n**4/9 + 10*n**3/9 - 4*n**2/3 + 9*n. Solve w(r) = 0 for r.
1, 2
Suppose 4/5*a**2 - 2/5*a - 2/5*a**3 + 0 = 0. Calculate a.
0, 1
Let j(g) be the third derivative of g**5/20 - g**4/4 + g**3/2 - g**2. Determine w so that j(w) = 0.
1
Suppose 17*i**3 - 18*i**3 - 59*i**2 + 63*i**2 = 0. What is i?
0, 4
Let a(d) be the third derivative of d**7/280 - d**6/60 - 5*d**3/6 - 6*d**2. Let y(o) be the first derivative of a(o). Find u such that y(u) = 0.
0, 2
Let k = -6 - -3. Let o be (-12)/(-9) - 2/k. Solve -o*f**4 + 2*f**5 + 0*f**5 - 2*f**3 + 0*f**2 + 2*f**2 + 0*f**3 = 0.
-1, 0, 1
Let g be (-2 - 0/(-3)) + -4. Let o be 24/(-14) + (-4 - g). Factor 0*a**3 + 4/7*a**4 - 4/7*a**2 + 0 - 2/7*a**5 + o*a.
-2*a*(a - 1)**3*(a + 1)/7
Let n be -3*4/6 + 6. Determine k, given that 6*k**3 + 4*k - 2*k**n - 5*k**3 + 10*k**2 - 2*k**5 + 5*k**3 = 0.
-1, 0, 2
Let m be (-8)/(-10) - (-144)/(-30). Let t be (-3)/m - (-26)/8. Factor 2*s - 20/3*s**2 + 2*s**5 - 2/9 + 92/9*s**3 - 22/3*s**t.
2*(s - 1)**3*(3*s - 1)**2/9
Suppose -60 = 4*k + 336. Let m = k + 497/5. Factor 0 + m*u**2 - 2/5*u.
2*u*(u - 1)/5
Suppose 10 = q + 4*q. Let p = -10/3 + 23/6. Find f, given that -15/4*f**5 - 4*f**4 - p + 9/2*f**q - 1/4*f + 4*f**3 = 0.
-1, -2/5, 1/3, 1
Let u(m) be the third derivative of m**7/70 - m**6/10 + m**5/4 - m**4/4 + 22*m**2. Factor u(d).
3*d*(d - 2)*(d - 1)**2
Factor -42*x**3 + 32*x**3 + 4*x + 20 - 4 - 22*x**2.
-2*(x + 1)*(x + 2)*(5*x - 4)
Let o = 2 - 9. Let m(w) = w + 12. Let g be m(o). Suppose z**g - 5*z**5 + z**4 + 3*z**5 = 0. Calculate z.
0, 1
Let o be 5*8*(-7)/(-56). Find t such that -21/5*t**4 + 24/5*t - 73/5*t**3 + 17/5*t**2 + 4/5 + 49/5*t**o = 0.
-1, -2/7, 1
Let j(m) = -m**3 - 7*m**2 + 8*m. Let o be j(-8). Let w(n) be the third derivative of 0*n + 0*n**3 + 1/360*n**6 + 2*n**2 + 0 - 1/180*n**5 + o*n**4. Factor w(k).
k**2*(k - 1)/3
Let f(x) = 3*x**4 - 3*x**3 + 2*x**2 + 2. Let t = 1 - -3. Let k = 6 - t. Let i(m) = -m**4 + m**3 - m**2 - 1. Let r(j) = k*i(j) + f(j). Factor r(z).
z**3*(z - 1)
Let v(n) be the first derivative of 7*n**3 + 15/4*n**4 + 0*n + 3*n**2 - 1. Factor v(y).
3*y*(y + 1)*(5*y + 2)
Let s(d) be the first derivative of d**3/12 - d/4 + 7. Factor s(k).
(k - 1)*(k + 1)/4
Factor 22/15*t**2 - 16/15 - 28/5*t.
2*(t - 4)*(11*t + 2)/15
Let b(i) be the first derivative of 3*i**2 + 2/3*i**3 + 4*i + 4. Factor b(q).
2*(q + 1)*(q + 2)
Let v(k) be the first derivative of 1 - 1/5*k**5 + k + 0*k**2 + 0*k**4 + 0*k**3 - 1/15*k**6. Let m(w) be the first derivative of v(w). What is y in m(y) = 0?
-2, 0
Suppose 6 = -2*l + 4*r, -2*r - 3 = -4*l + r. Let s(x) be the first derivative of -1/3*x**2 + 0*x + 4 - 4/27*x**l. Factor s(c).
-2*c*(2*c + 3)/9
Let x(y) = -y + 11. Let i be x(6). Suppose -2*r + r = d + i, -r - 25 = 5*d. Factor r*g - 2/5*g**2 + 0.
-2*g**2/5
Let g(a) be the first derivative of a**3 - 3*a**2 + 3*a - 7. Solve g(m) = 0.
