2 - 16*d + 14. Let w(i) = 7*i**2 + 5*i - 5. Let c(z) = -5*a(z) - 14*w(z). Suppose c(o) = 0. What is o?
-5, 0
Determine u so that 0*u + 0 - 4/3*u**2 - 2/3*u**3 = 0.
-2, 0
Let p(y) = 11 - 16 + 4 + y. Let i(d) = -4*d**3 - 8*d**2 + d - 5. Let z(r) = i(r) - 5*p(r). Factor z(o).
-4*o*(o + 1)**2
Let z(x) be the second derivative of -x**5/60 + x**4/9 - x**3/6 + 4*x. Let z(o) = 0. Calculate o.
0, 1, 3
Let n(x) be the first derivative of 7*x**4/2 + 38*x**3/3 + 39*x**2/4 - 9*x - 4. Let n(q) = 0. Calculate q.
-3/2, 2/7
Let l = -348 - -351. Let y be (0 - (-2 + 1)) + -1. Factor -d + y - 3/2*d**2 + d**l + 3/2*d**4.
d*(d - 1)*(d + 1)*(3*d + 2)/2
Suppose 0 = -2*z + z + 4. Determine q, given that 1/5*q**z + 2/5*q**3 + 0*q + 0 + 1/5*q**2 = 0.
-1, 0
Let m be 5/150*68 + -2. Let p(g) be the first derivative of -m*g**5 + 0*g**2 + 2 + 0*g + 0*g**3 + 1/9*g**6 + 1/6*g**4. Factor p(x).
2*x**3*(x - 1)**2/3
Let w(y) = -2*y**3 + y**2 - 5. Let d(p) = 3*p**3 - 2*p**2 + 9. Let x(m) = 3*d(m) + 5*w(m). Let o be x(0). Suppose -2/9 + 2/9*r**o + 0*r = 0. What is r?
-1, 1
Let i(k) be the first derivative of -k**6/3 - 12*k**5/5 - 9*k**4/2 - 8*k**3/3 - 50. Find v, given that i(v) = 0.
-4, -1, 0
Suppose x - 8 = -3. Let h be x*((-12)/(-20) - 0). Suppose 4/9*w**2 + 0*w + 8*w**4 + 0 + 34/9*w**h = 0. Calculate w.
-1/4, -2/9, 0
Let k = 2/11 + 16/33. Find g, given that 2/3*g**4 + 4/3*g**3 - 2/3*g - k*g**5 - 4/3*g**2 + 2/3 = 0.
-1, 1
Factor -2/17*k**2 + 0 - 2/17*k**3 + 0*k.
-2*k**2*(k + 1)/17
Let f(z) be the third derivative of z**7/630 + z**6/180 + z**5/180 - z**2. Factor f(p).
p**2*(p + 1)**2/3
Factor 3/5 + 3/5*l - 3/5*l**2 - 3/5*l**3.
-3*(l - 1)*(l + 1)**2/5
Factor -p**2 + 2*p - 14*p + 3*p**3 + 0*p - 8*p**2.
3*p*(p - 4)*(p + 1)
Let u(r) be the first derivative of 2*r**5/15 + r**4/6 - 10. Determine j so that u(j) = 0.
-1, 0
What is p in -18/5*p + 3/5*p**2 - 21/5 = 0?
-1, 7
Let b(v) be the first derivative of 1/360*v**6 + 1/3*v**3 + 2 + 0*v - 1/12*v**4 + 1/120*v**5 + 0*v**2. Let k(z) be the third derivative of b(z). Factor k(l).
(l - 1)*(l + 2)
Let t be (-6)/(-9)*6*(-3)/(-30). Let z = 616/5 + -122. Factor z*s**3 + 0 + 2/5*s + 6/5*s**2 + t*s**4.
2*s*(s + 1)**3/5
Suppose -4*h + t + 2 = -t, -3*t = 3*h - 15. Suppose 4 = 2*g - h. Factor 0 - 1/2*s**4 + 0*s**2 + 0*s + 1/2*s**g.
-s**3*(s - 1)/2
Suppose 0 = z - 2*a, 2*z - a - 5 + 2 = 0. Determine m, given that 0*m - 2/9 + 2/9*m**z = 0.
-1, 1
Let f = -17 - -24. Let g(m) be the second derivative of 0*m**6 + 0*m**2 - 1/6*m**3 + 0*m**4 + 1/10*m**5 + m + 0 - 1/42*m**f. What is v in g(v) = 0?
-1, 0, 1
Let n(l) be the third derivative of 7*l**5/15 - 22*l**4/3 + 8*l**3 - 24*l**2. Find z, given that n(z) = 0.
2/7, 6
Let k(s) be the first derivative of -2/3*s**2 - 1/9*s**3 + 2 - 2*s + 1/18*s**4. Let o(c) be the first derivative of k(c). Solve o(x) = 0.
