 (1/3)/((-1)/(-45)). Suppose n*w**4 + 7*w + 21*w**2 - w + 3*w**5 + 0*w + 27*w**3 = 0. What is w?
-2, -1, 0
Suppose 5 = -5*p + 15. Let q(t) be the third derivative of 0*t + 3*t**p - 1/8*t**4 - 1/6*t**3 + 0 - 1/120*t**6 - 1/20*t**5. Factor q(y).
-(y + 1)**3
Let l(d) be the third derivative of 0*d**3 - d**2 + 0 + 0*d + 1/80*d**5 + 1/32*d**4. Determine c so that l(c) = 0.
-1, 0
Let c(p) = 8*p**3 - 9*p**2 - 2*p + 1. Let z(n) = -9*n**3 + 9*n**2 + 3*n. Let s(o) = -3*c(o) - 2*z(o). Let s(b) = 0. What is b?
-1/2, 1
Let d(z) be the third derivative of -5/72*z**4 + 1/180*z**5 + 0*z + 2/9*z**3 + 0 - 7*z**2. Solve d(k) = 0.
1, 4
Suppose 0 = -4*o + 2*a + 44 + 16, -56 = -3*o - 4*a. Solve -n**3 + 3*n**3 - 8 + 0*n + o*n + 4*n**3 + 22*n**2 = 0.
-2, 1/3
Factor 0 - 1/3*n + 1/3*n**3 - 1/3*n**2 + 1/3*n**4.
n*(n - 1)*(n + 1)**2/3
Let m(o) be the second derivative of 1/21*o**3 - 1/35*o**5 + 0 + 0*o**4 - 3*o + 0*o**2 + 0*o**6 + 1/147*o**7. Determine b, given that m(b) = 0.
-1, 0, 1
Let l(r) be the third derivative of 1/18*r**4 - 1/180*r**6 + 0*r**3 - 2*r**2 + 0*r - 1/90*r**5 + 0. Factor l(p).
-2*p*(p - 1)*(p + 2)/3
Factor 9 - 6*k + 3/4*k**3 - 3/4*k**2.
3*(k - 2)**2*(k + 3)/4
Let h = 4 + -3. Suppose o - 3*b - 1 = -0, -5*b = -o + h. Solve -4*l**2 + 3 - 4*l**4 - o + 6*l**4 = 0 for l.
-1, 1
Let y be (2 + -4)*1/(-12). Find n, given that -1/6*n**2 + 1/3*n - y = 0.
1
Suppose 7 = 4*u - k - 10, 2*u = 3*k + 21. Let h(m) be the second derivative of m**2 + 2*m + 0 - 1/10*m**5 + 1/2*m**4 - m**u. Find z such that h(z) = 0.
1
Let h(i) be the second derivative of -2/3*i**3 + 1/7*i**7 - 1/10*i**5 + 0 + 2*i - 1/3*i**6 + 5/6*i**4 + 0*i**2. Suppose h(x) = 0. What is x?
-1, 0, 2/3, 1
Suppose -5*r = -2*d + 28, -3*d + 4*r + 20 = -2*d. Let z(g) be the second derivative of 0 + 3*g + 9/2*g**4 - d*g**2 + 4*g**3. Factor z(m).
2*(3*m + 2)*(9*m - 2)
Let u(o) = 8*o**2 + o + 6*o**4 - 5*o - 1 + 7 + 10*o**4 + 22*o**3. Let h(r) = -r**4 - r**3 - r**2 - 1. Let a(q) = -6*h(q) - u(q). Solve a(g) = 0 for g.
-1, 0, 2/5
Let i(t) be the second derivative of -t**6/360 + t**4/24 + t**3/3 - 4*t. Let h(g) be the second derivative of i(g). Let h(d) = 0. What is d?
-1, 1
Let i = 55/183 + 2/61. Let v(w) be the second derivative of 0 + i*w**3 - 2*w**2 + 1/6*w**4 + 3*w. Let v(y) = 0. What is y?
-2, 1
Let o(n) be the first derivative of n**5/15 + n**4/3 + 5*n**3/9 + n**2/3 + 1. Find m such that o(m) = 0.
-2, -1, 0
Let q(o) be the second derivative of 3*o + 0*o**2 + o**3 + 3/20*o**5 - 3/4*o**4 + 0. Factor q(z).
3*z*(z - 2)*(z - 1)
Let n be -2 - (3 + (-1 - -1)). Let f(b) = -b**3 - 4*b**2 + 3*b - 5. Let i be f(n). Factor 2*s**4 + 4*s**i + 2*s**5 - 4*s**5 + s**3 - 5*s**5.
-s**3*(s - 1)*(3*s + 1)
Let f(r) be the second derivative of -1/8*r**3 + 3*r + 1/4*r**2 + 0 + 3/40*r**5 - 5/48*r**4. Factor f(s).