1
Let i be 0/(2/(-4)*-4). Suppose i = -3*g + 3*r - 9, -2*r = -9 - 1. Find z, given that 8/3*z + g*z**2 + 8/9 = 0.
-2/3
Factor 15*u**2 + 3*u**3 - 15*u**3 - 10*u + 7*u**3.
-5*u*(u - 2)*(u - 1)
Let w be (134/6)/(4/(-6)). Let v = -33 - w. Suppose v + 0*z - 1/2*z**2 = 0. Calculate z.
-1, 1
Suppose -12 = -3*f - 2*r, 4*r + 12 = 3*f - r. Let u(b) be the second derivative of 0*b**3 + 1/40*b**5 + 1/24*b**f + 0*b**2 + 2*b + 0. Factor u(w).
w**2*(w + 1)/2
Let o be (-3)/(6/(-4))*9/108. Let v(y) be the second derivative of 1/30*y**5 + o*y**4 + 0 + 2/9*y**3 + y + 0*y**2. Factor v(a).
2*a*(a + 1)*(a + 2)/3
Let s = 44 + -38. Let u(j) be the second derivative of 1/30*j**s + 0*j**3 - 2*j - 1/20*j**5 + 0 + 0*j**4 + 0*j**2. Find i, given that u(i) = 0.
0, 1
Suppose -2*b = -5*k + k - 8, 0 = 4*b - 3*k - 11. Factor -b*c**3 + c**3 + 3*c**3.
2*c**3
Suppose 4*c - 8 = d, -3*d - 3*c - 12 + 3 = 0. Let q be ((-2)/(-5))/(d/(-4)). Suppose -4/5*v - q - 2/5*v**2 = 0. What is v?
-1
Let h = -11 - -15. Let 6*s - 6*s - 6*s**h + 3*s**5 + 3*s**3 = 0. What is s?
0, 1
Let h(r) be the second derivative of 0 - 1/30*r**5 - 1/3*r**3 - 1/6*r**4 - 1/3*r**2 + 5*r. Factor h(g).
-2*(g + 1)**3/3
Let l(i) be the first derivative of -10/9*i**3 + 0*i + 2/3*i**2 + 1/2*i**4 + 4. Factor l(c).
2*c*(c - 1)*(3*c - 2)/3
Let w be -1 + (-3)/(-6)*6. Factor -3*g**5 + 3*g**3 + 2*g**2 + 0*g**2 - w*g**2.
-3*g**3*(g - 1)*(g + 1)
Let m(g) = 9*g**3 + 5. Suppose 0 = -3*p + 2*p + 26. Suppose 3*c = -3*v - 1 - 2, -p = 2*c - 4*v. Let w(r) = 14*r**3 + 8. Let f(h) = c*w(h) + 8*m(h). Factor f(t).
2*t**3
Let i(x) be the third derivative of 1/630*x**7 + 0 + 1/60*x**5 - 1/72*x**4 - 3*x**2 + 0*x**3 - 1/120*x**6 + 0*x. Factor i(z).
z*(z - 1)**3/3
Suppose 0*g + 13 = 2*g + 3*v, 5*g + 3*v - 28 = 0. Suppose 4*a - 11 = -3. Solve -2*j**3 + 3*j**5 - 2*j**3 + 5*j**g + a - 4*j - 16*j**2 + 14*j**4 = 0 for j.
-1, 1/4, 1
Let i(k) be the third derivative of -k**8/896 + k**7/280 - k**5/80 + k**4/64 - 8*k**2. Solve i(r) = 0 for r.
-1, 0, 1
Let i(g) = g**2 - 9*g + 10. Let r be i(8). Factor -3*h**4 - 3*h**r + 3*h + 2*h**4 + 0*h**2 + 3*h**3 - 2*h.
-h*(h - 1)**3
Let t(z) be the second derivative of 3*z**5/100 - 3*z**3/10 + 3*z**2/5 + 3*z. Solve t(g) = 0.
-2, 1
Let b = 339/430 + 1/86. Suppose 1/5*q**2 + b + 4/5*q = 0. What is q?
-2
Determine b so that -10/3*b**5 + 0 + 0*b - 8/3*b**2 + 14/3*b**4 + 16/3*b**3 = 0.
-1, 0, 2/5, 2
Suppose -2*d + 0 = 8. Let n(y) = 3*y**2 + y. Let q(x) = 5*x**2 + 2*x. Let i(z) = d*q(z) + 7*n(z). Factor i(u).
u*(u - 1)
Let t = 11 - -3. Let w be (12/t)/((-4)/(-28)). Suppose 4*m**3 - 3*m**5 + 4*m + m**5 - w*m = 0. Calculate m.
-1, 0, 1
Let w(n) = -n**3 - 7*n**2 - 41*n - 15. Let p(g) = 2*g**3 + 10*g**2 + 62*g + 22. Let j(b) = 5*p(b) + 8*w(b). Factor j(r).
