1
Let n(m) be the third derivative of m**6/960 + m**5/480 - 5*m**4/192 + m**3/16 - 23*m**2. Solve n(v) = 0.
-3, 1
Let f(a) be the third derivative of -a**6/360 + a**5/60 - a**4/24 + 2*a**3/3 + 3*a**2. Let x(l) be the first derivative of f(l). Determine h so that x(h) = 0.
1
Let d(h) be the third derivative of h**5/15 - h**4/3 + 7*h**2. Factor d(w).
4*w*(w - 2)
Suppose -105*f**2 + 126*f - f**3 + 135*f**2 + 5*f**3 + 98 - 2*f**3 = 0. What is f?
-7, -1
Factor 2/5*y + 0 + 2/5*y**3 - 4/5*y**2.
2*y*(y - 1)**2/5
Let b = 11 - 6. Factor t**2 - 34 + 38 - b*t**2.
-4*(t - 1)*(t + 1)
Let u(q) be the third derivative of 4*q**2 + 0*q + 0*q**3 - 1/525*q**7 + 1/840*q**8 + 1/150*q**5 - 1/300*q**6 + 0 + 0*q**4. Suppose u(h) = 0. Calculate h.
-1, 0, 1
Let y = 194656 - 132171639/679. Let i = -3/97 - y. Let 8/7 - 8/7*u + i*u**2 = 0. Calculate u.
2
Let i(k) be the second derivative of 2*k**7/21 - 2*k**6/15 - 3*k**5/5 + k**4/3 + 4*k**3/3 + 7*k. Factor i(w).
4*w*(w - 2)*(w - 1)*(w + 1)**2
Let x = 1455/4 - 363. Factor 3/4*l**2 + 3/2*l - x*l**3 + 0.
-3*l*(l - 2)*(l + 1)/4
Let v(k) be the second derivative of -k**5/4 - 5*k**4/6 + 40*k. Factor v(r).
-5*r**2*(r + 2)
Let o(q) = 3. Let x(h) = -h**2 - 6*h + 15. Let y(k) = 24*o(k) - 3*x(k). Let y(t) = 0. Calculate t.
-3
Let 8*d + 32*d**5 - 44*d**5 - 11*d**3 + 2 - 34*d**4 - 17*d**3 = 0. What is d?
-1, -1/3, 1/2
Suppose -5*a - 4*b - 7 = -27, -2*b = -10. Let f = 9/2 - 17/4. Solve a*q + 0 - f*q**3 + 1/4*q**2 = 0.
0, 1
Factor 2/11*q**2 - 2/11*q**3 + 0 + 4/11*q.
-2*q*(q - 2)*(q + 1)/11
Suppose n + 0*x - 1 = x, 5*n + 2 = -2*x. Suppose -17*q + 12*q + 15 = n. Factor 7/2*o**4 + 0 + 0*o + 1/2*o**2 + 5/2*o**q + 3/2*o**5.
o**2*(o + 1)**2*(3*o + 1)/2
Suppose -11*h + 13 = -9. Factor 0 - 2/7*o**3 - 8/7*o**h - 8/7*o.
-2*o*(o + 2)**2/7
Suppose -2 = n - 6. Let f(z) be the third derivative of 1/90*z**5 + z**2 - 1/36*z**n + 0*z + 0 - 2/9*z**3. Factor f(a).
2*(a - 2)*(a + 1)/3
Factor 0*u**2 + 1/4*u + 0 - u**3.
-u*(2*u - 1)*(2*u + 1)/4
Let j(f) be the second derivative of -1/27*f**4 + 0 - 1/27*f**3 + 1/189*f**7 + 0*f**2 - 4*f + 0*f**5 + 2/135*f**6. Factor j(b).
2*b*(b - 1)*(b + 1)**3/9
Let b be (((-4)/2)/(1/1))/(-3). Factor 2/3*j**2 + 1/3*j**5 + 0*j**3 + 0 - b*j**4 - 1/3*j.
j*(j - 1)**3*(j + 1)/3
Suppose -10*x + 5*x**5 - 15*x**2 + x**5 - 5*x**4 - 15*x**3 - x**5 + 40*x**2 = 0. What is x?
-2, 0, 1
Let l be (-4)/6*(-2 + -1). Find m such that -2*m**l + 8/3*m + 1/3*m**4 + 0*m**3 - 1 = 0.
-3, 1
Let k be 0/1 - (-12)/10. Let m be 96/190 - (4 + (-444)/114). Find t, given that 4/5*t - k*t**3 + m*t**2 + 0 = 0.
-2/3, 0, 1
Let w(v) be the second derivative of -v**5/20 + v**3/6 - 23*v. Factor w(g).
-g*(g - 1)*(g + 1)
Let d(r) be the third derivative of 0*r + 1/18*r**3 - 5*r**2 + 0 - 1/144*r**4 - 1/360*r**5. Find w, given that d(w) = 0.