(s - 1)*(2*s - 1)*(3*s + 2)/4
Solve -3*t**2 - 58 - 54*t - 14 + 21 = 0 for t.
-17, -1
Determine p, given that 8/7*p**3 - 8/7*p - 4/7*p**4 + 0 + 4/7*p**2 = 0.
-1, 0, 1, 2
Let j(n) be the second derivative of 2*n**6/15 + 3*n**5/5 + 2*n**4/3 - 5*n. Factor j(i).
4*i**2*(i + 1)*(i + 2)
Suppose 0 = -0*p - 2*p + 10. Let d(r) be the third derivative of 0*r + 0 - 1/30*r**p - 1/4*r**4 - 2/3*r**3 - 2*r**2. Factor d(o).
-2*(o + 1)*(o + 2)
Let p = 4 - 0. Let j be p/(-2) - 22/(-10). Factor 1/5*s**2 + j*s + 0.
s*(s + 1)/5
Let v(q) be the first derivative of 14*q**3/51 + 5*q**2/17 - 4*q/17 - 19. Factor v(d).
2*(d + 1)*(7*d - 2)/17
Let t(k) be the third derivative of 0*k - 1/90*k**5 - 1/36*k**4 + 2/9*k**3 - 4*k**2 + 0. Factor t(z).
-2*(z - 1)*(z + 2)/3
Find m such that 14*m - 8*m**4 + 4/3*m**2 - 40/3*m**3 - 2/3*m**5 + 20/3 = 0.
-10, -1, 1
Let t be ((-5)/(-10))/(1/6). Factor -m**2 - 7*m**5 + 3*m - m**t + m**4 + 8*m**5 - 3*m.
m**2*(m - 1)*(m + 1)**2
Factor -p**4 + 0*p**3 + 8*p**3 - 2*p**3 + 4*p - 6*p**2 - 2*p**3 - 1.
-(p - 1)**4
Let f(n) be the second derivative of 2*n**2 - 1/6*n**4 + n + 0 - 1/3*n**3. Let f(q) = 0. What is q?
-2, 1
Suppose 0 = -3*a - 6, 0 = -3*g - 3*a - 5 - 1. Suppose g = 3*f + 2*f. Find y, given that f + 0*y**2 + 1/2*y**3 + 0*y = 0.
0
Let g be (3/(-27))/((-3)/9*1). Let l(c) be the second derivative of -2/9*c**4 + 1/3*c**2 + g*c**3 + c + 0. Factor l(r).
-2*(r - 1)*(4*r + 1)/3
Let g(c) be the second derivative of -c**6/120 - c**5/30 - c**4/24 + 3*c**2/2 + 4*c. Let y(m) be the first derivative of g(m). Solve y(l) = 0 for l.
-1, 0
Let j(f) be the second derivative of f**4/54 - 4*f**3/27 + 4*f**2/9 + 10*f. Suppose j(i) = 0. What is i?
2
Let p(h) be the first derivative of 0*h + 1/10*h**5 + 1/8*h**4 - 1/6*h**3 - 1/4*h**2 - 1. Suppose p(m) = 0. What is m?
-1, 0, 1
Let t(n) = 3*n**3 + n + 2. Let s(x) = x**3 + 1. Let y(d) = -2*s(d) + t(d). Let u(b) = 4*b**4 + 16*b**3 + 12*b. Let w(z) = u(z) - 12*y(z). Factor w(r).
4*r**3*(r + 1)
Suppose 3*l + l - x = -19, 0 = l - 5*x. Let z be 2/(1 - l)*1. Factor -1/3*f**2 + 1/3*f**3 - z*f + 1/3*f**4 + 0.
f*(f - 1)*(f + 1)**2/3
Let t be (3*6/(-63))/(4/(-6)). Determine g, given that -t*g + 0 - 3/7*g**2 = 0.
-1, 0
Let f(v) = 22*v**3 + 18*v**2 + 8*v + 4. Let n(y) = -21*y**3 - 18*y**2 - 7*y - 3. Let t(i) = 3*f(i) + 4*n(i). Let t(s) = 0. What is s?
-2/3, -1/3, 0
Factor 1/3*g**4 + 0*g + 2/3*g**2 + g**3 + 0.
g**2*(g + 1)*(g + 2)/3
Let t(x) be the first derivative of x**5/5 - x**4/2 + x**2 - x + 2. Let t(m) = 0. What is m?
-1, 1
Let x(n) be the first derivative of n**4/4 - 4*n**3/3 - n**2/2 + 4*n + 18. Factor x(y).
(y - 4)*(y - 1)*(y + 1)
Suppose 4*f - 5*f - 2 = 0. Let a be (-2)/3 - 2/f. Factor q + 1/3*q**3 - q**2 - a.