2*(r - 5)*(r + 1)**2
Factor -b**4 + 5*b**3 - 3*b**4 + b**4 - 8*b**3.
-3*b**3*(b + 1)
Let i(w) be the second derivative of -w**6/150 + w**4/30 - w**2/10 + 14*w. Factor i(l).
-(l - 1)**2*(l + 1)**2/5
Let h = 13 + -9. Let k(o) be the first derivative of -3/5*o**5 + 3 - 1/5*o**3 + 0*o - 6/5*o**h + 3/5*o**2. Factor k(r).
-3*r*(r + 1)**2*(5*r - 2)/5
Let h be -2 + 14 + (2 - 3). Let j = h - 7. Factor 3*f**3 + 1/2*f + 0 - 2*f**j + 1/2*f**5 - 2*f**2.
f*(f - 1)**4/2
Suppose 2*a = 4*a. Let p(w) be the first derivative of a*w - 2 + 0*w**2 - 1/3*w**3. Factor p(q).
-q**2
Let x = -2104/5 + 421. Let c be 3/4 + 11/(-20). Factor -x*k**4 + 0*k**3 + 0*k + 0 + c*k**2.
-k**2*(k - 1)*(k + 1)/5
Let h(v) be the third derivative of v**5/30 + v**4/3 + 4*v**3/3 - 15*v**2. Determine d so that h(d) = 0.
-2
Let s(p) be the first derivative of 2*p**3/27 - 4*p**2/3 + 8*p + 1. Factor s(t).
2*(t - 6)**2/9
Suppose f = 5*a + 6, 3 = -f - 5*a - 1. Let j be f/(1 + -2) - -4. Solve c + 0*c**2 + 2*c**3 + 0*c - j*c**2 = 0.
0, 1/2, 1
Suppose -h + 5 = -3*k, -4*h - k + 105 = 4*k. Let q be 2/(-5) + 48/h. Factor -2/5*p - 6/5*p**q + 0.
-2*p*(3*p + 1)/5
Let v = 275/816 + -1/272. Factor -v*k**3 + 0 - 4/3*k**2 - 4/3*k.
-k*(k + 2)**2/3
Let x(u) = -5*u**2 - 17*u - 23. Let i(c) = -2*c**2 - 6*c - 8. Suppose 0*k - 2 = 2*h + 4*k, h = 3*k - 26. Let y(z) = h*i(z) + 4*x(z). Factor y(q).
2*(q - 2)*(q + 1)
What is c in -7/6*c + 3/2*c**2 + 1/3 + 1/6*c**4 - 5/6*c**3 = 0?
1, 2
Let h(k) = k**4. Let z(m) = 2*m**4 - 2*m**3 - m**2 - 3. Let l(b) = -3*h(b) + z(b). Let r(i) be the first derivative of l(i). Factor r(s).
-2*s*(s + 1)*(2*s + 1)
Let v(l) be the first derivative of 1/8*l**2 + 1/4*l - 1/12*l**3 + 3 - 1/16*l**4. What is z in v(z) = 0?
-1, 1
Suppose 0*a = 3*m - a + 16, -2*m - 5*a = 39. Let g be 42/24*(-3)/m. Factor 1/4 + 7/4*j**2 + g*j**3 + 5/4*j.
(j + 1)**2*(3*j + 1)/4
Suppose 2*l - 4 = -2*j, 0*l - l - 4*j = 1. Find n such that -10/11*n**2 + 2/11*n**l + 16/11*n - 8/11 = 0.
1, 2
Let v(h) = -5*h**2 - 2*h + 3. Let u(g) = 10*g**2 + 3*g - 7. Let w(s) = 3*u(s) + 7*v(s). Factor w(j).
-5*j*(j + 1)
Let d(o) be the first derivative of 1/4*o**4 - 2/3*o**3 + 1/2*o**2 - 1 + 0*o. Factor d(v).
v*(v - 1)**2
Suppose 3/2*x**2 + 3/2 - 3*x = 0. What is x?
1
Let z(k) = k**3 - k**2 - k + 10. Let l be z(0). Let a be 6/l*4 + -2. Factor -8/5*d**4 + 0*d**2 + a*d**3 + 0*d + 0.
-2*d**3*(4*d - 1)/5
Let s = 7 - 2. Let b(l) = l**2 + l + 1. Let o(n) = 0*n**3 - 21*n - 8*n**3 - n**3 - 1 + 16*n**2. Let y(q) = s*b(q) + o(q). Find a, given that y(a) = 0.
2/3, 1
Factor -3*t**2 + 10*t**2 - 4*t**3 + t**2.
-4*t**2*(t - 2)
Let l = 0 - 0. What is a in a**4 - 2 + l*a**4 + 1 + 0*a**3 + 2*a**3 - 2*a = 0?
-1, 