 2/5 + 32/5*v**2.
2*(4*v + 1)**2/5
Factor 0*p**2 + 17*p**4 - 3*p**3 - 14*p**4 + 0*p**2.
3*p**3*(p - 1)
Let k(b) be the second derivative of -1/6*b**4 + 2/3*b**3 - 2*b + 0 - b**2. Factor k(x).
-2*(x - 1)**2
Factor 4 + 4*m**4 - 8*m**2 - 2*m + 3*m**3 + 8*m**3 - 3*m**3 - 4*m**5 - 2*m.
-4*(m - 1)**3*(m + 1)**2
Let p = 8 + -5. Suppose p*c = -2*c + 5*g + 25, c + g = 1. Factor -m**2 - c*m**3 + 1 - m**5 + 0 - 1 - 3*m**4.
-m**2*(m + 1)**3
Let p(s) be the third derivative of -s**10/453600 + s**8/60480 + s**5/30 - 3*s**2. Let q(o) be the third derivative of p(o). Suppose q(b) = 0. What is b?
-1, 0, 1
Let u be (-5 - (-123)/27)/((-32)/24). Solve -7/6*k**2 - 1/2*k + 1/2*k**3 + u + 5/6*k**4 = 0 for k.
-1, 2/5, 1
Let x(t) = -t**3 - 2*t**2 + t - 4. Let f be x(-3). Find r, given that r**2 + 3*r - 3*r**2 - f*r**2 - 7*r - r**3 = 0.
-2, 0
Let f(v) be the second derivative of v**5/30 - v**3/3 + v**2 - 2*v. Let m(s) be the first derivative of f(s). Factor m(a).
2*(a - 1)*(a + 1)
Suppose 0 = 5*m + 3*q + 2*q - 30, 4*q = -3*m + 16. Let 0*b - b + m + 9*b + 2*b**2 = 0. Calculate b.
-2
Let x(l) = -4*l**3 - 5*l**2 + 5*l - 2. Let g(o) = -39*o**3 - 51*o**2 + 51*o - 21. Let f(j) = -2*g(j) + 21*x(j). What is m in f(m) = 0?
-1, 0, 1/2
Let a(d) be the second derivative of -2*d**6/15 - d**5 - 3*d**4 - 14*d**3/3 - 4*d**2 - 40*d. What is o in a(o) = 0?
-2, -1
Factor 0 + 0*r**2 + 1/5*r**3 + 1/5*r**5 - 2/5*r**4 + 0*r.
r**3*(r - 1)**2/5
Let v(k) = 4*k + 20. Let d be v(-5). Let s(j) be the second derivative of d + 0*j**2 + 1/12*j**3 + 1/40*j**5 - 2*j + 1/12*j**4. What is w in s(w) = 0?
-1, 0
Let r(k) = -k**4 + k**2 - k + 1. Let p(x) = 5*x**5 + 19*x**4 - 5*x**3 - 19*x**2 + 4*x - 4. Let f(s) = p(s) + 4*r(s). Find n such that f(n) = 0.
-3, -1, 0, 1
Let f(x) = x**3 + 3*x**2 - x - 1. Suppose -13 = 4*a - 1. Let n be f(a). Let 3*i + n*i - 6*i - i**2 = 0. What is i?
-1, 0
Let p = -13 - -6. Let o = p - -7. Determine h, given that o*h**2 + 0*h - 1/2*h**3 + 0 - 1/2*h**4 = 0.
-1, 0
Let b(g) be the second derivative of 0*g**2 + 1/90*g**6 + 1/36*g**4 - 5*g + 0*g**3 + 0 + 1/30*g**5. What is v in b(v) = 0?
-1, 0
Suppose -58 = -10*a - 38. Find p, given that -4/15*p - 2/3*p**4 + 0 - 2/15*p**5 - 6/5*p**3 - 14/15*p**a = 0.
-2, -1, 0
Factor 4/7*y**2 + 0 - 2/7*y - 2/7*y**3.
-2*y*(y - 1)**2/7
Let j(w) = -w**2 + 1. Suppose 0 = -4*u - 5*v + 6, -4*v + 10 + 2 = -4*u. Let c be j(u). Let -1/3*f**2 + c*f + 0 = 0. Calculate f.
0
Let x(z) = -5*z**4 - 6*z**3 + z**2 + 4*z. Let m(c) = 11*c**4 + 12*c**3 - c**2 - 7*c. Suppose 4*i + 3 = -17. Let l(w) = i*x(w) - 2*m(w). Factor l(k).
3*k*(k - 1)*(k + 1)*(k + 2)
Solve -5*u**2 - 87 + 20*u + 3*u**2 + 37 = 0.
5
Solve -18/17 - 2/17*x**3 - 6/17*x + 10/17*x**2 = 0 for x.
