q + 4/3*q**3 = 0. Calculate q.
-1, 3
Let u(t) be the third derivative of -t**8/504 + t**7/315 + t**6/36 + t**5/30 + 10*t**2. Factor u(a).
-2*a**2*(a - 3)*(a + 1)**2/3
Suppose -3/2*z**2 - 6*z**3 + 3/2 + 6*z = 0. Calculate z.
-1, -1/4, 1
Let c(g) = g**2 - 4*g + 5. Let k be c(4). Suppose -3*j = k*v - 37, 0*j + 5*j + v = 25. Factor -5*w**4 + 0*w - j*w**3 + 2*w + 5*w**4 + 2*w**5.
2*w*(w - 1)**2*(w + 1)**2
Let a be (-12)/(-3)*42/12. Suppose -a - 1 = -5*g. Find k, given that -27/5*k**2 - 6/5 - 3/5*k**4 + g*k**3 + 21/5*k = 0.
1, 2
Suppose -2/13*v**3 + 0 + 0*v + 4/13*v**2 = 0. Calculate v.
0, 2
Factor 147 + 15*z**2 - 12*z**2 + 4*z + 38*z.
3*(z + 7)**2
Let d(o) = 15*o**2 + 7*o - 46. Let z(c) = 10*c**2 + 5*c - 30. Let y(t) = -5*d(t) + 8*z(t). Determine v so that y(v) = 0.
-2, 1
Let a be 28/70*10/66. Let z(d) be the first derivative of -1/11*d**2 + 1 + 0*d + a*d**3. Factor z(p).
2*p*(p - 1)/11
Factor -2/3*g**2 - 4*g - 6.
-2*(g + 3)**2/3
Let q(g) be the first derivative of g**5/100 - g**3/10 - g**2/5 - 3*g - 3. Let m(s) be the first derivative of q(s). Factor m(p).
(p - 2)*(p + 1)**2/5
Let p = 371 + -371. Determine k, given that -4/7*k + 6/7*k**2 + p - 2/7*k**4 + 0*k**3 = 0.
-2, 0, 1
Suppose 8*x = 5*x + 4*x. Let y(g) be the third derivative of 0*g - 11/30*g**5 + 2*g**2 - 1/15*g**7 - 1/6*g**4 + 0*g**3 - 4/15*g**6 + x. Factor y(p).
-2*p*(p + 1)**2*(7*p + 2)
Let r(z) = -z**3 + 2. Suppose -5*y = -10, 5*y = h - 3*h + 6. Let p be r(h). What is k in 14*k**3 - 16*k**3 + p*k**2 + 4 - 6*k - 6*k - k**2 = 0?
1/2, 2
Let i(x) be the third derivative of -x**5/140 + x**4/14 - 3*x**3/14 - 12*x**2. Solve i(y) = 0.
1, 3
Let c(f) be the first derivative of -f**6/9 + 4*f**5/15 - 4*f**3/9 + f**2/3 + 46. Factor c(u).
-2*u*(u - 1)**3*(u + 1)/3
Let i(d) = 7 - 3*d**3 - 2 - d**2 + 0 + 3*d. Let f = -9 + 13. Let u(m) = 4*m**3 + m**2 - 4*m - 6. Let s(o) = f*u(o) + 5*i(o). Let s(t) = 0. Calculate t.
-1, 1
Let l be 16/20*(-15)/(-2). Let s = 46/7 - l. Suppose -s*x + 2/7*x**2 + 2/7 = 0. What is x?
1
Suppose 0 = -4*r + 9 - 1. Find s such that -4/7 + 10/7*s + 6/7*s**r = 0.
-2, 1/3
Let g(q) be the first derivative of -q**6/2 + 3*q**5 - 15*q**4/2 + 10*q**3 - 15*q**2/2 + 3*q + 24. Factor g(p).
-3*(p - 1)**5
Suppose 9*l - 4*l = 0. Let q(t) be the third derivative of 0*t - 1/15*t**4 + 3/100*t**6 - t**2 - 2/25*t**5 + 1/75*t**7 + l + 0*t**3. Let q(c) = 0. What is c?
-2, -2/7, 0, 1
Let l(p) be the third derivative of -p**7/1995 + p**5/570 - 5*p**2. Factor l(i).
-2*i**2*(i - 1)*(i + 1)/19
Suppose -4*i - 2*i = -4*i. Solve i + 0*h + 6/7*h**4 + 0*h**2 + 3/7*h**5 + 0*h**3 = 0 for h.
-2, 0
Suppose -l = b - 15, -3*b + 3 = 4*l - 46. Suppose -2*h + 2 = -2*v, 0 = -v - 0*h - 2*h + b. Factor -2/7*g**v - 2/7*g**2 + 0*g + 0.
-2*g**2*(g + 1)/7
Let k(i) be the third derivative of 1/8*i**4 - 1/20*i**6 + i**2 + 1/112*i**8 + 0*i**5 + 0 + 0*i**3 + 0*i + 0*i**7. What is q in k(q) = 0?
