b) = 0?
1, 2
Factor -4/5*k**4 + 12/5*k**2 + 0*k + 0 - 8/5*k**3.
-4*k**2*(k - 1)*(k + 3)/5
Factor -293*l**2 - 239*l**2 + 277*l - 687*l - 93*l**2 + 121*l**4 - 96*l**4 + 1010*l**3.
5*l*(l - 1)*(l + 41)*(5*l + 2)
Let k = 29338/3 - 9712. Find n, given that 8 + 70/3*n**5 - 302/3*n**4 + 142*n**3 - 16/3*n - k*n**2 = 0.
-2/7, 3/5, 1, 2
Let y(x) be the second derivative of 0 - 20*x + 2/15*x**4 + 0*x**2 + 1/25*x**5 + 2/15*x**3. Factor y(q).
4*q*(q + 1)**2/5
Let t(w) = -5*w**4 + 2*w**3 + 8*w**2 - 1. Let k(c) = -7*c**2 - 3*c**3 - 2*c**2 + 6*c**4 - 13 + 13. Let q(i) = -2*k(i) - 3*t(i). Factor q(y).
3*(y - 1)**2*(y + 1)**2
Let o = -58 + 52. Let j(b) = -b**5 - 2*b**4 - 3*b**3 - 6*b**2. Let k(l) = -l**5 - 2*l**4 - 2*l**3 - 5*l**2. Let s(p) = o*k(p) + 5*j(p). Factor s(u).
u**3*(u - 1)*(u + 3)
Factor -3995*w + 2004*w + 2*w**2 + 1999*w.
2*w*(w + 4)
Let a = -23099/5 - -4621. Solve 38/5*c**2 - 66/5*c - a*c**3 + 18/5 = 0 for c.
1/3, 3
Let v(t) be the second derivative of t**6/50 + 363*t**5/50 + 972*t**4 + 255879*t**3/5 - 1594323*t**2/10 - 592*t. Determine h so that v(h) = 0.
-81, 1
Let m(u) = 2*u**3 - 4*u**2 + 3*u - 3. Let w be m(2). Let 4*b**2 + 4 - 10*b + b**2 - 9*b**2 - 2*b**w + 12*b**2 = 0. What is b?
1, 2
Suppose 177/2*r + 51/2 - 21/8*r**2 = 0. Calculate r.
-2/7, 34
Let j be (-2)/3 + 1 + 200/30. Suppose -l - 20 + j = -4*n, 2*l = 4*n - 10. Factor -1/2*y**l - 1/2*y**2 + 1/2 + 1/2*y.
-(y - 1)*(y + 1)**2/2
Let u(o) be the first derivative of o**6/6 - 29*o**5/20 + 55*o**4/12 - 43*o**3/6 + 6*o**2 - 42*o + 21. Let p(c) be the first derivative of u(c). Factor p(l).
(l - 3)*(l - 1)**2*(5*l - 4)
Let m(v) = 5*v**2 - 65*v + 2. Let o be m(13). Determine d so that 5/2*d**2 - o*d**3 - d + 0 + 1/2*d**4 = 0.
0, 1, 2
Let w be (2/3)/(11/2112). Let z = 128 - w. Factor 1/3*u**2 + z*u - 1/3.
(u - 1)*(u + 1)/3
Let s be -3 + -5 - 840/(-102). Factor 2/17*n**4 + 4/17*n - 2/17*n**2 + 0 - s*n**3.
2*n*(n - 2)*(n - 1)*(n + 1)/17
Suppose -3*b - 5 - 4 = 0, 4*u - 2*b = 34. Suppose 3*l + u - 13 = 0. Factor -1/3*d + 0 - d**3 - 1/3*d**4 - d**l.
-d*(d + 1)**3/3
Let a(s) be the first derivative of 65*s**4/4 + 40*s**3 - 10*s**2 + 104. Factor a(g).
5*g*(g + 2)*(13*g - 2)
Suppose 12 = -3*x + 18. Suppose -3*b + x*b + 2 = 0. Factor j - 3*j**b + 5/4*j**3 + 0.
j*(j - 2)*(5*j - 2)/4
Suppose -p + 4 = 1. Solve -p*i - 11*i**2 + 11*i**2 + 3*i**3 = 0 for i.
