 + 5*v(t). Determine r, given that n(r) = 0.
-2/7, 0, 1
Let u = 17 + -22. Let d(a) = -2*a**3 + a**2 + 2*a + 4. Let h(z) = -2*z**3 + 2*z**2 + 2*z + 4. Let x(l) = u*h(l) + 6*d(l). Factor x(p).
-2*(p - 1)*(p + 1)*(p + 2)
Suppose -2/5*p**2 + 1/5*p**3 + 2/5 - 1/5*p = 0. Calculate p.
-1, 1, 2
Let i(k) = -k**3 - 7*k**2 + 3*k + 54. Let o be i(-6). Determine t, given that o*t + 0 - 2/7*t**3 + 0*t**2 - 2/7*t**5 + 4/7*t**4 = 0.
0, 1
Let o(y) be the first derivative of y**6/57 - 6*y**5/95 + y**4/19 + 3. Factor o(f).
2*f**3*(f - 2)*(f - 1)/19
Factor 5/4*m**2 - 1/4*m**3 + 1 - 2*m.
-(m - 2)**2*(m - 1)/4
Let f = -13 + 17. Let t(d) be the second derivative of 2*d - 1/12*d**3 + 0 + 1/30*d**6 + 1/4*d**2 - 1/8*d**f + 1/40*d**5. Suppose t(k) = 0. What is k?
-1, 1/2, 1
Let a(m) be the second derivative of m**7/126 - m**6/45 + m**4/18 - m**3/18 + m. Find c, given that a(c) = 0.
-1, 0, 1
Let y(q) be the third derivative of -q**8/5040 + q**7/2520 + q**6/1080 - q**5/360 - 4*q**3/3 - 4*q**2. Let n(p) be the first derivative of y(p). Factor n(i).
-i*(i - 1)**2*(i + 1)/3
Factor -4/3*h**2 - 1/3*h**3 + 0*h + 0.
-h**2*(h + 4)/3
Suppose 7*a - 2*a + 30 = 0. Let n be -2 - (-2 - a/(-3)). Factor 2*m**2 - 4*m**4 - 2*m**3 - 2*m**5 - 2*m**n.
-2*m**3*(m + 1)**2
Let z(q) = 8*q**4 - 4*q**2 + 4*q. Let f(s) = -17*s**4 + 7*s**2 - 9*s + 1. Let i(x) = 4*f(x) + 9*z(x). Let i(h) = 0. What is h?
-1, 1
Let r(h) = -1160*h**4 + 890*h**3 + 325*h**2 - 55*h + 55. Let v(m) = -43*m**4 + 33*m**3 + 12*m**2 - 2*m + 2. Let y(n) = 2*r(n) - 55*v(n). Factor y(w).
5*w**2*(w - 1)*(9*w + 2)
Let w = -4261/9 - -475. Factor 4/9 + 2*x**2 + 2/9*x**4 + w*x + 10/9*x**3.
2*(x + 1)**3*(x + 2)/9
Let c be 744/56*(-96)/9. Let t = c - -142. Suppose t*w**2 + 2/7*w + 0 = 0. What is w?
-1, 0
Let a(x) be the first derivative of -x**7/840 - x**6/120 - x**5/60 + x**3 + 1. Let d(w) be the third derivative of a(w). Determine c, given that d(c) = 0.
-2, -1, 0
Suppose 0 = -14*z - 14 + 42. Factor -2/7*t**z + 0 + 0*t.
-2*t**2/7
Let q(i) be the second derivative of i**8/5040 + i**7/945 + i**6/540 - 3*i**4/4 - 10*i. Let p(h) be the third derivative of q(h). Solve p(s) = 0.
-1, 0
Factor -3*q**5 + 3*q**3 + 2*q**2 - 5*q**2 + 3*q**4 - 5*q**4 + 5*q**4.
-3*q**2*(q - 1)**2*(q + 1)
Determine t so that 1/2*t**2 - 5/2*t - 7 = 0.
-2, 7
Suppose -2*i**3 + 0*i**2 + i**2 + 0*i**3 + i**3 = 0. What is i?
0, 1
Let s(o) be the first derivative of -4*o**5/5 + 11*o**4/4 + o**3 - 8*o**2 - 4*o + 5. Solve s(m) = 0 for m.
-1, -1/4, 2
Let g(b) = -2*b**4 + b**3 - 24*b**2 + 29*b + 2. Let l(y) = 3*y**4 - 3*y**3 + 49*y**2 - 57*y - 3. Let w(t) = -11*g(t) - 6*l(t). Factor w(m).
(m - 1)**2*(m + 4)*(4*m - 1)
Suppose 0 = 5*b - p - 19, b + 5*p - 4*p + 1 = 0. Find u such that -b*u**4 + 9*u**3 - 3/4 + 9/2*u - 39/4*u**2 = 0.
