 2/11*r**2 - 8/11*r + 8/11 = 0. What is r?
2
Let p be (3/(-5))/(81/(-12) + 6). Let 0*t - 6/5*t**3 + p*t**2 + 0 - 4/5*t**4 = 0. What is t?
-2, 0, 1/2
Factor -l**3 + 2 + 4*l**3 - l**2 + 7*l**2 - 8 - 3*l.
3*(l - 1)*(l + 1)*(l + 2)
Let p(k) be the first derivative of 2/15*k**3 + 1/5*k**2 - 4/5*k - 6. Let p(z) = 0. Calculate z.
-2, 1
Factor 2*b**2 - 7 + 8*b + 4*b**3 + 7 - 14*b**2.
4*b*(b - 2)*(b - 1)
Suppose 0*v - 4*v - 200 = 0. Let s = 152/3 + v. Solve -s*q + 2/3*q**2 - 4/3 = 0 for q.
-1, 2
Let s(w) be the first derivative of 1 - 1/360*w**6 - 1/3*w**3 + 0*w**4 + 0*w**2 + 0*w + 1/60*w**5. Let t(k) be the third derivative of s(k). Factor t(j).
-j*(j - 2)
Let 3/5*l**3 - 12/5 - 18/5*l**2 + 27/5*l = 0. What is l?
1, 4
Let m(o) be the first derivative of o**4/12 + 34. What is k in m(k) = 0?
0
Let q(i) be the second derivative of -i**4/4 - i**3 - 7*i. Factor q(j).
-3*j*(j + 2)
Let z = 19/66 + 1/22. Let k(w) be the first derivative of -1/15*w**5 - z*w**3 + 1/6*w**2 + 0*w + 1/4*w**4 - 1. Let k(l) = 0. What is l?
0, 1
Suppose -5 = 5*m - 20. Let -m*c**2 + 3*c**4 - 2*c**4 - 2*c - 3*c**5 + c**3 + 4*c**5 + 2*c**4 = 0. Calculate c.
-2, -1, 0, 1
Let c(i) = i**3 + 6*i**2 + 5*i + 5. Let f be c(-5). Factor -1/4*s**3 - 1/4*s**f + 0*s**2 + 0*s - 1/2*s**4 + 0.
-s**3*(s + 1)**2/4
Let g(b) be the second derivative of -b**7/5040 + b**6/360 - b**5/60 + b**4/4 + 3*b. Let i(n) be the third derivative of g(n). Factor i(d).
-(d - 2)**2/2
Let d(k) be the third derivative of 0*k - 7*k**2 - 1/30*k**5 + 1/24*k**4 + 0*k**3 + 0 + 1/120*k**6. Factor d(h).
h*(h - 1)**2
Let j(y) be the second derivative of 0 + 5/24*y**4 + 1/2*y**2 - 3*y + 7/12*y**3. Determine k so that j(k) = 0.
-1, -2/5
Factor 8/3*c + 1/3*c**4 + 2*c**3 + 0 + 4*c**2.
c*(c + 2)**3/3
Let o = 5/11 - -7/33. Solve 2/3*p + 0 - o*p**2 = 0.
0, 1
Let -q**2 + 0 + 1/2*q**3 + 1/2*q = 0. What is q?
0, 1
Suppose -m - 11 = -7*f + 2*f, 0 = f - 5*m - 7. Let n be f/(-5) + 6/10. Factor -n*d**2 + 2/5*d - 1/5.
-(d - 1)**2/5
Suppose -4*q = 2*a - 2, 0*q + q + 2 = 0. Let g = -34 + 137/4. Find u such that -1/4*u**a + 1/2*u**3 + g*u**4 - 1/4*u - 1/2*u**2 + 1/4 = 0.
-1, 1
Factor 1 + 3*r**2 + 5 - 6 - 3*r**3.
-3*r**2*(r - 1)
Let s(i) be the first derivative of -1/75*i**6 + 0*i**2 + 1/50*i**5 + 3*i + 3 + 1/30*i**4 - 1/15*i**3. Let q(a) be the first derivative of s(a). Factor q(y).
-2*y*(y - 1)**2*(y + 1)/5
Let b(v) be the first derivative of -6*v**3 + 16*v**2 + 8*v - 5. Determine f, given that b(f) = 0.
-2/9, 2
Let q(g) be the second derivative of g**5/90 + g**4/27 - g**3/27 - 2*g**2/9 - 6*g. Factor q(n).
2*(n - 1)*(n + 1)*(n + 2)/9
Suppose 0 - 1/6*h**2 + 1/6*h = 0. What is h?
0, 1
Suppose 0 = -4*z + 5 + 107. Suppose -i = -8*i + z. Factor 0 - 2*g**3 + 2*g**2 + 2/3*g**i - 2/3*g.