-1, 0, 1
Let f(j) be the third derivative of j**6/6 + 23*j**5/60 - 17*j**3/6 - 17*j**2. Let z(g) = -7*g**3 - 8*g**2 + 6. Let v(b) = 6*f(b) + 17*z(b). Factor v(s).
s**2*(s + 2)
Factor -3 - 1/2*i**4 - 7/2*i**3 - 17/2*i - 17/2*i**2.
-(i + 1)**2*(i + 2)*(i + 3)/2
Let k be (4/(-40))/((-6)/40). Find r, given that -4/15*r**4 - k + 6/5*r + 14/15*r**2 - 6/5*r**3 = 0.
-5, -1, 1/2, 1
Suppose -3*t = 6, -3*t - 6 = -4*m - m. Factor 127*r**4 - 129*r**4 - 4*r**2 - 6*r**3 + m*r**3.
-2*r**2*(r + 1)*(r + 2)
Let r be (30/36)/((-145)/(-87)). Factor 5/4*q**2 + r*q + 0.
q*(5*q + 2)/4
Let o(w) be the first derivative of -w**5/30 + 11*w**4/24 - 3*w**3/2 + 25*w**2/12 - 4*w/3 - 142. Factor o(g).
-(g - 8)*(g - 1)**3/6
Let c(q) be the first derivative of 2*q - 2*q**2 + 2/3*q**3 + 1. Factor c(z).
2*(z - 1)**2
Let o be (-34)/(-119) + 640/14. Let x = -46 + o. Factor x*d**3 - 8/5*d**2 + 0 + 2/5*d**4 + 0*d.
2*d**2*(d - 2)*(d + 2)/5
Factor 2 - 44/3*s**2 - 25/3*s.
-(4*s + 3)*(11*s - 2)/3
Let x(o) be the first derivative of 3*o**4/4 - 2*o**3 - 226. Solve x(h) = 0.
0, 2
Suppose v = -111 + 113. Let z(w) be the first derivative of -6804/65*w**5 - 2484/13*w**4 - 464/13*w**v + 4 - 64/13*w - 243/13*w**6 - 4768/39*w**3. Factor z(x).
-2*(x + 2)**2*(9*x + 2)**3/13
Let c(x) be the third derivative of -x**5/20 - x**4/4 - 4*x**2. Factor c(f).
-3*f*(f + 2)
Let h(a) be the second derivative of -a**6/180 - a**5/20 + 10*a**3/3 + 6*a. Let b(s) be the second derivative of h(s). Solve b(u) = 0 for u.
-3, 0
Let q(k) = -104*k + 731. Let c be q(7). Factor -1/2*x**4 + 3/2*x - 5/2*x**2 - 1/3 + 11/6*x**c.
-(x - 1)**3*(3*x - 2)/6
Let l = 14453 + -18210779/1260. Let u(m) be the third derivative of -1/252*m**4 - l*m**6 + 0*m**3 + 0*m + 0 + 1/315*m**5 - 4*m**2. Factor u(i).
-2*i*(i - 1)**2/21
Find t such that 20 - 2/5*t**3 + 24/5*t**2 - 18*t = 0.
2, 5
Let x be 210577/(-342) + (-2)/4. Let u = 618 + x. Find p, given that 74/9*p**3 - 44/3*p**2 - u + 88/9*p - 14/9*p**4 = 0.
2/7, 1, 2
Suppose 3*v = v - 4. Let b be 0 - ((-2)/v)/((-6)/12). Factor 0 - 2/3*t**3 + 0*t - 2/3*t**4 + 0*t**b.
-2*t**3*(t + 1)/3
Suppose 4*c - 24 = -0*c. Suppose -r + 5 = 4*b - 0, -c = 2*r. Let 8*q**2 + 5*q**3 - 4*q**4 - 12*q**b + 3*q**3 = 0. What is q?
