(-6)/27. Solve 0*c**d + 1/4 + 1/4*c**4 - 1/2*c**2 + 0*c = 0.
-1, 1
Factor -3*t + 8*t**3 + 11*t**3 + 2*t**3 - 3*t**5 - 15*t**3.
-3*t*(t - 1)**2*(t + 1)**2
Let y(v) be the third derivative of 0 + 5/84*v**6 - 3/7*v**4 + 8/21*v**3 + 1/7*v**5 + 0*v + v**2. Solve y(q) = 0.
-2, 2/5
Suppose 128*o**3 + 1248/7*o**2 + 512/7*o + 64/7 + 28*o**4 = 0. Calculate o.
-2, -2/7
What is f in 0 + 0*f**2 - 1/2*f**3 + 0*f - 3/4*f**5 - 5/4*f**4 = 0?
-1, -2/3, 0
Factor 48 - 62 + c**2 + 30 + 4*c + 4*c.
(c + 4)**2
Let w(b) be the third derivative of b**5/20 - b**4/2 - 18*b**2. Find l such that w(l) = 0.
0, 4
Let l(h) = -h**3 - 6*h**2 - 7*h - 7. Let c be l(-5). Let 0 + 0*i - 1/2*i**4 + i**c - 1/2*i**2 = 0. What is i?
0, 1
Let o(h) be the second derivative of -h**7/1155 + h**6/330 - h**5/330 - h**2/2 + 5*h. Let v(p) be the first derivative of o(p). What is b in v(b) = 0?
0, 1
Suppose -2*f - 2*f - 24 = 0. Let b be (f/(-4))/(12/16). What is m in -m**3 - 2*m**b - 2*m**3 - 6*m - 7*m**2 = 0?
-2, -1, 0
Let s be (-1)/((-4)/(-2)) + (-51)/(-18). Factor s*t**2 - 16/3*t + 4/3.
(t - 2)*(7*t - 2)/3
Find y such that 0*y + 0 + 0*y**2 - 15/8*y**4 - 21/8*y**5 + 3/4*y**3 = 0.
-1, 0, 2/7
Let l(x) = x**3 - 5*x**2 - 7*x + 8. Let w be l(6). Suppose -5*c = -w*c. Factor r**3 + c - 1/2*r**2 + 0*r - 1/2*r**4.
-r**2*(r - 1)**2/2
Let j(a) be the first derivative of -9*a**4/20 + a**3/5 + 3*a**2/5 + 1. Factor j(b).
-3*b*(b - 1)*(3*b + 2)/5
Let i(n) be the second derivative of n**6/6 - 5*n**5/4 + 5*n**4/3 + n. Determine u, given that i(u) = 0.
0, 1, 4
Let i(l) be the third derivative of -l**6/360 - l**5/60 + 2*l**3/9 - 5*l**2. Solve i(b) = 0.
-2, 1
Let l be 20/24 + 1/(-3) - -4. Solve 3*o - l - 1/2*o**2 = 0 for o.
3
Let c(v) be the third derivative of v**6/900 + v**5/150 + v**4/60 + v**3/2 + 3*v**2. Let x(h) be the first derivative of c(h). Determine w so that x(w) = 0.
-1
Let l(i) be the third derivative of i**8/672 + i**7/420 - 6*i**2. Factor l(n).
n**4*(n + 1)/2
Let c(z) = 6*z**3 - 23*z**2 + 13*z - 11. Let o(i) = 15*i**3 + 45*i + 2*i**3 - 81*i**2 - 39 + 4*i**3. Let h(v) = -18*c(v) + 5*o(v). Factor h(m).
-3*(m - 1)**3
Let v(u) be the third derivative of 0*u**3 + 0*u**5 - 1/168*u**8 + u**2 - 1/12*u**4 + 0*u**7 + 0*u + 0 + 1/30*u**6. What is b in v(b) = 0?
-1, 0, 1
Suppose 3*d - d + 18 = 0. Let z be (2 + 21/d)*-1. Suppose -z - n**4 + 2*n + 10/3*n**3 - 4*n**2 = 0. What is n?
1/3, 1
Let j(q) = -10*q**3 + q**2 - q - 12. Let c(a) = a**3 + a. Let u(n) = 18*c(n) + 2*j(n). Factor u(t).
-2*(t - 2)**2*(t + 3)
Let x be 2/(-7) + (-2172)/(-105). Let o = x - 20. Let -2/5*n**4 + 2/5*n**2 + 2/5*n**3 - o*n**5 + 0*n + 0 = 0. What is n?
-1, 0, 1
Find j such that 2*j**2 - 11*j**4 - 18*j**5 + 41*j**4 + 5*j**3 - 19*j**3 = 0.
0, 1/3, 1
Let m = 13 - 9. Suppose -2*h - 2 + m = 0. Factor 8*r**2 - 18*r - h + 5 + 0.
