27 + a**2/9 - 2*a. Suppose q(w) = 0. Calculate w.
1
Let h(w) be the first derivative of w**4/10 - w**2/5 + 7. Let h(k) = 0. What is k?
-1, 0, 1
Determine v, given that 10/3*v**4 + 8/3*v**2 - 8/3*v + 0 + 26/3*v**3 = 0.
-2, -1, 0, 2/5
Let v(m) be the second derivative of m**5/25 + 19*m**4/60 + 11*m**3/30 - 2*m**2/5 + 16*m - 2. Suppose v(l) = 0. Calculate l.
-4, -1, 1/4
Suppose -k = -6*k. Factor 2*z + 0*z + 2*z**2 + z**2 + k*z.
z*(3*z + 2)
Let -2/9 - 8/9*c**3 + 14/9*c**2 - 4/9*c = 0. What is c?
-1/4, 1
Suppose 2*c - 3*c + 2 = 0. Let m = 4 - 2. Factor -4*o**c + 5*o**m + o**2 + 0*o**2.
2*o**2
Let u(i) = 9*i**5 - 3*i**4 + 7*i**3 - 4*i**2 + 5*i - 7. Let y(x) = -4*x**5 + x**4 - 3*x**3 + 2*x**2 - 2*x + 3. Let o(z) = 6*u(z) + 14*y(z). Factor o(d).
-2*d*(d - 1)*(d + 1)**3
Let j(l) = -l**2 + 9*l + 10. Let m be j(10). Factor -3/2*w**5 + 0 + 0*w**2 + 0*w + 3/2*w**4 + m*w**3.
-3*w**4*(w - 1)/2
Find u such that 6*u**2 - 2*u**2 + u + 4 + 7*u = 0.
-1
Determine r so that -57/5*r**3 + 21/5*r**4 - 3/5*r**5 + 12/5 - 48/5*r + 15*r**2 = 0.
1, 2
Let b be (2/6)/((-21)/(-6)). Let n(o) be the first derivative of -b*o**3 + 2/7*o**2 - 2/7*o + 1. Factor n(x).
-2*(x - 1)**2/7
Let o be ((-136)/(-51))/(14/6). Factor -2/7*m**2 - o + 8/7*m.
-2*(m - 2)**2/7
Let x(w) be the third derivative of w**8/40 - 31*w**7/350 + 9*w**6/100 + w**5/100 - w**4/20 - 7*w**2. Let x(l) = 0. What is l?
-2/7, 0, 1/2, 1
Let t(f) = -f**4 + f**2 - 1. Let v(y) = 6*y**4 + y**3 - 7*y**2 + 5. Let h(c) = -15*t(c) - 3*v(c). Solve h(u) = 0 for u.
-2, 0, 1
Let z be 0/(((-6)/(-9))/((-4)/6)). What is q in z - 2/7*q**5 - 6/7*q**3 + 0*q - 2/7*q**2 - 6/7*q**4 = 0?
-1, 0
Factor 2/15*z + 0*z**2 - 2/15*z**3 + 0.
-2*z*(z - 1)*(z + 1)/15
Suppose -3*z + 2*r = -4*z + 6, -3*z = -5*r + 15. Solve z + 4/9*i + 2/9*i**2 = 0.
-2, 0
Let p(t) be the first derivative of 2/7*t + 5/7*t**4 + 2/7*t**5 + 1 + 1/21*t**6 + 5/7*t**2 + 20/21*t**3. Factor p(z).
2*(z + 1)**5/7
Let s(q) be the first derivative of q**5/10 + q**4/4 - 2*q**3/3 - q**2/2 + 3*q/2 + 9. Determine l so that s(l) = 0.
-3, -1, 1
Let u(b) be the third derivative of 4*b**2 + 0*b + 1/40*b**6 + 0*b**3 - 3/20*b**5 + 1/4*b**4 + 0. What is r in u(r) = 0?
0, 1, 2
Let x be 5 + (3 - 2) - 62/11. Suppose -10/11*z + x*z**2 + 2/11*z**5 + 8/11*z**3 + 4/11 - 8/11*z**4 = 0. What is z?
-1, 1, 2
Factor -14*g**5 - 7*g**5 - 52*g**4 + 10*g**2 + 25*g**3 - 28*g**4 + 66*g**5.
5*g**2*(g - 1)**2*(9*g + 2)
Suppose -3*a - 5*x = -5, 12*x - 15*x = 2*a - 3. Suppose -2/5*i**2 + 0*i - 2/5*i**4 + 4/5*i**3 + a = 0. What is i?
0, 1
Suppose -2*y - 19 = -23. Let a(v) be the first derivative of -1/10*v**4 + 1 + 2/25*v**5 + 1/5*v**y - 2/15*v**3 + 0*v. Find w such that a(w) = 0.