1/2, 1
Let k(i) be the second derivative of -i**7/1890 - i**6/1620 + i**5/135 + i**4/36 + 5*i**3/6 - 2*i. Let m(t) be the second derivative of k(t). Factor m(f).
-2*(f + 1)**2*(2*f - 3)/9
Solve 10*n**2 - 4*n + 20*n**2 - 32*n**2 = 0.
-2, 0
Let y = 146 + -2335/16. Let f(m) be the first derivative of -1/8*m**2 - 1 + 1/4*m + y*m**4 - 1/12*m**3. Factor f(n).
(n - 1)**2*(n + 1)/4
Let g(j) be the second derivative of j**6/2 - 21*j**5/20 + j**4/2 - 2*j. Solve g(h) = 0.
0, 2/5, 1
Let p = -1/294 - -395/882. Factor 0 + p*z - 2/9*z**2.
-2*z*(z - 2)/9
Suppose -9 = 2*q - 3. Let k(x) = 2 - 8*x - 3 - 4 - 20*x**2 + 6*x**4 + 3. Let t(u) = -2*u**4 + 7*u**2 + 3*u + 1. Let v(d) = q*k(d) - 8*t(d). Factor v(h).
-2*(h - 1)**2*(h + 1)**2
Let o = 6 - 1. Let v = o + -3. Factor -10/3*q - v*q**2 - 4/3.
-2*(q + 1)*(3*q + 2)/3
Let l(c) be the second derivative of c**7/168 + c**6/120 - c**5/16 - c**4/48 + c**3/3 - c**2/2 - 24*c. Factor l(u).
(u - 1)**3*(u + 2)**2/4
Let k be (2 + (-1 - 1))/1. Factor v**3 + 0 + k - v.
v*(v - 1)*(v + 1)
Solve 8/7*b**3 - 32/7*b + 0*b**2 + 32/7 - 2/7*b**4 = 0 for b.
-2, 2
Let f(i) be the second derivative of -i**6/15 - 3*i**5/10 - i**4/3 + 12*i. Find w, given that f(w) = 0.
-2, -1, 0
Suppose -j - 3 = -4*t - t, -5*t + 15 = 5*j. Suppose 4/3*r**3 - 3/2*r**5 + 1/6*r + 0 - r**j + r**4 = 0. Calculate r.
-1, 0, 1/3, 1
Let q(c) be the second derivative of -c**7/5460 - c**6/780 - c**5/260 - c**4/156 + c**3/3 - 3*c. Let i(b) be the second derivative of q(b). Factor i(m).
-2*(m + 1)**3/13
Let k = -58 + 61. Let y(h) be the third derivative of 1/240*h**5 + 0*h - 1/480*h**6 + 1/96*h**4 + 4*h**2 - 1/24*h**k + 0. Factor y(c).
-(c - 1)**2*(c + 1)/4
Let o(m) be the second derivative of -m**5/60 - m**4/18 - 3*m. Solve o(l) = 0 for l.
-2, 0
Let g**2 + 36*g - 40*g - 4*g**3 + 23*g**2 - 8 - 8*g**4 = 0. What is g?
-2, -1/2, 1
Let -4 - 4/3*r**3 - 4/3*r**2 + 20/3*r = 0. What is r?
-3, 1
Let q(d) be the first derivative of d**6/14 + d**5/5 + 3*d**4/28 - d**3/7 - d**2/7 - 7. Factor q(i).
i*(i + 1)**3*(3*i - 2)/7
Suppose 4*d - 2 = 2. Let l(z) be the first derivative of -1/10*z**2 - 1/20*z**4 - d + 0*z + 2/15*z**3. Determine x, given that l(x) = 0.
0, 1
Let p(c) = c**2 - 10*c + 4. Let l be p(10). Suppose -4*r**2 + l*r**2 + r**3 = 0. Calculate r.
0
Let y(o) be the third derivative of o**5/450 + o**4/180 - 18*o**2. Factor y(v).
2*v*(v + 1)/15
Let x(g) = -2*g**3 - 7*g**2 - 13*g - 5. Let b(j) = j**3 + 4*j**2 + 7*j + 2. Let q(i) = -5*b(i) - 2*x(i). Factor q(s).
-s*(s + 3)**2
Let i = 327/70 + -6/35. Let w(q) be the first derivative of -i*q**4 - 4*q**3 + 1 - q**2 + 0*q. Find t, given that w(t) = 0.
-1/3, 0
Let r(d) be the third derivative of d**7/945 - d**6/135 + d**5/54 - d**4/54 - d**2. Let r(p) = 0. Calculate p.
0, 1, 2
Let h(n) = -n**3 - 10*n**2 - 10*n - 6. Let w be h(-9). What is k in 4*k**w + 0*k**3 - 2*k**5 - 2*k**4 + 6*k**2 - 2*k**3 - 4*k**2 = 0?