2*(r - 2)*(4*r - 1)
Let o(d) be the second derivative of 1/4*d**4 + 21/40*d**5 + 0 - 4*d + 0*d**2 + 0*d**3 - 5/14*d**7 + 1/20*d**6. Suppose o(g) = 0. Calculate g.
-1/2, -2/5, 0, 1
Let h be 2/(-3) + 104/120. Solve 0 + h*p + 1/5*p**2 = 0.
-1, 0
Let r be (4/384)/(1/2). Let l(h) be the third derivative of 0*h + 0*h**3 - r*h**4 - h**2 - 1/120*h**5 + 0. Let l(q) = 0. What is q?
-1, 0
Suppose -3*l + l = -4. Factor 5*d**3 - 2*d**4 + 2*d - 7*d**2 + d**3 + d**l.
-2*d*(d - 1)**3
Let v be (-296)/(-3996) - (-262)/108. Factor v*j + 7/2*j**2 + 3/2*j**3 + 1/2.
(j + 1)**2*(3*j + 1)/2
Suppose -4*d - 5*f = -11, -20 + 6 = -d - 5*f. Let h be (-2 + 0)/(0 + d). Factor 3*a**3 + 3*a**4 + a**3 + 2*a**h - a**4.
2*a**2*(a + 1)**2
Let c(d) be the second derivative of 3*d**5/40 - 5*d**4/4 + 9*d**3/4 - 17*d. Factor c(p).
3*p*(p - 9)*(p - 1)/2
Let k = -12 + -21. Let t be 2 - (4 + -3)*k. Factor -3*f**2 + t*f + f**2 - 37*f.
-2*f*(f + 1)
Let o(n) be the second derivative of 2*n**4/3 + n**3 - n**2 + 6*n. Find z, given that o(z) = 0.
-1, 1/4
Suppose 0*w = 5*w. Suppose -10 = 5*n, w = 3*u + 3*n + 3 - 9. Suppose -3/2*h**2 - 3/2*h**3 + 0 + 3/2*h**u + 3/2*h = 0. Calculate h.
-1, 0, 1
Let b(t) = -t**5 - 3*t**4 + 7*t**3 - 5*t**2 - 2*t + 4. Let n(z) = 3*z**5 + 8*z**4 - 20*z**3 + 14*z**2 + 6*z - 11. Let w(g) = 11*b(g) + 4*n(g). Factor w(k).
k*(k - 2)*(k - 1)*(k + 1)**2
Let i(h) = -6*h**2 + h - 3. Let d(n) be the first derivative of -2*n**3 + n**2 - 4*n - 2. Let r(c) = 3*d(c) - 4*i(c). Suppose r(s) = 0. What is s?
-1/3, 0
Let y(r) be the third derivative of -4*r**2 - 1/33*r**3 - 1/22*r**4 - 1/165*r**6 - 3/110*r**5 + 0 + 0*r. Find z, given that y(z) = 0.
-1, -1/4
Let n(i) be the second derivative of i**9/7560 - i**8/1680 + i**6/180 - i**5/60 + i**4/3 + 4*i. Let m(k) be the third derivative of n(k). Factor m(o).
2*(o - 1)**3*(o + 1)
Let s(u) be the third derivative of u**7/70 - u**6/30 - u**5/60 + u**4/12 - 4*u**2. Factor s(x).
x*(x - 1)**2*(3*x + 2)
Let i(l) be the first derivative of -l**7/945 + l**6/270 - l**5/270 - l**2 - 6. Let w(b) be the second derivative of i(b). Determine d so that w(d) = 0.
0, 1
Let q = 29 + -21. Let s be (q + 0)/(-1 + 3). Factor 2*m**2 - s*m + 1 - 1 + 0.
2*m*(m - 2)
Suppose -y - 3 = 1. Let t = -2 - y. Solve 0 + 2*n**2 + 4/3*n**5 - 2/3*n**3 - 2/3*n - t*n**4 = 0 for n.
-1, 0, 1/2, 1
Suppose 0 = -2*a + 11 - 7. Suppose a*u = -3*u - b + 8, 0 = 3*u + 3*b. Solve -6/5*p - 9/5 - 1/5*p**u = 0.
-3
Let q be 40/25 - (-4)/10. Let l(v) be the first derivative of -1 - 1/2*v**q - 1/5*v**5 - v**3 - 3/4*v**4 + 0*v. Factor l(i).
-i*(i + 1)**3
Let h(t) = -t**4 + 35*t**3 - 45*t**2 - 131*t + 270. Let u(z) = -15*z**4 + 490*z**3 - 630*z**2 - 1835*z + 3780. Let j(g) = 55*h(g) - 4*u(g). Factor j(c).