-1, 3
Let y be (3 + 14/(-4))*0. Let d(p) be the third derivative of p**2 + 0*p**3 + 1/240*p**6 + y*p + 1/60*p**5 + 1/48*p**4 + 0. Factor d(m).
m*(m + 1)**2/2
Let r = -30/19 - -308/171. Determine w so that r*w**5 + 0*w**2 + 0 + 8/9*w**4 + 8/9*w**3 + 0*w = 0.
-2, 0
Suppose 0 = -2*f + 4*f - 10. Let t(m) = m**2 + 2*m + 2. Let v be t(-3). Factor -10*d**3 + 2 - 3 - v*d**4 + 0*d**2 - 10*d**2 - 5*d - d**f.
-(d + 1)**5
Let y(d) = -8*d**3 - 3*d**2 + 147*d - 192. Let p(t) = -4*t**3 - 2*t**2 + 74*t - 96. Let n(i) = 13*p(i) - 6*y(i). Suppose n(r) = 0. Calculate r.
-6, 2
Let x(b) be the third derivative of -b**8/672 + b**7/420 + b**6/40 + 13*b**2. Suppose x(i) = 0. Calculate i.
-2, 0, 3
Let x(h) = 324*h**2 + 144*h + 11. Let o(d) = -486*d**2 - 216*d - 17. Let b(g) = -5*o(g) - 7*x(g). What is f in b(f) = 0?
-2/9
Factor 20*t**5 + 56*t**2 + 140*t**4 + 8*t + 30*t**5 + 19*t**3 + 119*t**3.
2*t*(t + 1)**2*(5*t + 2)**2
Let a(i) be the second derivative of 1/10*i**4 + 2/15*i**3 + 0*i**5 + 0*i**2 + 4*i - 1/75*i**6 + 0. Factor a(w).
-2*w*(w - 2)*(w + 1)**2/5
Factor 0*k + 1/4*k**2 - 3/4*k**3 + 1/2*k**4 + 0.
k**2*(k - 1)*(2*k - 1)/4
Suppose 2*q**4 + 0 + 23/2*q**3 - 9/2*q + 15*q**2 = 0. What is q?
-3, 0, 1/4
Let l(v) be the first derivative of -v**7/280 + v**6/160 - 2*v**2 + 3. Let q(z) be the second derivative of l(z). Suppose q(s) = 0. What is s?
0, 1
Let r be (-126)/(-168) - (-6)/(-8). Determine i, given that 12/7*i - 3/7*i**2 + r = 0.
0, 4
Let s(c) be the first derivative of -c**6/14 + 9*c**5/35 - 9*c**4/28 + c**3/7 + 2. What is k in s(k) = 0?
0, 1
Let s = 15 - 12. Suppose 2*v = s*v. Factor v - 8/3*x**2 - 2/3*x.
-2*x*(4*x + 1)/3
Let c = 12 + -10. Solve 6*g + 84*g**4 + 0*g**2 - 14*g**c + 5*g**2 - 81*g**3 = 0.
-2/7, 0, 1/4, 1
Let s(h) = 5*h**2 - 1. Let k be s(-1). Suppose 0*d - k = -2*q - d, 0 = 4*d. Suppose 4/3 + 14/3*t**q + 6*t = 0. What is t?
-1, -2/7
Factor 0*n + 1/2 - 1/2*n**2.
-(n - 1)*(n + 1)/2
Let m(c) = c**5 + 6*c**4 + 2*c**3 - 12*c**2 - 11*c - 6. Let b(n) = n**4 + n**3 - n**2 - n - 1. Let d(o) = 4*b(o) - m(o). Factor d(q).
-(q - 2)*(q + 1)**4
Let n(y) be the third derivative of 0*y**3 - 1/40*y**6 + 1/8*y**4 + 1/20*y**5 - 1/70*y**7 + 0*y - 7*y**2 + 0. Factor n(u).
-3*u*(u - 1)*(u + 1)**2
Suppose s - 4*s = -12. Let t(w) = 3*w**2 - 8*w + 9. Let g(b) = 13*b**2 - 33*b + 36. Let z(x) = s*g(x) - 18*t(x). Factor z(f).
-2*(f - 3)**2
Let h(m) be the third derivative of -3/16*m**4 + 1/40*m**5 + 0 + 0*m + 1/2*m**3 + 2*m**2. Factor h(p).
3*(p - 2)*(p - 1)/2
Suppose z = -3*z - 2*y - 2, -4*z + 4*y = -4. Let w be 6/40 + (-2)/(-8). Let 0 - w*a**2 + z*a + 1/5*a**4 + 1/5*a**3 = 0. What is a?
-2, 0, 1
Suppose 0*q + 19 = 2*v - 5*q, 3*v + 6 = -4*q. Let o be -1 + (2 - (-2)/1). Factor 2*u + u**4 - 3*u**v + u**2 - 7*u**4 - 10*u**o.