-1, 0, 1
Let a(q) = q**5 + q**4 + q**3 - q**2 + q - 1. Let k(o) = 9*o**5 + o**4 + o**3 - o**2 + 5*o - 5. Let u(g) = 5*a(g) - k(g). Factor u(x).
-4*x**2*(x - 1)**2*(x + 1)
Let a be 0/(-10)*(-4)/(-20). Factor 0 - 3/2*g**4 + a*g**2 + 0*g + g**3.
-g**3*(3*g - 2)/2
Suppose -3 = 4*t - 5*t. Solve -2*q**4 - 2*q - 7*q**4 + q**2 + t*q + 8*q**4 - q**3 = 0.
-1, 0, 1
What is g in -12/7*g**5 + 0 + 0*g**2 - 8/7*g**3 + 4*g**4 + 0*g = 0?
0, 1/3, 2
Let f(l) be the third derivative of l**5/30 - l**4/6 + l**3/3 + 4*l**2. Find y, given that f(y) = 0.
1
Let z(s) = -s - 5. Let c be (-6)/8 - (-85)/(-20). Let r be z(c). Factor r - 1/4*k**3 + 0*k**4 + 0*k + 1/4*k**5 + 0*k**2.
k**3*(k - 1)*(k + 1)/4
Let y be -3 + 1 - 5/(-1). Factor 11*o**2 - y*o - 4*o - 4*o**3 + 2*o - 2.
-(o - 2)*(o - 1)*(4*o + 1)
Let x(t) be the second derivative of -1/4*t**4 + t - 3*t**2 - 3/2*t**3 + 0. Determine d so that x(d) = 0.
-2, -1
Determine x, given that 16*x**2 - 1 + 18*x + 4 - 1 = 0.
-1, -1/8
Let c(q) be the third derivative of 1/8*q**4 + 0*q**3 + 0 - 1/60*q**5 + 0*q + 2*q**2. Factor c(k).
-k*(k - 3)
Let u(n) = -9*n**4 - n**3 + 4*n**2 - 4*n. Let c(d) = -5*d**4 - d**3 + 2*d**2 - 2*d. Let a = -6 + 11. Let q(r) = a*c(r) - 3*u(r). Suppose q(y) = 0. Calculate y.
-1, 0, 1
Let b(c) be the second derivative of 2*c**7/21 + 4*c**6/15 - 3*c**5/5 + 32*c. Factor b(w).
4*w**3*(w - 1)*(w + 3)
Let j = -403540/159 - -2538. Let w = 940/1113 + j. Factor -6/7*a + 2/7 + w*a**2 - 2/7*a**3.
-2*(a - 1)**3/7
Let a(u) = u**2 - 12*u + 13. Let w be a(11). Let o(f) be the first derivative of -1/12*f**3 + 0*f**w + 0*f - 2. Let o(b) = 0. Calculate b.
0
Let j = -8 + 32. Suppose 11*b**5 - 6*b + 4 + 0*b + j*b**4 - 28*b**2 - 14*b**3 + 6*b**3 + 3*b**5 = 0. What is b?
-1, 2/7, 1
Let w = -403 - -883. Factor 4*u**4 + w*u - 4*u**5 - 480*u.
-4*u**4*(u - 1)
Let g(h) = h**4 - 3*h**3 - 2*h**2 + 3*h + 4. Let l(b) = -5*b**2 - 4*b - b**4 + 7*b**2 + 2*b**3 - 5 + 2*b**3. Let c(w) = -4*g(w) - 3*l(w). Solve c(k) = 0 for k.
-1, 1
Suppose -5 = 2*b + a, 4*b - 1 = 2*a + 9. Let b*z**2 + 3*z**2 - 11*z**3 + 3*z**5 + 30*z - 4 + z**4 - 22*z = 0. What is z?
-2, -1, 2/3, 1
Let v(i) = i**3 + 4*i**2 - i - 1. Let q(o) = -o**3 - 3*o**2 + o + 1. Let h(a) = 3*q(a) + 2*v(a). What is b in h(b) = 0?
-1, 1
Let r = 73 + -73. Factor 0 + r*o + 2/3*o**3 + 0*o**2.
2*o**3/3
Let i(x) = x**2 + 4. Let w be i(0). Let g be (w/6)/((-2)/(-12)). Solve 2*k**2 + 2/3*k**g + 2*k**3 + 2/3*k + 0 = 0.
-1, 0
Factor -4/15*p**2 - 14/15*p - 8/15 + 2/15*p**3.
2*(p - 4)*(p + 1)**2/15
Determine t so that 5 + 6*t - 9*t**2 + 0*t**2 + 10*t**2 = 0.
-5, -1
Let w(p) be the second derivative