(q - 1)**3/3
Let q(z) be the first derivative of -14*z**3/9 - 11*z**2 + 20*z/3 + 7. Suppose q(o) = 0. What is o?
-5, 2/7
Suppose 0 = 5*s + 2*v - 3722, 0 = -s - 6*v + v + 749. Let 12*o**2 - 12*o + 105*o**3 + 48*o**2 - s*o**4 + 12*o**3 + 336*o**5 = 0. Calculate o.
-2/7, 0, 1/4, 2
Let o(d) be the third derivative of d**8/504 + 2*d**7/105 + 13*d**6/180 + 2*d**5/15 + d**4/9 - 5*d**2. Let o(b) = 0. Calculate b.
-2, -1, 0
Suppose -4 - 2 = -2*y. Suppose 8 = -y*g + 5*g. Factor 2*k**2 + k**4 - 4*k**2 + k**g.
2*k**2*(k - 1)*(k + 1)
Factor -6/7*k**2 + 34/7*k - 20/7.
-2*(k - 5)*(3*k - 2)/7
Let r(t) be the second derivative of t**4/12 + t**3/12 - t**2/4 + 19*t. Factor r(w).
(w + 1)*(2*w - 1)/2
Let b be ((-192)/30)/((-1)/5). Let x = b + -158/5. Suppose 0 + 4/5*d - x*d**2 = 0. Calculate d.
0, 2
Let x be (3 - (-28)/(-12))*5/5. Determine k so that -x*k**2 - 2/3*k**4 + 0 + 0*k - 4/3*k**3 = 0.
-1, 0
Let v = 0 + -6. Let a be v/9 - (-2)/3. Factor 3*f**3 - 2*f**4 + f**5 + a*f**2 - f**4 - f**2.
f**2*(f - 1)**3
Let b = -124 + 131. Let o(q) be the third derivative of 1/8*q**4 + 0 + 0*q + 1/70*q**b + 3/20*q**5 - 2*q**2 + 3/40*q**6 + 0*q**3. Factor o(h).
3*h*(h + 1)**3
Let y(d) = -4*d**3 - 27*d**2 - 45*d - 29. Let i(u) = -4*u**3 - 26*u**2 - 46*u - 30. Let v(p) = 3*i(p) - 2*y(p). Suppose v(w) = 0. Calculate w.
-2
Let g(m) = -96*m**4 + 116*m**3 + 144*m**2 + 28*m. Let f(b) = 97*b**4 - 117*b**3 - 144*b**2 - 29*b. Let v(j) = -4*f(j) - 3*g(j). Factor v(n).
-4*n*(n - 2)*(5*n + 2)**2
Let -123 + 56 + 61 + 3*u - 3*u**3 + 6*u**2 = 0. What is u?
-1, 1, 2
Let l(b) = -b**2 + 6*b. Let p be l(6). Let d = -116/85 - -30/17. Factor p + d*s + 2/5*s**2.
2*s*(s + 1)/5
Let o(v) be the third derivative of v**8/50400 + v**7/6300 + v**6/1800 + v**5/60 - 3*v**2. Let b(g) be the third derivative of o(g). Factor b(z).
2*(z + 1)**2/5
Let z(s) be the second derivative of 9*s**5/140 - s**4/28 - s**3/7 - 6*s. Find f such that z(f) = 0.
-2/3, 0, 1
Let x be 4948/2544 - 1/4. Let f = x - 3/106. Factor 0*t + f*t**4 + t**3 + 0 - 2/3*t**2.
t**2*(t + 1)*(5*t - 2)/3
Let b(r) be the first derivative of r**5/90 + r**4/18 + r**3/9 - r**2/2 + 4. Let p(s) be the second derivative of b(s). Factor p(q).
2*(q + 1)**2/3
Let g be (-7)/(175/20)*(-20)/6. Factor g*f - 4/3 + 5/3*f**2.
(f + 2)*(5*f - 2)/3
Let m be 4/2*(3/(-1) + 4). Let p(z) be the second derivative of 0 - 1/24*z**4 - 1/6*z**3 + 3*z + 0*z**m. Let p(a) = 0. Calculate a.
-2, 0
Let t be (0 - (-2)/7)*98/42. Factor 2/3*z**4 + 0*z - 2/3*z**2 + 0 + t*z**3 - 2/3*z**5.
-2*z**2*(z - 1)**2*(z + 1)/3
Let n = -891/2 + 458. Let i = n + -12. Determine p so that 3*p**2 + 4 - i*p**3 - 6*p = 0.
2
Let x(u) be the second derivative of 17*u**5/4 - 175*u**4/6 + 190*u**3/3 - 20*u**2 - u. Determine p, given that x(p) = 0.
2/17, 2
Supp