-2*u*(u + 1)**2*(3*u - 1)
Let r(v) = v**2 + v - 1. Let l(m) = -4*m**2 + 2*m + 2. Let h be (-8)/12 + (-4)/3. Let t(a) = h*r(a) - l(a). Factor t(q).
2*q*(q - 2)
Let g be 39/6 + (-12)/8. Let w(m) be the first derivative of 0*m**2 + 1/5*m**g - 1/3*m**3 + 0*m + 1/4*m**4 - 1/6*m**6 - 1. Let w(x) = 0. What is x?
-1, 0, 1
Let m = 2 - -6. Suppose 4*g - 4 - m = 0. Factor -2*d - 4*d**g + 2*d**2 + 7*d**2 - 2*d**2 - 1.
-(d - 1)**2*(4*d + 1)
Let m(p) be the third derivative of p**8/56 - 3*p**7/70 - p**6/5 + p**5/4 + 3*p**4/2 + 2*p**3 - 21*p**2. Let m(i) = 0. What is i?
-1, -1/2, 2
Let i = 23 - 20. Let l(z) be the second derivative of 0 + 2/7*z**2 + z - 1/42*z**4 - 1/21*z**i. Factor l(t).
-2*(t - 1)*(t + 2)/7
Let v be 6/(2 - 0/4). Let u be v/(-4)*(-12)/18. Factor 1/4 + 3/4*g - 3/4*g**4 + u*g**2 - 1/4*g**5 - 1/2*g**3.
-(g - 1)*(g + 1)**4/4
Let j(g) = 3*g**3 + 2*g**2 + 2*g + 1. Let a(o) = o**3. Let y(c) = -2*a(c) - j(c). Let p be y(-1). Factor x**3 + 2*x**3 - x**p - 2*x**4.
-3*x**3*(x - 1)
Let h(p) be the third derivative of 2*p**7/105 + 2*p**6/15 + 2*p**5/5 + 2*p**4/3 + 2*p**3/3 - 9*p**2. Let h(r) = 0. Calculate r.
-1
Let d(f) be the second derivative of 2*f**6/15 - 3*f**5/5 - f**4/3 + 2*f**3 - 6*f. Factor d(q).
4*q*(q - 3)*(q - 1)*(q + 1)
Let u(h) be the third derivative of 1/480*h**6 - 1/96*h**4 + 2*h**2 + 1/840*h**7 + 0*h - 1/80*h**5 + 1/12*h**3 + 0. Factor u(t).
(t - 1)**2*(t + 1)*(t + 2)/4
Let y(k) = -k**3 + 3*k**2 + 1. Let a be y(3). Suppose 2 = t - a. Factor 8 + 12*o + 3*o**2 - 3 + o**3 + t + 3*o**2.
(o + 2)**3
Let g be 56/105*(-4 + 31). Find s, given that 3/5 - 21/5*s**3 - g*s**4 + 69/5*s**2 - 27/5*s + 48/5*s**5 = 0.
-1, 1/4, 1
Suppose -12*a**2 - 3*a**4 + 0*a**4 + 16*a + 16 - 8*a**3 + 7*a**4 = 0. What is a?
-1, 2
What is l in -3/2*l**2 + 9/2 + 3*l = 0?
-1, 3
Let l(b) be the second derivative of b**2 + 2*b + 0 - 1/6*b**4 - 1/5*b**5 + 1/6*b**3. Let w(c) = c**3 + c**2 - 1. Let o(f) = l(f) + 3*w(f). Factor o(a).
-(a - 1)**2*(a + 1)
Let u(t) = -20*t + 27*t**2 + 71*t + 93*t**2 + 6 + 46*t**3. Let w(a) = -91*a**3 - 240*a**2 - 102*a - 12. Let o(k) = 5*u(k) + 2*w(k). Factor o(z).
3*(z + 2)*(4*z + 1)**2
Let y = -4668/7 - -669. Let t(c) be the first derivative of 66/35*c**5 - 62/21*c**3 - 3 + 5/14*c**4 - 20/21*c**6 + y*c**2 - 4/7*c. Solve t(o) = 0.
-1, 1/4, 2/5, 1
Let n(v) be the first derivative of 7*v**6/120 - 11*v**5/300 - v**4/6 - 2*v**3/15 + 2*v**2 - 3. Let w(g) be the second derivative of n(g). Factor w(q).
(q - 1)*(5*q + 2)*(7*q + 2)/5
Factor 0*o + 0 - 2/11*o**2.
-2*o**2/11
Let g(h) be the second derivative of h**9/15120 - h**8/3360 + h**6/360 - h**5/120 - h**4/4 - h. Let m(o) be the third derivative of g(o). Factor m(j).
(j - 1)**3*(j + 1)
Determine d so that 5*d**3 - 4*d**4 - d**3 - 4*d**5 + 0*d**4 + 4*d**2 + 0*d**4 = 0.
-1, 0, 1
Suppo