w**3 - 1/5*w**5 + 0 + 1/21*w**7 - 1/3*w**4 + 1/15*w**6 + w**2. Factor c(b).
2*(b - 1)**2*(b + 1)**3
Let q(u) be the third derivative of -u**6/360 + u**5/180 + 15*u**2. Factor q(d).
-d**2*(d - 1)/3
Let p(k) be the second derivative of k + 0 + 1/12*k**4 + 0*k**3 + 0*k**2. Factor p(i).
i**2
Let w = 14 + -2. Let o be w/(-18) + (-16)/(-6). What is v in 5*v**3 - 2*v**4 - 2*v - v**3 + 4*v**4 - o*v**2 - 2*v = 0?
-2, -1, 0, 1
Let x = 14/335 + -8251/13065. Let z = x + 12/13. Factor -2/3*d**2 + 0 - 1/3*d - z*d**3.
-d*(d + 1)**2/3
Let u(z) be the first derivative of -z**6/360 + z**5/60 - z**3 + 2. Let l(v) be the third derivative of u(v). Suppose l(o) = 0. What is o?
0, 2
Suppose 3*t - 21 = 5*v, -4*t = 4*v + 1 + 3. Factor y + y**2 + 2*y**3 - 2*y**3 + y**4 - t*y**4 - y**3.
-y*(y - 1)*(y + 1)**2
Determine f, given that -75/2*f**2 + 0*f + 0 - 3/2*f**4 + 15*f**3 = 0.
0, 5
Let p(g) = -4*g + 3. Let u(j) = -9*j + 5. Let a(o) = -7*p(o) + 3*u(o). Let v be a(8). Let -1/2*y**v + 1/2*y**5 + 1/2*y**4 + 0*y - 1/2*y**3 + 0 = 0. Calculate y.
-1, 0, 1
Let h(o) be the second derivative of -2*o**7/21 + 3*o**5/5 + 2*o**4/3 - 15*o. Factor h(l).
-4*l**2*(l - 2)*(l + 1)**2
Let x(g) = -g**2 + g. Let a(b) = -2*b**2 + 2*b. Let t(s) = -6*a(s) + 13*x(s). Factor t(i).
-i*(i - 1)
Suppose 0 = 9*x - 4*x - 50. Let p = x + -6. Let -14/5*q**5 - 16/5 - 44/5*q**2 + 10*q**3 + 24/5*q**p - 72/5*q = 0. Calculate q.
-1, -2/7, 2
Let o = 15 - 12. Suppose 1 + 5 = o*l. Factor 3/2*j**2 + 0 + 1/2*j - l*j**3.
-j*(j - 1)*(4*j + 1)/2
Suppose 14 - 2 = 2*w. Suppose 5*g + w - 21 = 0. Suppose 0 + 0*v - 4*v**5 + 4/3*v**2 + 26/3*v**4 - 6*v**g = 0. Calculate v.
0, 1/2, 2/3, 1
What is k in 45 + 5*k**2 - 12*k - 2*k**2 - 36 = 0?
1, 3
Let v(u) = 20*u**3 + 5*u**2 - 8*u + 17. Let y(c) = 7*c**3 + 2*c**2 - 3*c + 6. Let h(d) = -6*v(d) + 17*y(d). Suppose h(s) = 0. What is s?
0, 1, 3
Let o be ((-52)/(-13))/(0 - -1). Let c(g) be the first derivative of -1/7*g**o - 2/35*g**5 + 0*g**3 - 1 + 2/7*g**2 + 2/7*g. Determine a so that c(a) = 0.
-1, 1
Factor 0 - 12/11*i**3 + 10/11*i**2 + 2/11*i**4 + 0*i.
2*i**2*(i - 5)*(i - 1)/11
Let m = 255 + -253. Factor -5/4*k**m - 3/4*k - 1/4*k**3 + 9/4.
-(k - 1)*(k + 3)**2/4
Let z(i) be the first derivative of -1/10*i**5 + 0*i**2 + 0*i**4 + 0*i + 0*i**3 - 2. Factor z(m).
-m**4/2
Let i = 432/5 + -86. Find q, given that 8/5*q - 8/5*q**2 + 0 + i*q**3 = 0.
0, 2
Let h(i) be the second derivative of i**6/45 + 17*i**5/120 + i**4/3 + 13*i**3/36 + i**2/6 - 4*i. Suppose h(c) = 0. Calculate c.
-2, -1, -1/4
Let s(j) be the second derivative of j**5/5 - 7*j**4/3 + 16*j**3/3 + 32*j**2 - 10*j. Factor s(l).
4*(l - 4)**2*(l + 1)
Determine i, given that -802*i**4 + 2*i**5 - 2*i**3 + 802*i**4 = 0.
-1, 0, 1
Let u(v) be the third derivative of v**5/15 - v**4/6 + 4*v**2. What is o in u(o) = 0?
0, 1
Let x = 8/503 - -6586/28671. Let k = x + 457/228. Suppose 3/4*m**2 - 1 + k*m**3 - 2*m = 0. Calculate m.
-2/3, 1
Suppose -k + 5*k - 4 = 0. Let z(b) be the first derivative of 2/3*b**3 + b**2 + 0*b + k. Determine s so that z(s) = 0.
-1, 0
Let x = -82 - -167. Let c be 34/x*(0 + 3). Find t such that c*t + 2/5*t**3 - 6/5*t**2 - 2/5 = 0.
1
Let p(m) be the second derivative of m**6/1260 + m**5/210 - 2*m**3/3 - 4*m. Let y(f) be the second derivative of p(f). Factor y(q).
2*q*(q + 2)/7
Let g = -4 + 4. Suppose 0*x - 3*x = -6. Find l such that -1/2*l**x + g + 0*l = 0.
0
Let s be 0/((-1)/2*2). Suppose -4*v - 8 = 4*n, -3*n + s = v + 10. Suppose 2/7*f**4 + 0*f**v - 2/7 - 4/7*f**3 + 4/7*f = 0. What is f?
-1, 1
Let c be (-3 + 6)*1 - 10. Let l = c - -7. Determine t so that l - 2/9*t - 2/9*t**2 = 0.
-1, 0
Suppose -3*j + 4*j - 3*j = 0. Factor 10/3*i**2 + j - 2/3*i.
2*i*(5*i - 1)/3
Let s be (-7 + 4 - -5) + 54/(-33). Let n = 37 + -405/11. Suppose 0 + s*k + n*k**2 = 0. What is k?
-2, 0
Let b = -84 + 90. Let w(q) be the first derivative of 1/5*q**4 + 3 + 0*q + 0*q**2 + 2/5*q**5 + 1/5*q**b + 0*q**3. What is p in w(p) = 0?
-1, -2/3, 0
Determine c, given that 24*c - 24*c + 4*c**2 = 0.
0
Let l(m) be the first derivative of -m**6/120 + m**5/40 - m**3/12 + m**2/8 + m - 4. Let n(p) be the fi