Suppose 4*v = -3*w - 11, 4*v = -5*w + v. Factor 2/3*d**w + 7/3*d**2 - d**4 + 2/3*d + y.
-d*(d - 2)*(d + 1)*(3*d + 1)/3
Let g(s) = 4*s**2 - 32*s + 60. Let i(t) = 4*t**2 - 36*t + 55. Let h(d) = d + 1. Let v(k) = 4*h(k) + i(k). Let x(a) = 5*g(a) - 4*v(a). What is j in x(j) = 0?
4
Let z(b) be the first derivative of -3 + 4*b + 3*b**2 + 2/3*b**3. Factor z(r).
2*(r + 1)*(r + 2)
Let k be 2/3*(2 + 1). Factor 10 + 14*n + 6*n + 4*n**3 - k + 5*n**2 + 11*n**2.
4*(n + 1)**2*(n + 2)
Let q(y) be the first derivative of 2/9*y**3 + 0*y + 3 + 1/3*y**2. Find l, given that q(l) = 0.
-1, 0
Suppose -331 + 361 = 10*t. Let g be -1*(2/1 - 4). Factor t - 2*j + 1/3*j**g.
(j - 3)**2/3
Let m(l) = -l**2 + 7*l - 6. Let s(f) = -f**2 + 8*f - 6. Let t(c) = 3*m(c) - 2*s(c). Factor t(z).
-(z - 3)*(z - 2)
Let i(w) = 6*w**2 - 78*w + 2. Let m(q) = -13*q**2 + 157*q - 5. Let b(u) = -5*i(u) - 2*m(u). Factor b(l).
-4*l*(l - 19)
Let r(f) be the third derivative of -f**6/1080 + f**5/360 - 2*f**3/3 + 3*f**2. Let s(q) be the first derivative of r(q). Determine v, given that s(v) = 0.
0, 1
Factor 175*t**2 - 180 + 7*t**3 + 669*t - 189*t + 8*t**3.
5*(t + 6)**2*(3*t - 1)
Let i(p) be the third derivative of p**5/30 + 6*p**2. Factor i(w).
2*w**2
Let f(b) be the third derivative of -b**8/6720 + b**6/720 - b**4/6 + 2*b**2. Let a(l) be the second derivative of f(l). Factor a(m).
-m*(m - 1)*(m + 1)
Let u be (-2)/(-3 - 8/(-3)). Suppose -2 = q - u. Factor 3*j**q + 3*j**2 - 2*j**2 - j**4 + 2*j**3 - 3*j**2 - 2*j**5.
-2*j**2*(j - 1)**2*(j + 1)
Let l(p) = 9*p**4 - p**3 - 13*p**2 + p - 1. Let s = -2 + 3. Let d(w) = -w**3 + w**2 + w. Let x(t) = s*l(t) + 5*d(t). Suppose x(g) = 0. Calculate g.
-1, 1/3, 1
Solve 7/2*d**2 - 1 + 5/2*d = 0.
-1, 2/7
Let n(f) be the third derivative of 1/60*f**5 + 0 - 7*f**2 + 1/3*f**4 + 0*f + 8/3*f**3. Factor n(v).
(v + 4)**2
Let j(g) = g**2 - g + 3. Let w be j(0). Suppose 4*d = -5*x - 10, 0 = 2*d + w*d + 25. Factor -2*c**2 + 2*c**3 + 1 - x*c + 0 + 1.
2*(c - 1)**2*(c + 1)
Let j(p) = -p**3 + p**2 - 2*p + 22. Let k be j(0). Let b = k + -19. Find f such that -4/5*f**4 + 2*f**b + 2/5*f + 0 - 8/5*f**2 = 0.
0, 1/2, 1
Let z(f) be the third derivative of 2/27*f**3 + 1/270*f**5 + 6*f**2 + 0*f - 1/36*f**4 + 0. Find x such that z(x) = 0.
1, 2
Let y(v) = 3*v - 1. Let j be y(3). Suppose j = m + 3. Factor -m*t**2 - 3*t - 1 + 0*t**3 - 2*t**2 - t**3 + 4*t**2.
-(t + 1)**3
Let j = 6623/126 + -366/7. Let m(c) be the first derivative of -1/5*c**5 + 1/3*c**3 + 0*c - 2 - 1/3*c**2 + 7/12*c**4 - j*c**6. Solve m(a) = 0.
-1, 0, 2/5, 1
Let t = 3 - 1. Factor -105*n**2 - 2*n**4 - 4 - 16*n + 81*n**2 - t*n**4 - 16*n**3.
-4*(n + 1)**4
Find a such that -1/4*a - 1/8*a**4 + 1/4*a**3 + 0*a**2 + 1/8 = 0.
-1, 1
Factor -2*m**2 + 6/5*m + 4/5.