-1, 0, 1
Suppose 2*o - 3*x + 105 = 5*o, -4*x = 20. Let k be (-1)/5 - (-8)/o. Find z such that 1/2 - 1/2*z**2 + k*z = 0.
-1, 1
Let k(c) be the second derivative of c**6/10 + 3*c**5/20 - 3*c**4/4 - 5*c**3/2 - 3*c**2 + 9*c. Factor k(q).
3*(q - 2)*(q + 1)**3
Suppose -d = -0*d - 30. Let o be (-4)/10 - (-102)/d. Factor 2/3 - 2/3*r - 2/3*r**2 + 2/3*r**o.
2*(r - 1)**2*(r + 1)/3
Let f(d) be the third derivative of -2*d**2 - 1/210*d**7 - 1/36*d**4 + 1/360*d**6 + 0*d**3 + 0*d + 1/60*d**5 + 0 + 1/1008*d**8. Find b, given that f(b) = 0.
-1, 0, 1, 2
Factor -9/8*n**2 - 1/8*n**4 - 5/8*n**3 - 7/8*n - 1/4.
-(n + 1)**3*(n + 2)/8
Let v = 6 - -6. What is x in -v*x + 0*x**2 - 6*x**2 - 9 - x**2 + 3*x**2 = 0?
-3/2
Factor -1/5*h**2 - 1/5*h**3 - 3/5 + h.
-(h - 1)**2*(h + 3)/5
Let o = 274/201 + -2/67. Let s be (1/(-2))/(1/(-4)). What is z in -2/3*z**s - 2/3 + o*z = 0?
1
Let v(z) be the third derivative of z**6/660 - z**5/165 - z**4/132 + 2*z**3/33 - 2*z**2. Let v(g) = 0. What is g?
-1, 1, 2
Factor -2*r + 6*r - 4*r + r**3 - r.
r*(r - 1)*(r + 1)
Let v(x) be the second derivative of x**7/42 + x**6/10 + x**5/10 - x**4/6 - x**3/2 - x**2/2 - 22*x. Suppose v(l) = 0. Calculate l.
-1, 1
Suppose 4*o = 2*q + 20, 5*o - q = q + 26. Suppose y + 12 = 3*j, -y = 4*j - 3 - o. Factor -1/2 + 3/4*k**2 - 1/4*k**4 + 1/4*k - 1/4*k**j.
-(k - 1)**2*(k + 1)*(k + 2)/4
Let g(h) be the second derivative of -32*h**4/3 - 16*h**3/3 - h**2 + 3*h. Factor g(o).
-2*(8*o + 1)**2
Let z(s) be the third derivative of -1/30*s**5 + 0*s**3 + 0 + 1/120*s**6 - 3*s**2 + 0*s + 1/24*s**4. Suppose z(k) = 0. Calculate k.
0, 1
Suppose 2*l = 4 + 6. Let g(w) = -w**2 + 7*w - 6. Let d be g(l). Let 4*i**2 - i**d - 2*i**2 - i**4 = 0. What is i?
-1, 0, 1
Let d(s) be the first derivative of 0*s**2 - 1 + 1/8*s**3 + 2*s + 1/40*s**6 - 3/80*s**5 - 1/16*s**4. Let r(m) be the first derivative of d(m). Factor r(z).
3*z*(z - 1)**2*(z + 1)/4
Let j(l) be the first derivative of -l**3/3 + l**2/2 + 2*l - 3. Let j(d) = 0. Calculate d.
-1, 2
Let j(y) be the first derivative of -6 + 1/2*y**4 + 2/15*y**5 + 4/9*y**3 + 0*y + 0*y**2. Find h such that j(h) = 0.
-2, -1, 0
Let y(p) = p**2 + 7*p - 5. Let m be y(-8). Factor -2*l**5 - 10*l**4 - 4*l + 7*l**m + 6*l**2 - 25*l**3 - 20*l**2 + 0*l.
-2*l*(l + 1)**3*(l + 2)
Solve -1/3*i**5 + 0*i**2 - 4/3*i**3 - 4/3*i**4 + 0 + 0*i = 0.
-2, 0
Let c be 1/(1/(-3))*(-12)/18. Let s(a) be the third derivative of 0*a - c*a**2 - 1/30*a**5 + 0*a**3 + 0*a**4 + 0. Find f such that s(f) = 0.
0
Determine b, given that 2/3*b**2 - 2 + 4/3*b = 0.
-3, 1
Let k be -1 - (3 - 3)/(-1). Let n be (8 - 3) + (k - 2). Solve 2/7 - 2/7*s**n + 0*s = 0.
-1, 1
Let d(b) be the second derivative of -b**5/10 + b**4/6 - 8*b - 3. Factor d(m).