-2, 1
Suppose 0 = 5*i + 5*v - 15, -28 + 5 = -5*i - v. Suppose -q**3 - q**3 + 3*q**3 + q**i + 2*q**4 = 0. What is q?
-1, 0
Find h such that -2/5 - 2/5*h**4 - 12/5*h**2 + 8/5*h**3 + 8/5*h = 0.
1
Let y(j) = -4*j**3 + j**2 + 5*j + 5. Let z(p) = 5*p**3 - 5*p - 6. Let h(b) = -6*y(b) - 5*z(b). Factor h(v).
-v*(v + 1)*(v + 5)
Factor 4/9*r**3 + 2/9*r**4 - 2/9*r**2 + 0 - 4/9*r.
2*r*(r - 1)*(r + 1)*(r + 2)/9
Let y be 3 + -1 - 2*-7. Suppose 2*m + 2 = -0*s - 5*s, 2*s = -5*m + y. Factor -4*x**3 + x**4 + 2*x**3 + x**m.
2*x**3*(x - 1)
Let c be 4*1*(-6)/(-12). Let a(y) be the first derivative of -9/4*y**4 - 13/5*y**5 - 2/3*y**3 + 0*y**c + 0*y - y**6 + 2. Determine r so that a(r) = 0.
-1, -2/3, -1/2, 0
Let j be (-4 - 33/(-6))*(-4)/(-33). Suppose 2/11*i**3 - 2/11*i + 2/11*i**2 - j = 0. What is i?
-1, 1
Suppose n - 5*n = -8. Let u be -2*n*(0 - 1). Factor -2*x**4 + 0*x - 2*x**2 + u*x**2 + x**5 - x.
x*(x - 1)**3*(x + 1)
Let j(o) be the first derivative of 3*o**4/4 - o**3 - 3*o**2/2 + 3*o + 8. Factor j(s).
3*(s - 1)**2*(s + 1)
Suppose -4*n = -5*s - 37, -2*s - 13 = 4*n - 5*n. Factor y**n - y**4 + 5 - 7*y - 1 - 3*y**2 + 3*y + 3*y**3.
-(y - 2)**2*(y - 1)*(y + 1)
Let d(z) be the third derivative of z**5/75 - z**4/10 + 4*z**3/15 + 2*z**2. Factor d(h).
4*(h - 2)*(h - 1)/5
Solve -1/2*u**2 + 5/2 - 2*u = 0 for u.
-5, 1
Let c = 944 + -12270/13. Factor c - 2/13*m - 2/13*m**2 + 2/13*m**3.
2*(m - 1)**2*(m + 1)/13
Let w = -293/80 + 65/16. Suppose 0 + w*v - 2/5*v**2 = 0. What is v?
0, 1
Find k, given that -16/3*k**4 + 4/3*k**2 + 7*k**3 + 0 + k**5 - 4*k = 0.
-2/3, 0, 1, 2, 3
Let g(j) be the second derivative of 0 + 2*j + 0*j**2 - 1/10*j**5 + 0*j**3 + 1/6*j**4. Factor g(n).
-2*n**2*(n - 1)
Let k(g) = -11*g**2 - 32*g + 3. Let q be k(-3). Solve 1/7*n**2 + q - 2/7*n = 0 for n.
0, 2
Let s(g) = g**2 - 5*g. Suppose -3*y - y + 20 = 0. Let f be s(y). Factor f*r**2 + 2*r - 6*r - r**2 - r**2.
-2*r*(r + 2)
Let m(b) be the second derivative of -b**5/20 + b**3/6 + 5*b. Factor m(g).
-g*(g - 1)*(g + 1)
Let m(d) be the second derivative of d**5/120 - d**4/4 + 3*d**3 - 18*d**2 - 10*d. Let m(w) = 0. Calculate w.
6
Let s = 76 + -71. Let z(o) be the second derivative of -1/2*o**2 + 0*o**4 + 1/4*o**3 + 0 - 1/40*o**s - 2*o. Factor z(f).
-(f - 1)**2*(f + 2)/2
Let a = 35 - 104/3. Let y(l) be the first derivative of l + a*l**3 - 2 + l**2. Factor y(s).
(s + 1)**2
Factor -20*p + 0*p - 12 - 4*p**2 - 14 + 2.
-4*(p + 2)*(p + 3)
Let r(x) be the third derivative of -1/48*x**4 - 1/1440*x**6 - 1/3*x**3 + 0 - 1/160*x**5 - 2*x**2 + 0*x. Let n(c) be the first derivative of r(c). Factor n(d).
-(d + 1)*(d + 2)/4
Suppose -1 - 3 = -2*d. Factor -8 - 2*f**d - 6*f + 6*f + 8*f.