2*g*(g - 1)**3/3
Suppose -4*x + p - 5*p = 4, 0 = -3*x + 2*p + 17. Find m, given that -m**2 + 3 - x + 1 = 0.
-1, 1
Let f(w) be the third derivative of w**6/200 + 3*w**5/100 + 3*w**4/40 + w**3/10 - 8*w**2. Suppose f(h) = 0. Calculate h.
-1
Let x(v) be the third derivative of v**6/660 - v**4/44 - 2*v**3/33 - 9*v**2. Let x(l) = 0. What is l?
-1, 2
Factor -2/5*z**2 + 0 - 4*z.
-2*z*(z + 10)/5
Let x(w) be the first derivative of 14*w**6/3 + 36*w**5/5 + 2*w**4 - 7. Let x(d) = 0. Calculate d.
-1, -2/7, 0
Let q(t) be the first derivative of -t**4/6 - 2*t**3/3 + 3*t**2 + 18*t - 17. Factor q(h).
-2*(h - 3)*(h + 3)**2/3
Let x(d) be the first derivative of 2/3*d**3 + 0*d**4 - 1 - 2/5*d**5 + 1/2*d**2 - 1/6*d**6 + 0*d. Factor x(b).
-b*(b - 1)*(b + 1)**3
Let g = -8 + 12. Suppose z**3 + z - z**g + 2*z**2 - z**2 - 2*z**3 = 0. What is z?
-1, 0, 1
Let p(r) = r**3 - 11*r**2 + 3*r - 2. Let u be p(11). Let t = u - 92/3. Factor -1/3*c + 1/3*c**4 + 0 - 1/3*c**2 + t*c**3.
c*(c - 1)*(c + 1)**2/3
Let a be (4/(-18))/(56/(-66)). Let d = a + 1/42. Solve 2/7*k**3 + 0 + 0*k**2 - d*k = 0 for k.
-1, 0, 1
Let m(l) be the second derivative of -l**6/216 + l**5/180 - 2*l**3/3 + 4*l. Let b(w) be the second derivative of m(w). Determine h, given that b(h) = 0.
0, 2/5
Find l, given that -3/2*l**2 + 0 - 6*l = 0.
-4, 0
Let p(q) be the second derivative of 4/9*q**3 + 0 + 4/15*q**5 - 2/45*q**6 - 5/9*q**4 + 0*q**2 - 5*q. Let p(f) = 0. Calculate f.
0, 1, 2
Let j(u) be the first derivative of -1/3*u**4 - u + 0*u**2 - 3 + 1/20*u**5 + 2/3*u**3. Let k(l) be the first derivative of j(l). Factor k(y).
y*(y - 2)**2
Let b(o) = -2*o + 2. Let r be b(4). Let x(s) = 7*s**3 + s**2 + 2*s - 10. Let w(d) = -6*d**3 - 3*d + 9. Let t(c) = r*w(c) - 5*x(c). Factor t(k).
(k - 2)**2*(k - 1)
Let q be -2*1*(30/(-8) + 3). Factor 3/2*p**5 - 3/2*p**3 + q*p**2 + 0*p + 0 - 3/2*p**4.
3*p**2*(p - 1)**2*(p + 1)/2
Let u = 1/21 - -5/42. Let z(v) be the first derivative of 0*v + 3 - 1/2*v**2 - 2/3*v**3 + u*v**6 + 2/5*v**5 + 0*v**4. Factor z(c).
c*(c - 1)*(c + 1)**3
Let g(b) be the first derivative of -b**5/15 + 2*b**3/3 - 2*b**2 + 9. Let w(t) be the second derivative of g(t). Determine d so that w(d) = 0.
-1, 1
Let h(w) be the first derivative of -w**4/20 - 2*w**3/15 + w**2/10 + 2*w/5 - 13. Suppose h(l) = 0. Calculate l.
-2, -1, 1
Let y(n) = 6*n**2 + 4*n - 9. Let x = 18 - 12. Let d(b) = -5*b**2 - 3*b + 8. Let a(p) = x*y(p) + 7*d(p). Factor a(l).
(l + 1)*(l + 2)
Factor 2/5*v**5 - 2*v**4 - 2/5 + 2*v - 4*v**2 + 4*v**3.
2*(v - 1)**5/5
Let z(j) = -j**5 + j**4 - j**3 + j**2 + j + 1. Let x(o) = -3*o**5 + 7*o**4 + o**3 - 5*o**2 + o + 1. Let m(k) = -2*x(k) + 2*z(k). Factor m(r).
4*r**2*(r - 3)*(r - 1)*(r + 1)
Let v(h) be the third derivative of -2*h**7/49 - 19*h**6/210 + 2*h**4/21 + 8*h**2. Let v(f) = 0. What is f?