5*(c - 3)**3*(c + 2)
Suppose -m + 9 = -4*s + 4*m, 2*s - 3 = m. Let n(p) be the third derivative of -1/12*p**3 - 2*p**2 + 0 + 1/48*p**s + 0*p + 1/120*p**5 - 1/240*p**6. Factor n(j).
-(j - 1)**2*(j + 1)/2
Let l(h) = -h**2 + 11*h + 2. Let n = 2 - -9. Let p be l(n). Find c such that -10*c + 2*c**3 + c**2 - 4*c**2 + p*c**4 - 4 - 3*c**2 = 0.
-1, 2
Let k be (0 + 1)/(2/4). Factor 11*s - 3*s**2 - 3*s**4 - 5*s + 6*s**k - 6*s**3.
-3*s*(s - 1)*(s + 1)*(s + 2)
Let f(x) = x**2 + 5*x. Let t be f(-5). Factor 0*c**3 + 4/5*c**2 + t*c - 2/5 - 2/5*c**4.
-2*(c - 1)**2*(c + 1)**2/5
Suppose 4*y = -0 + 24. Let t(u) = -55*u**3 + 3*u**2 - 5*u. Let n(m) = -m - m**2 - 27*m**3 + 3*m**2 - m. Let v(d) = y*t(d) - 13*n(d). Factor v(j).
j*(3*j - 2)*(7*j + 2)
Let q(t) be the second derivative of -7*t**5/40 - t**4/12 + 21*t. Let q(m) = 0. What is m?
-2/7, 0
Suppose 0*o - 4*d - 4 = -4*o, 5*o - 15 = -5*d. Let b be 6/(-15)*10/(-4). Let -4*l**2 + 3*l**o + 5*l - 2*l - b - l = 0. Calculate l.
1
Let l(v) = -29*v**2 - 144*v - 52. Let n(o) = 57*o**2 + 287*o + 106. Let f(h) = -13*l(h) - 6*n(h). Factor f(q).
5*(q + 4)*(7*q + 2)
Let a(i) = i**3 - 6*i**2 - 6*i + 9. Let o be a(7). Let b = o - 16. Find t such that -2/3*t + 4/3*t**2 + b - 4/3*t**4 + 0*t**3 + 2/3*t**5 = 0.
-1, 0, 1
Suppose 0 = 3*f - 7*f - 72. Let x be 4/f - 92/(-90). Factor x*w - 2/5*w**2 - 2/5.
-2*(w - 1)**2/5
Let v(s) = s**5 - 4*s**4 - 3*s**3 + 12*s**2 + 18*s + 10. Let m(i) = -2*i**5 + 4*i**4 + 4*i**3 - 11*i**2 - 17*i - 11. Let x(d) = -2*m(d) - 3*v(d). Factor x(u).
(u - 2)*(u + 1)**2*(u + 2)**2
Find m such that -4 - 3*m**3 + 3*m + 3*m + m**3 = 0.
-2, 1
Let m = -22 - -89/4. Let a(v) be the first derivative of 1 - 1/4*v**2 + m*v + 1/12*v**3. Let a(c) = 0. Calculate c.
1
Let g = 5 + -3. Let c(x) = x**3 - 5*x**2 + 5*x - 1. Let q be c(4). Find r such that 9/4*r**g - q*r + 1 = 0.
2/3
Let d(o) be the first derivative of -o**3/6 - 3*o**2/4 - 7. Let d(b) = 0. What is b?
-3, 0
Let v(h) = h**3 - 2*h**2 - 5*h + 12. Let a be v(2). Factor 0 + 0*g + 1/3*g**3 + 0*g**a.
g**3/3
Suppose -3*z + 3*s = 3, 3*s - 2 = -3*z + 5*s. What is f in -332/7*f**2 + 120/7*f - 16/7 - 240/7*f**z + 50/7*f**5 + 418/7*f**3 = 0?
2/5, 1, 2
Suppose 0 = 3*g - 7 - 2. Factor 4 + g*p - 3*p**2 - p + 2 - 5*p.
-3*(p - 1)*(p + 2)
Let g(u) = -5*u**2 + 4*u. Let q(c) = -c**2 + c. Let f(h) = g(h) - 6*q(h). Find v, given that f(v) = 0.
0, 2
Let x(p) = -p**2 + p + 6. Let f be x(-2). Let b(u) be the second derivative of 1/30*u**6 - 1/12*u**4 + 0*u**2 + 1/6*u**3 + f - u - 1/20*u**5. Factor b(t).
t*(t - 1)**2*(t + 1)
Let x = -672 + 674. Factor 4/13 + 8/13*n**x - 10/13*n - 2/13*n**3.
-2*(n - 2)*(n - 1)**2/13
Let z(p) be the third derivative of p**6/660 + 2*p**5/165 + 5*p**4/132 + 2*p**3/33 - 11*p**2. Factor z(