-2*(m - 1)*(5*m + 2)/5
Let f(t) be the third derivative of t**8/336 - t**7/105 - t**6/120 + t**5/30 + 13*t**2. Solve f(p) = 0.
-1, 0, 1, 2
Let w = 81 - 77. Factor 0*p**2 + 0 + 1/4*p**5 + 1/4*p**w + 0*p + 0*p**3.
p**4*(p + 1)/4
Suppose 0 = -4*m - 2*c - 3*c + 37, 3 = -4*m + 3*c. Let o be 4*3/(12*m). Find u, given that -1/3*u**2 - o*u + 0 = 0.
-1, 0
Suppose -3*m = -0*m. Suppose -n + m*n + 3*z - 10 = 0, -4*n + 28 = 5*z. What is p in -p**2 - 4*p**3 + p**4 + n*p**2 + 4*p**3 - 2*p**3 = 0?
0, 1
Let i(w) be the third derivative of 1/8*w**4 - 4*w**2 + 0 + 0*w + 1/60*w**5 + 1/3*w**3. Find p such that i(p) = 0.
-2, -1
Factor -49/4*p**3 - 8*p - 1 - 77/4*p**2.
-(p + 1)*(7*p + 2)**2/4
Let n(s) = -9*s**4 + 3*s**3 + 6*s**2 - 6*s - 3. Let a(m) = -m**5 + 8*m**4 - 2*m**3 - 6*m**2 + 5*m + 2. Let w(z) = 3*a(z) + 2*n(z). Factor w(v).
-3*v*(v - 1)**3*(v + 1)
Let i = 44/9 + -43/9. Let k(r) be the second derivative of 1/54*r**4 + 0 + 2*r + i*r**3 + 2/9*r**2. Suppose k(f) = 0. Calculate f.
-2, -1
Let g(z) be the third derivative of z**7/6300 - z**6/900 - z**4/3 - 10*z**2. Let i(n) be the second derivative of g(n). Factor i(j).
2*j*(j - 2)/5
Suppose -2*d + 4 = -4. Factor -3*s - 4*s**5 + 3*s + 3*s**4 - d*s**2 + 5*s**5.
s**2*(s - 1)*(s + 2)**2
Let i = -1 + 3. Let w be (-8)/8*(i - 2). Suppose w + 1/3*v**2 + 2/3*v = 0. Calculate v.
-2, 0
Suppose 3*i - 2*x + 0*x + 2 = 0, -2*i + 5*x - 16 = 0. Let k = 1403 - 9819/7. Suppose 0 + 6/7*l**i + k*l = 0. Calculate l.
-1/3, 0
What is h in -6*h**2 - 6*h**3 + 2*h**2 + 2*h**2 + 5*h**3 = 0?
-2, 0
Let t = 41 + -28. Let q = t + -13. Solve 2/11*r**4 - 2/11*r**2 - 2/11*r**3 + 2/11*r + q = 0 for r.
-1, 0, 1
Let h(m) be the first derivative of 4/7*m + 22/35*m**5 + 2 + 46/21*m**3 - 11/7*m**2 - 2/21*m**6 - 23/14*m**4. What is r in h(r) = 0?
1/2, 1, 2
Let n(q) be the second derivative of q**6/120 + q**5/80 - q**4/48 - q**3/24 + 4*q. Determine i, given that n(i) = 0.
-1, 0, 1
Let p(f) be the first derivative of 10*f**6/3 - 6*f**5 + 5*f**4/16 + 5*f**3/2 + 5*f**2/8 + 16. Factor p(y).
5*y*(y - 1)**2*(4*y + 1)**2/4
Let w(l) = 3*l + 3 + 1 - 6 + 2*l**2. Let g(b) = 6*b**2 + 8*b - 6. Let r(o) = 3*g(o) - 8*w(o). Factor r(z).
2*(z - 1)*(z + 1)
Let b = -3 - -3. Let l(s) = s**3 - s**2 - s + 3. Let d be l(b). Factor 1/4*v**2 + 0 + 0*v + 1/4*v**4 + 1/2*v**d.
v**2*(v + 1)**2/4
Let 9 + 4*r - 2*r - 10 - r**2 = 0. What is r?
1
Let j(o) = o**3 + o**2 - o - 1. Let k(y) = -3*y**4 - 6*y**3 - 12*y**2 - 18*y - 9. Let n(b) = 6*j(b) - k(b). Factor n(t).
3*(t + 1)**4
Let i(r) = -5*r**5 - 5*r**4 - 2*r**3 - 6. Let n(y) = 11*y**5 + 11*y**4 + 4*y**3 + 13. Let f(c) = 13*i(c) + 6*n(c). Solve f(p) = 0 for p.
-2, 0, 1
Let s = 48363418/315 - 153534. Let c = s - 4/45. Suppose 2/7*p - c + 2/7*p**2 = 0. Calculate p.