-1, -2/3, 0, 2/5
Let v(r) = -5*r**2 + r + 8. Let g = -1 + 3. Let z(j) = -j**2 - j + 1. Let k(t) = g*z(t) - v(t). Factor k(l).
3*(l - 2)*(l + 1)
Let u = -2 - -6. Solve -u*g**3 + 2 - 10*g + g + 7*g**3 + 4 = 0.
-2, 1
Let w = 8 + -4. Find d, given that 8/3*d + 16*d**2 + 128/3*d**3 + 128/3*d**w + 1/6 = 0.
-1/4
Let c(n) = 4*n**2 - 190*n + 97. Let i be c(47). Factor 2/3*g**i + 0*g + 0 - 2/3*g**4 + 0*g**2.
-2*g**3*(g - 1)/3
Determine h, given that 5*h**4 - 4*h**3 - 39*h**2 + 24*h**2 - 7*h**3 + h**3 = 0.
-1, 0, 3
Determine q so that 14*q**3 - 2 + 2 + 10*q**2 - 47*q + 43*q = 0.
-1, 0, 2/7
Suppose 0 = 23*a - 26*a. Factor a*q + 0 + 1/6*q**3 + 1/6*q**2.
q**2*(q + 1)/6
Let r(w) = -w**2 - w - 2. Let a(v) = -4*v**2 - 4*v - 9. Let q(p) = 2*a(p) - 9*r(p). Solve q(h) = 0.
-1, 0
Let j(i) = -13*i - 73. Let x be j(-6). Factor 3/2*t + 1 - 2*t**3 + 1/2*t**x - t**2 + 0*t**4.
(t - 2)*(t - 1)*(t + 1)**3/2
Suppose b - 5*b = -28. Factor -2*i**2 - b*i**3 + 2*i + 2*i**4 + 5*i**3 + 0*i**2.
2*i*(i - 1)**2*(i + 1)
Let y be 57/36 + 9/(-6). Let z(j) be the second derivative of 1/48*j**4 + y*j**3 + 3*j + 0 + 1/8*j**2. Suppose z(w) = 0. What is w?
-1
Let c be (3 - (-100)/(-30))/(1/(-9)). Factor c*l**3 - 3/4 - 6*l**2 + 15/4*l.
3*(l - 1)*(2*l - 1)**2/4
Let f(p) = p**5 - 1. Let v(z) = 7*z**5 - 2*z**3 - 5. Let x(d) = -5*f(d) + v(d). Factor x(l).
2*l**3*(l - 1)*(l + 1)
Suppose 5*s = -v + 1, s + 0*v + 3*v - 3 = 0. Let j be s/(1 + -2) + 4. Factor 0 - j*q**2 + 3*q**2 + 3 + 3*q**3 - 2*q**2 - 3*q.
3*(q - 1)**2*(q + 1)
Solve -74*x**2 + 3 - 3 + 70*x**2 = 0.
0
Suppose 2*k = f - 1, 0*k - 5*k - 3*f + 25 = 0. Factor k - 2*p**3 + p - 2*p**2 + 5*p - 4*p.
-2*(p - 1)*(p + 1)**2
Let l(g) be the third derivative of g**5/10 + g**4/8 + g**2. Let l(p) = 0. What is p?
-1/2, 0
Let v(x) be the second derivative of 4*x - 3/20*x**5 + 0*x**3 + 0*x**2 + 1/14*x**7 + 0*x**4 + 0*x**6 + 0. Let v(f) = 0. Calculate f.
-1, 0, 1
Let d(b) be the first derivative of 1/12*b**3 + 3*b + 1 + 1/24*b**4 + 0*b**2. Let i(a) be the first derivative of d(a). Solve i(p) = 0.
-1, 0
Let s(w) be the first derivative of 2*w**5/5 + 5*w**4/2 + 16*w**3/3 + 4*w**2 - 56. Factor s(q).
2*q*(q + 1)*(q + 2)**2
Factor 0 + 0*y + 1/3*y**2.
y**2/3
Let f(i) be the first derivative of 0*i**4 - 1/30*i**3 - 1 - 1/2*i**2 + 0*i + 1/300*i**5. Let y(o) be the second derivative of f(o). Let y(b) = 0. Calculate b.
-1, 1
Determine v, given that 0 + 0*v**2 - 1/2*v**3 + 1/2*v = 0.
-1, 0, 1
Let w(o) be the second derivative of o**4/4 + 3*o**3/2 - 8*o. What is a in w(a) = 0?
-3, 0
Let n(i) be the second derivative of 1/240*i**5 + 0 + i**2 + 0*i**3 + i - 1/96*i**4. Let r(l) be the first derivative of n(l). Determine s, given that r(s) = 0.
0, 1
Let h(c) = -2*c**5 + 6*c**4 