-1, 0, 1
Let v be 2*(1 - 15/16). Let a(l) be the third derivative of 0 + 0*l**3 + v*l**4 + 1/10*l**5 + 0*l + 1/40*l**6 - 3*l**2. Find n such that a(n) = 0.
-1, 0
Let y(m) = 2*m**3 + m**2 - 1. Let o be y(-1). Let q(v) = v**2 + v. Let x be q(o). Determine n, given that -n**2 + 2*n**2 - x*n**2 + 2 + n = 0.
-1, 2
Let u(h) be the first derivative of h**5/5 + h**4/2 + h**3/3 + 2. Factor u(m).
m**2*(m + 1)**2
Let y(v) be the third derivative of -1/1848*v**8 + 0*v + 0*v**4 + 0*v**3 + 0 - 1/1155*v**7 - 3*v**2 + 1/330*v**5 + 1/660*v**6. Factor y(f).
-2*f**2*(f - 1)*(f + 1)**2/11
Let t(j) be the second derivative of j**6/30 - j**5/20 - j**4/12 + j**3/6 - 8*j. Factor t(u).
u*(u - 1)**2*(u + 1)
Let b(o) be the third derivative of 3*o**2 + 1/150*o**6 + 0*o - 1/150*o**5 + 0 - 1/525*o**7 + 0*o**4 + 0*o**3. Solve b(m) = 0.
0, 1
Let d be 4 - (-4 + -6 + 3). Suppose -16*p = -d*p - 10. Factor -1/4 + 1/4*o**p + 0*o.
(o - 1)*(o + 1)/4
Let s(m) = -2*m**4 + 8*m**2 - 8*m. Let t(h) be the first derivative of 1/5*h**5 + 0*h**4 + 3/2*h**2 - h**3 - 4 + 0*h. Let v(y) = -3*s(y) - 8*t(y). Factor v(q).
-2*q**4
Let d(i) be the third derivative of 5*i**8/336 + i**7/42 - 5*i**6/24 - i**5/12 + 5*i**4/3 - 10*i**3/3 + 16*i**2. Factor d(w).
5*(w - 1)**3*(w + 2)**2
Let u be (5 - -1) + 0 + -3. Find a such that 4*a**u - 2*a**3 + 2*a**3 - a**3 = 0.
0
Let l be (1/(-2))/(6/(-36)). Let z(b) be the second derivative of 0 - 3*b - 1/4*b**l + 0*b**2 + 1/8*b**4. Factor z(h).
3*h*(h - 1)/2
Let r = -162 - -165. Factor -3/5*g - 1/5 - 1/5*g**r - 3/5*g**2.
-(g + 1)**3/5
Let t be (-2)/(-10) + 21/(-105). Let -2/9*h**3 + t - 2/9*h**4 + 2/9*h**2 + 2/9*h = 0. What is h?
-1, 0, 1
Factor h**4 - 12*h**2 + 135*h**3 - 123*h**3 - 5*h**4 + 4*h.
-4*h*(h - 1)**3
Factor 240*d + 549*d**2 - 171*d**3 + 62*d**2 - 26*d**2 - 674*d**3 + 20.
-5*(d - 1)*(13*d + 2)**2
Let r be (3 + -1)/((-4)/(-6)). Suppose -2*h - 4*s = 3*h - 10, -3*h + 6 = 3*s. Solve r*z**4 - 3*z + 2*z**3 - 2*z**2 + z**5 - 1 + 2*z**5 - h*z**5 = 0.
-1, 1
Let z(g) be the third derivative of -g**7/105 - g**6/60 + g**5/10 + g**4/12 - 2*g**3/3 - 58*g**2. Factor z(q).
-2*(q - 1)**2*(q + 1)*(q + 2)
Let r(h) be the first derivative of -h**6/180 - h**5/60 - 5*h**3/3 - 5. Let j(k) be the third derivative of r(k). Suppose j(l) = 0. Calculate l.
-1, 0
Factor -o**4 + 7*o**4 - 2*o**4 - o**4 + 3*o**5.
3*o**4*(o + 1)
Let t = -5 - -2. Let i be (((-9)/4)/3)/t. Factor -1/2*f - i*f**2 + 0.
-f*(f + 2)/4
Let c(o) be the first derivative of 3 + 9/2*o**2 - 3*o - 3*o**3 + 3/4*o**4. Factor c(y).
3*(y - 1)**3
Let v be (-1)/(1/(2/(-1))). Factor 3/2*g + 5/2*g**3 - 1/4 - 3*g**v - 3/4*g**4.
-(g - 1)**3*(3*g - 1)/4
Suppose -3*f - 2*f - 20 = -2*o, 4*f = -16. Factor 2/7*t + 2/7*t**2 + o.
2*t*(t + 1)/7
Suppose 0 = -4*r + 7 + 5. Factor 19*i**4 - 6*i**2 + 19*i**4 - r*i**3 - 35*i**4.