-2*m**2*(m - 1)
Factor -2/11*m**5 - 2/11*m**4 + 0 + 0*m + 2/11*m**3 + 2/11*m**2.
-2*m**2*(m - 1)*(m + 1)**2/11
Let q = 131 - 653/5. Factor 0*n**2 + 0*n + 0 + 0*n**4 - q*n**5 + 2/5*n**3.
-2*n**3*(n - 1)*(n + 1)/5
Factor 9/4*x**2 + 7/4*x + 5/4*x**3 + 1/4*x**4 + 1/2.
(x + 1)**3*(x + 2)/4
Factor 5/4*y**2 + 15/4*y + 5/2.
5*(y + 1)*(y + 2)/4
Factor -3/5*h - 1/5 - 3/5*h**2 - 1/5*h**3.
-(h + 1)**3/5
Find r such that -13*r + 5*r - 18*r + 24 - 2*r + 4*r**3 = 0.
-3, 1, 2
Suppose -5*o + 15 - 5 = 0. Let s(w) = 4*w**2 - 5*w. Let d(x) = 3*x**2 - 3*x + x - x**2. Let i(l) = o*s(l) - 5*d(l). Factor i(r).
-2*r**2
Let d = -52/7 - -423/56. Find q, given that 0 + d*q**2 + 1/4*q = 0.
-2, 0
Suppose 0*x = 4*j + 2*x - 8, 0 = -3*j - x + 8. Let m(s) = -s**3 + 4*s**2 + 5. Let f be m(j). Factor 5/3*w**2 + 0 - 1/3*w**4 - 1/3*w**f + 2/3*w + w**3.
-w*(w - 2)*(w + 1)**3/3
Let 3/2*b**4 - 3 + 3/2*b**2 + 9/2*b - 9/2*b**3 = 0. Calculate b.
-1, 1, 2
Let r(k) = 4*k**2 + 13*k + 13. Let m(p) = 20*p**2 + 66*p + 66. Let o(n) = -3*m(n) + 14*r(n). Find q such that o(q) = 0.
-2
Factor 0 + 2/7*u**3 + 2*u**2 + 0*u.
2*u**2*(u + 7)/7
Let o = -25 + 6. Let i = 23 + o. Suppose 2/7*r**5 + 0*r**3 - 2/7*r + 0 - 4/7*r**i + 4/7*r**2 = 0. What is r?
-1, 0, 1
Let x be 57/27 + 10/(-6). Determine s so that -2/9*s**2 - 2/9 - x*s = 0.
-1
Let q(p) be the second derivative of -21*p**5/40 - 13*p**4/4 - 13*p**3/4 + 9*p**2/2 + 19*p. Factor q(w).
-3*(w + 1)*(w + 3)*(7*w - 2)/2
Let z(t) be the first derivative of 5*t**6/6 + 6*t**5 + 15*t**4 + 40*t**3/3 + 26. Factor z(c).
5*c**2*(c + 2)**3
Let s(k) be the second derivative of 22/15*k**6 + 1/3*k**4 + 8/21*k**7 + 0*k**2 + 0 + 7*k + 9/5*k**5 - 2/3*k**3. Determine d, given that s(d) = 0.
-1, 0, 1/4
Factor 0*h**2 - 4/7 + 2/7*h**3 - 6/7*h.
2*(h - 2)*(h + 1)**2/7
Let z = 20 + -20. Let r(i) be the second derivative of 1/6*i**4 - i**2 + z*i**3 + 0 - i. Factor r(y).
2*(y - 1)*(y + 1)
Let o(n) be the third derivative of n**6/540 + n**5/270 + 34*n**2. Factor o(i).
2*i**2*(i + 1)/9
Let 1/3*q**2 + 0*q + 1/3*q**5 + q**3 + q**4 + 0 = 0. What is q?
-1, 0
Solve -6*j**2 - 32/5*j**3 - 13/5*j - 2/5 - 3/5*j**5 - 16/5*j**4 = 0.
-2, -1, -1/3
Let l(a) = a**5 - a**3 - a**2 + a + 1. Let x(s) = 28*s**5 + 21*s**4 - 21*s**3 - 16*s**2 - 12*s - 8. Let m(h) = -24*l(h) - 3*x(h). Suppose m(b) = 0. Calculate b.
-2/3, -1/4, 0, 1
Let x be -12*(-1)/6*2. Let p be (-77)/(-28) - (-1)/x. Factor -4/9*w**2 + 0 + 0*w + 2/9*w**p.
2*w**2*(w - 2)/9
Let h(n) = 16*n**2 + 22*n + 18. Let j(q) = -q**2 - q - 1. Let l(c) = 2*h(c) + 36*j(c). Factor l(w).
-4*w*(w - 2)
Let o = 0 + 4. Suppose -2 = -5*g - 7, 2*g + o = c. What is x in -2*x + 3 + x - 2*x**c - x**3 - 3 = 0?
-1, 0
Suppo