-1, 2
Solve -3*y + 4*y**2 + y**3 - 9/2*y**4 + 2*y**5 + 1/2 = 0 for y.
-1, 1/4, 1
Let z be 21/(-14)*8/(-3). Let p be 11/12 + 3/z. Factor -4/3 - 1/3*s**3 - 8/3*s - p*s**2.
-(s + 1)*(s + 2)**2/3
Let r(h) be the third derivative of -h**6/1440 - h**5/480 - h**3/6 - 2*h**2. Let m(w) be the first derivative of r(w). Suppose m(n) = 0. What is n?
-1, 0
Let d(r) = 6*r**2 - 9*r + 8. Let s(l) = -5*l**2 + 9*l - 8. Let p(t) = 4*d(t) + 5*s(t). Determine j, given that p(j) = 0.
1, 8
Let w(b) be the third derivative of -b**5/210 + b**4/28 - 2*b**3/21 + 3*b**2. Find l, given that w(l) = 0.
1, 2
Let l = 8 - 3. Determine x, given that -22*x**5 - l*x**2 + 2*x + 2*x**2 - x**3 + 21*x**5 + 3*x**4 = 0.
-1, 0, 1, 2
Let f(t) = -t**3 + 8*t**2 + 9*t + 2. Let w be f(9). Suppose 3*b - w*b - 2 = 0. Factor 3*o**b + 3*o**3 - o**3 + 2 - 5*o**2 - 7*o + 5*o.
2*(o - 1)**2*(o + 1)
Let p(a) = 20*a**4 - 12*a**3 + 8*a**2 + 8. Let g(c) = -7*c**4 + 4*c**3 - 3*c**2 - 3. Let j(m) = 8*g(m) + 3*p(m). Find y such that j(y) = 0.
0, 1
Let m(w) be the third derivative of -w**5/90 + w**4/36 + 6*w**2. Let m(x) = 0. Calculate x.
0, 1
Factor 1/7 + 3/7*q**2 + 3/7*q + 1/7*q**3.
(q + 1)**3/7
Let g(i) = i. Let v be (-1 - 0) + 24/2. Let n(o) = -2*o**4 + 5*o**4 + 2*o**3 + v*o - o**2 - 4*o**4. Let h(y) = 22*g(y) - 2*n(y). Factor h(l).
2*l**2*(l - 1)**2
Let y = 6 - 12. Let f be (12/(-9))/(4/y). Factor -1/3*j + 0 + j**f - 2/3*j**3.
-j*(j - 1)*(2*j - 1)/3
Factor -6/5*k - 1/5*k**2 - 8/5.
-(k + 2)*(k + 4)/5
Let u(p) be the second derivative of -1/42*p**7 + 3*p + 0*p**4 + 0*p**5 + 0 - 1/15*p**6 + 0*p**3 + 0*p**2. Factor u(x).
-x**4*(x + 2)
Let k = -1015/9 - -113. Let v be 488/468 - (-6)/(-39). Find u such that -v*u**2 - 4/9 + 10/9*u + k*u**3 = 0.
1, 2
Suppose -2*w + 3*w - 6 = 0. Suppose w = 5*h - 4. Factor -2/7 - 2/7*x**3 + 2/7*x**h + 2/7*x.
-2*(x - 1)**2*(x + 1)/7
Solve -9/2*o**2 - 3/2*o**3 - 3*o + 0 = 0 for o.
-2, -1, 0
Let i be (((-6)/7)/((-12)/(-63)))/(-3). Factor 3/4*d**2 + 9/4*d + i.
3*(d + 1)*(d + 2)/4
Factor 18/13*t + 2/13*t**2 + 16/13.
2*(t + 1)*(t + 8)/13
Let u = -1461 - -1461. Solve g**3 + 1/3*g**2 + g**4 + 1/3*g**5 + 0 + u*g = 0 for g.
-1, 0
Let g(a) be the second derivative of 1/16*a**4 + 3*a + 1/120*a**6 - 3/80*a**5 + 0 - 1/24*a**3 + 0*a**2. Solve g(o) = 0 for o.
0, 1
Let z = 1564 + -1564. What is t in -4/9*t**2 + 2/9*t + 2/9*t**3 + z = 0?
0, 1
Determine b, given that 2*b - 3*b**2 - 7*b + 4 - 11*b**2 - 5*b = 0.
-1, 2/7
Let l = 81 - 81. Let x(w) be the first derivative of 0*w + 0*w**3 + 0*w**2 - 1/9*w**6 + 1/6*w**4 + l*w**5 + 1. Determine r, given that x(r) = 0.
-1, 0, 1
Factor 14/9*f**3 + 2*f**2 + 4/9*f**4 + 10/9*f + 2/9.