3*i**2*(i - 2)*(i + 1)
Let z = 57 + -111/2. Find d such that -d**4 - d**2 + z*d**3 + 1/4*d + 0 + 1/4*d**5 = 0.
0, 1
Let i = -7 - -10. Factor -70*h**4 - 168*h**i + 21*h**4 - 39*h**2 + 50*h + 18*h - 12.
-(h + 1)*(h + 3)*(7*h - 2)**2
Let y = -2/251 + 5532/1255. Determine a so that -10*a**3 + 2/5 + 14*a**2 - y*a = 0.
1/5, 1
Solve -4/3*c**2 - 28/3*c - 16 = 0 for c.
-4, -3
Let v(p) be the second derivative of 2*p**6/45 - p**5/5 + p**4/9 + 2*p**3/3 - 4*p**2/3 - p + 37. Factor v(y).
4*(y - 2)*(y - 1)**2*(y + 1)/3
Let k(m) be the first derivative of -1 + 2/3*m**3 - 2*m**2 + 1/2*m**4 + 0*m. Factor k(g).
2*g*(g - 1)*(g + 2)
Let f(z) = z**3 + 2*z**2. Let k(u) = -5*u**2 - u - 1. Let y be k(-1). Let t(c) = 3*c**3 + 5*c**2. Let d(p) = y*f(p) + 2*t(p). What is g in d(g) = 0?
0
Let x(g) be the second derivative of -g**9/12096 + g**7/3360 - g**3/6 + 4*g. Let r(t) be the second derivative of x(t). Solve r(u) = 0.
-1, 0, 1
Suppose 0*z - 4*z + 7 = 5*v, -6 = -z + 3*v. Let k(w) be the second derivative of 0 + 0*w**z + 0*w**2 - w + 1/18*w**4. Find t such that k(t) = 0.
0
Let d(g) be the first derivative of -1 + 5*g**3 + 21/5*g**5 + g**6 + 3/2*g**2 + 27/4*g**4 + 0*g. Factor d(i).
3*i*(i + 1)**3*(2*i + 1)
Let f be (3546/(-48))/((-6)/4). Let y = f - 49. Let 1/4*x**2 + 1/4*x - 1/4*x**4 - y*x**3 + 0 = 0. Calculate x.
-1, 0, 1
Let b = 45 + -65. Let x be (1/(-2))/(b/8). Factor -1/5*o + 1/5*o**4 - 1/5*o**2 + 0 + x*o**3.
o*(o - 1)*(o + 1)**2/5
Suppose -5*w = -5*v - 40, -8 + 12 = -2*w - 3*v. Factor 8/11*z + 0 + 74/11*z**3 + 18/11*z**5 + 40/11*z**2 + 60/11*z**w.
2*z*(z + 1)**2*(3*z + 2)**2/11
Factor 2*p**2 + 3 - 9*p - 7*p - 1 + 20*p.
2*(p + 1)**2
Let a(k) be the first derivative of k**6/30 - 9*k**5/25 + 8*k**4/5 - 56*k**3/15 + 24*k**2/5 - 16*k/5 + 13. Factor a(c).
(c - 2)**4*(c - 1)/5
Let m = 23/10 - -6/5. Let k(q) be the second derivative of -m*q**4 - 3*q + 0 + 49/10*q**5 - 8*q**3 - 4*q**2. Suppose k(b) = 0. What is b?
-2/7, 1
Let f = 18 - 14. Factor -2/5*k**2 - 2/5*k**3 + 2/5*k**f + 2/5*k + 0.
2*k*(k - 1)**2*(k + 1)/5
Let r be 35/84 - (-1)/4. Let h(c) be the third derivative of 0 - 1/4*c**5 - 1/2*c**4 + c**2 + 0*c + r*c**3 - 1/30*c**6. Factor h(j).
-(j + 2)**2*(4*j - 1)
Suppose 0 = 6*b - 2*b - 8. Let h be (1/2)/((-2)/(-12)). Solve -b*y**2 - h*y**2 + 2*y**4 + 3*y**2 = 0 for y.
-1, 0, 1
Factor 17*r + 0*r**2 + 28 - 49*r + 0*r**2 + 4*r**2.
4*(r - 7)*(r - 1)
Let l(m) = -7 + m**3 + 2*m**2 + 2*m + 2 + 4*m**2 + 2*m. Let u be l(-5). Factor 0*z**2 + u + 2/7*z**3 - 2/7*z.
2*z*(z - 1)*(z + 1)/7
Let d be (9/21)/(2/21). Find v, given that -d*v**4 + 10*v - 2 + 15*v**3 - 37/2*v**2 = 0.
2/3, 1
Let v(n) be the second derivative of n**10/75600 + n**9/37800 - n**8/16800 - n**7/6300 - n**4/12 + n. Let a(u) be the third derivative of v(u). Factor a(y).
2*y**2*(y