-2*(f - 2)**2
Let m(n) = -n**3 - 10*n**2 + 10*n - 9. Let v be m(-11). Factor v + 75*f**2 + 5*f + 11*f + 1 + 14*f.
3*(5*f + 1)**2
Let w(h) be the third derivative of 1/30*h**5 + 5*h**2 + 0*h**3 + 1/30*h**4 + 0*h + 0. Find u such that w(u) = 0.
-2/5, 0
Let l(g) be the second derivative of 0*g**4 + 0*g**5 + 1/105*g**6 - 5*g + 0*g**2 - 1/147*g**7 + 0 + 0*g**3. Factor l(m).
-2*m**4*(m - 1)/7
Let y(b) = -b**4 + 3*b**2 - 5*b - 3. Let k(q) = -3*q**4 + 9*q**2 - 14*q - 8. Let x(r) = -3*k(r) + 8*y(r). Determine g, given that x(g) = 0.
-2, 0, 1
Suppose 28*x - 97 = -13. Factor -3/2*i**2 - 3*i + 0 + 3/2*i**4 + 3*i**x.
3*i*(i - 1)*(i + 1)*(i + 2)/2
Let w(g) = 24*g**4 - 48*g**3 + 4*g**2 + 24*g - 12. Let b(h) = 24*h**4 - 47*h**3 + 5*h**2 + 23*h - 11. Let o(n) = -4*b(n) + 3*w(n). Let o(y) = 0. Calculate y.
-2/3, 1/2, 1
Let j(u) = -u**4 - u**3 + u**2. Let x(g) be the first derivative of -4*g**5/5 - 3*g**4/2 + 2*g**3/3 + 2*g**2 + 2*g + 8. Let v(m) = -2*j(m) + x(m). Factor v(k).
-2*(k - 1)*(k + 1)**3
Let -45/4*o + 3/4*o**2 + 21/2 = 0. What is o?
1, 14
Let r(a) be the second derivative of 0*a**5 + a - 1/120*a**6 + 1/16*a**4 + 0 + 1/12*a**3 + 0*a**2. Factor r(q).
-q*(q - 2)*(q + 1)**2/4
Let q be 1/9 + (-201)/(-135). Factor 0 + 2/5*a**5 + q*a**4 + 8/5*a**2 + 12/5*a**3 + 2/5*a.
2*a*(a + 1)**4/5
Let t be -1*(12/(-21))/(5 - 4). Factor 2/7*c**2 + 2/7 + t*c.
2*(c + 1)**2/7
Let b(a) be the third derivative of -a**6/200 + a**5/60 - a**4/60 - 8*a**2. What is n in b(n) = 0?
0, 2/3, 1
Let z(f) be the second derivative of -f**4/6 - 4*f**3/3 - 3*f**2 + 7*f. Factor z(n).
-2*(n + 1)*(n + 3)
Determine x, given that 2*x**3 + 2*x - 2*x**2 - 6*x + 0*x**2 = 0.
-1, 0, 2
Let 48 - 36*d - 51 + 31*d**2 - 139*d**2 = 0. What is d?
-1/6
Let s be (-51)/17 + (-2)/((-2)/3). Let q(l) be the third derivative of 3*l**2 + 0 + 1/6*l**3 + 0*l**4 - 1/60*l**5 + s*l. Factor q(y).
-(y - 1)*(y + 1)
Let p(j) be the third derivative of 3*j**5/40 - j**3/3 - j**2. Find q such that p(q) = 0.
-2/3, 2/3
Let q(x) = x**5 - x**2 + x + 1. Let t(c) = 9*c**5 + 3*c**4 - 6*c**3 - 12*c**2 + 9*c + 9. Let i(f) = -6*q(f) + t(f). Determine h, given that i(h) = 0.
-1, 1
Find y, given that -21/5*y**2 + 16/5*y - 4/5 + 9/5*y**3 = 0.
2/3, 1
Let -4/11*x + 6/11 - 2/11*x**2 = 0. What is x?
-3, 1
Suppose -4*o = 3*t - 16, 3*o + 5*t = 7*t + 12. Solve 10/7*p**3 - 2/7*p + 2/7*p**2 + 0 + 6/7*p**o = 0 for p.
-1, 0, 1/3
Let i(b) = -b**2 + 8*b + 11. Let w be i(9). Let q(v) be the third derivative of -1/18*v**4 + 0*v**3 + v**w + 0*v + 1/90*v**5 + 0. Factor q(p).
2*p*(p - 2)/3
Let b = 30 - 30. Factor 0 - 3/2*f**3 + 1/2*f**2 - 1/2*f**5 + b*f + 3/2*f**4.
-f**2*(f - 1)**3/2
Let i(q) be the first derivative of -q**6/600 - 3*q**5/100 - 9*q**4/40 + 4*q**3/3 - 6. Let g(y) be the third derivative of i(y). Factor g(w).
-3*(w + 3)**2/5
Let p be 10/(