-2, 1
Suppose 3 = i - x + 5, 4*i - x + 8 = 0. Let g be (-3 + 15/9)/i. Factor -4/3*v**2 + 1/3*v**3 - g + 5/3*v.
(v - 2)*(v - 1)**2/3
Let i(p) be the second derivative of -p**7/56 - 7*p**6/40 - 3*p**5/8 + 9*p**4/8 + 27*p**3/8 - 81*p**2/8 - 2*p. Determine v, given that i(v) = 0.
-3, 1
Let o(r) be the third derivative of 0*r + 1/210*r**6 - 1/42*r**4 + 0*r**5 + 11*r**2 + 1/735*r**7 - 1/21*r**3 + 0. Factor o(j).
2*(j - 1)*(j + 1)**3/7
Let s be 6*10/15 - (-12)/(-3). Solve 0*a + s*a**2 - 2/3*a**4 - 2/3*a**3 + 0 = 0.
-1, 0
Factor -22*m - 9*m**2 - 2 + 6*m + 8*m**2 - 13*m**2.
-2*(m + 1)*(7*m + 1)
Determine p so that -168*p**3 + 34/3*p + 8*p**2 - 4/3 = 0.
-2/7, 1/6
Let b = 10 + -5. Suppose -r - 2*r + 4 = v, r + b*v = -8. Solve 6*w**3 + 0*w + r*w - 3*w**2 - 5*w**3 = 0.
0, 1, 2
Let x(n) be the second derivative of n**4/3 + 4*n**3/3 - 6*n**2 + 3*n. Factor x(c).
4*(c - 1)*(c + 3)
Let v(s) = s**3 - s + 1. Let l(y) = -2*y**3 + 20*y**2 + 38*y + 10. Let i(x) = -l(x) - 6*v(x). Suppose i(g) = 0. What is g?
-2, -1
Let 8/5*f**2 + 2*f**5 - 16/5*f + 0 + 46/5*f**4 + 12*f**3 = 0. Calculate f.
-2, -1, 0, 2/5
Factor 0*l**3 + 3*l - l**3 + 0*l**2 + 2 + 0*l**2.
-(l - 2)*(l + 1)**2
Suppose -5*s = -3*j - 11, 0 = -6*s + s + 4*j + 13. Factor s - 2 + i**3 - 1 + 2*i - 4*i**2 + 3*i.
(i - 2)*(i - 1)**2
Let y = -2 + -3. Let j(w) = -3*w**3 + 3*w**2 + 2*w. Let n(z) = -6*z**3 + 6*z**2 + 5*z. Let c(o) = y*j(o) + 2*n(o). Factor c(d).
3*d**2*(d - 1)
Let r(p) be the second derivative of -2*p**7/21 + 11*p**6/30 - 9*p**5/20 + p**4/12 + p**3/6 - 23*p. Solve r(j) = 0 for j.
-1/4, 0, 1
Suppose 0 = g - 3, -2*g - 3 = -4*c - 5. Let h be (-1 - -3) + -1 + c. Suppose -1/4*w**3 - 5/4*w**2 - 1 - h*w = 0. What is w?
-2, -1
Let v(j) = -j**3 + 12*j**2 + j - 10. Let y be v(12). Let o(k) be the first derivative of 0*k - 1/4*k**2 - y - 1/6*k**3. Factor o(q).
-q*(q + 1)/2
Factor 30*p**2 - 81 + 162 - 81 + 5*p.
5*p*(6*p + 1)
Factor 6*m**2 - 12*m - 20*m**2 - 4*m**3 + 2*m**2 - 4.
-4*(m + 1)**3
Let r(i) be the second derivative of i**4/6 + i**3/3 - 25*i. Factor r(v).
2*v*(v + 1)
Let g(l) be the first derivative of -5*l**6/6 + l**5 + 15*l**4/2 + 10*l**3/3 - 25*l**2/2 - 15*l - 66. Determine s so that g(s) = 0.
-1, 1, 3
Let k(v) = v + 15. Let q(c) = -c**3 + 9*c**2 - 9*c - 7. Let x be q(8). Let j be k(x). Let j + 2/9*m**3 + 0*m - 2/9*m**2 = 0. What is m?
0, 1
Let c = 259 + -256. Factor 0 + 0*q - 14/5*q**c + 4/5*q**2.
-2*q**2*(7*q - 2)/5
Let k(i) be the second derivative of i - 1/180*i**5 + 0*i**3 + i**2 + 0 + 0*i**4. Let o(f) be the first derivative of k(f). Suppose o(u) = 0. Calculate u.
0
Factor -4*c**3 + 8*c + 2*c**2 - 41 + 2*c**3 + 33.
-2*(c - 2)*(c - 1)*(c + 2)
Determine u so that -9/7*u**2 + 27/7*u**3 - 9/7*u**5 - 6/7*u + 0 - 3/7*u**4 = 0.
-2, -1/3, 0, 1
Factor 4*y**2 + 314 - 72 -