2*(f + 1)**3*(2*f + 1)/9
Suppose 0 = a - 2*r - 3*r - 3, 0 = a - 2*r - 9. Let x = -9 + a. Factor 1 + 2*b**4 - 4*b**2 - b**x + 2*b**2.
(b - 1)**2*(b + 1)**2
Suppose -c - 4*f + 6 = 0, -c - 2*f + 6 = c. Suppose -4*d + 17 = -t, c*t = -3*d + 2*d + 11. Factor 0*n**3 + 0*n**2 + 4*n**2 - 2*n - 2*n**t.
-2*n*(n - 1)**2
Let k(h) be the third derivative of h**8/2016 + h**7/630 - h**5/180 - h**4/144 - 7*h**2. Factor k(x).
x*(x - 1)*(x + 1)**3/6
Let j(o) = -3*o**2 - 15*o. Let x(n) = n**2 + 5*n. Let l(f) = 4*j(f) + 11*x(f). What is b in l(b) = 0?
-5, 0
Let n be -5 - (2 + 2 + -7). Let z be (n - -2)/(8 + -9). Factor 0*y**3 + z + 1/5*y**4 - 1/5*y**5 + 0*y**2 + 0*y.
-y**4*(y - 1)/5
Suppose -2*j - 5*b - 11 - 9 = 0, -j - 12 = 3*b. Let 0*g**4 - 3/4*g**5 + 3/2*g**3 - 3/4*g + 0 + j*g**2 = 0. What is g?
-1, 0, 1
Suppose -6/11*j - 2/11 - 6/11*j**2 - 2/11*j**3 = 0. What is j?
-1
Let l(a) be the first derivative of 3*a**4/4 - 3*a**3 + 3. Factor l(d).
3*d**2*(d - 3)
Let q(y) be the third derivative of y**5/165 - y**4/132 - 16*y**2. Find w, given that q(w) = 0.
0, 1/2
Let d(c) = c**2 - 5. Let x(w) = -w**2 - w + 6. Let z(n) = 6*d(n) + 4*x(n). Factor z(i).
2*(i - 3)*(i + 1)
Let x(y) be the second derivative of -y**6/75 - y**5/25 + 2*y**3/15 + y**2/5 + 5*y. Let x(u) = 0. What is u?
-1, 1
Let w = 52/51 - -5/34. Determine y, given that 3/2*y**3 + 0 - w*y**2 - 1/3*y = 0.
-2/9, 0, 1
Let q = -585 + 585. Factor 0*g + q + 1/2*g**5 - 1/2*g**3 + 0*g**2 + 0*g**4.
g**3*(g - 1)*(g + 1)/2
Let h = 29/25 - 9/25. Solve 6/5*s**3 - h*s**2 - 6/5*s + 4/5 = 0.
-1, 2/3, 1
Let g = -723/8 + 54229/600. Let i(a) be the third derivative of 0*a + 0*a**7 + g*a**6 - 1/60*a**4 + 0*a**3 - 1/840*a**8 + 0*a**5 + 2*a**2 + 0. Factor i(f).
-2*f*(f - 1)**2*(f + 1)**2/5
Let c(y) be the second derivative of y**5/80 - y**3/24 + 3*y. Determine g so that c(g) = 0.
-1, 0, 1
Suppose 0 = 3*q - 4*q. Let f be -3 + q + 175/49. Factor 2/7*o**2 + f*o + 2/7.
2*(o + 1)**2/7
Let p(k) be the second derivative of k**4/48 - k**3/24 + 5*k. Find s, given that p(s) = 0.
0, 1
Let s be 60/100*15/6. Factor 2*i + 1/2 + s*i**2.
(i + 1)*(3*i + 1)/2
Let r(w) = -5*w - 1. Let c be r(-1). Find t such that -11*t**2 + 23*t**2 - 16*t**2 + 6*t**3 + t**5 + t - 4*t**c = 0.
0, 1
Let o = -13657/5 - -2656. Let c = -75 - o. Determine u, given that c*u**4 + 2/5*u**2 + 0 + 0*u + 4/5*u**3 = 0.
-1, 0
Factor 4*p**2 + 32*p**5 - 63*p**4 - 25*p**2 - 55*p**2 - 113*p**4 - 104*p - 16 + 290*p**3.
2*(p - 2)**3*(4*p + 1)**2
Let q(h) be the first derivative of -4/5*h**3 - 9/20*h**4 - 3/10*h**2 + 0*h - 3. Let q(g) = 0. Calculate g.
-1, -1/3, 0
Let m = -6 - -11. Find t such that -3*t + t**3 + 2*t**2 + 2 + m*t + 2*t**2 + 3*t = 0.
-2, -1
Let r be -2 + 6/105*5*10. Determine q, given that -2/7 - r*q**2 - 2/7*q**3 - 6/7*q = 0.
-1
Factor -3/2*m - 9/4 - 1/4*m**2.
-(m + 3)**2/4