0, 1
Let k = 72194283/295 - 244727. Let b = -1/59 - k. Find q, given that -3/5*q**3 + 6/5*q + b*q**2 + 0 = 0.
-1, 0, 2
Let d(p) be the third derivative of -p**6/60 - 2*p**5/15 + 7*p**4/3 - 32*p**3/3 - 30*p**2 - 1. Factor d(m).
-2*(m - 2)**2*(m + 8)
Let t(n) be the first derivative of -4*n**4 + 52*n**3/3 + 26*n**2 - 16*n + 224. Let t(c) = 0. Calculate c.
-1, 1/4, 4
Let j be ((-60)/55 - -1)/((-1)/(-1417)). Let b = 129 + j. Factor 2/11*g**2 - b*g + 2/11*g**3 - 2/11.
2*(g - 1)*(g + 1)**2/11
Let u(r) = 3*r - 3. Let z be u(6). Suppose 2*s + 3 = 4*v - z, 4*s = -12. Solve 3*d**v + 0*d - 8*d + 5*d = 0 for d.
-1, 0, 1
Suppose 90*i + 92*i = -229*i + 822. Factor 3 - 1/2*z**i + 5/2*z.
-(z - 6)*(z + 1)/2
Let b(t) be the first derivative of -5*t**4/4 - t - 11. Let u be b(-1). Factor -5*r**2 - r**u - 3*r**4 + 15*r**2 + 6*r**2.
-4*r**2*(r - 2)*(r + 2)
Let v be 5 - (-1 + -3)/4. Let f(z) be the first derivative of 1/6*z**3 + 0*z + 0*z**2 + 1/8*z**4 - 1/10*z**5 - 1/12*z**v + 3. Let f(y) = 0. Calculate y.
-1, 0, 1
Let l = -17/909 + 2761/1818. Solve -1/4*n**2 - 5/4 - l*n = 0 for n.
-5, -1
Factor 24 + 2/5*c**3 + 38/5*c**2 + 128/5*c.
2*(c + 2)**2*(c + 15)/5
Factor -980/3 + 2/15*m**3 + 182*m - 48/5*m**2.
2*(m - 35)**2*(m - 2)/15
Determine s, given that -4/21*s + 2/7*s**3 + 0 - 10/21*s**2 = 0.
-1/3, 0, 2
Let t(a) = -a**2 + 4*a + 3. Suppose 2*q = n - 3*n + 10, 0 = -q + 5*n - 1. Let p be t(q). Factor -12*r - 4*r**2 + p*r**4 + 19*r + r**4 - 9*r + 2*r**5.
2*r*(r - 1)*(r + 1)**3
Let a(w) be the first derivative of w**4/14 + 10*w**3/7 + 48*w**2/7 + 88*w/7 - 65. Factor a(p).
2*(p + 2)**2*(p + 11)/7
Let v(t) be the third derivative of 0 - 4/735*t**7 + 7*t**2 + 1/70*t**6 + 1/84*t**4 + 0*t - 2/105*t**5 + 1/1176*t**8 + 0*t**3. Find k, given that v(k) = 0.
0, 1
Let n(x) be the second derivative of -3*x**2 - 1/10*x**6 - 6*x + 0 + 3/4*x**5 - 9/4*x**4 + 7/2*x**3. Factor n(v).
-3*(v - 2)*(v - 1)**3
Let s(q) = 2*q**4 - 113*q**3 - 232*q**2 - 96*q - 7. Let j(t) = -t**4 + 114*t**3 + 231*t**2 + 98*t + 6. Let u(c) = 7*j(c) + 6*s(c). Factor u(h).
5*h*(h + 1)**2*(h + 22)
Let z(r) be the second derivative of -r**4/30 - 82*r**3/15 + 83*r**2/5 - 356*r. Factor z(b).
-2*(b - 1)*(b + 83)/5
Suppose -6 = 3*c - 36. Let z(k) = k**3 - 8*k**2 - 6*k - 12. Let y be z(c). Suppose -y*d - 3*d**2 + 127*d - 1 + 3 = 0. Calculate d.
-1, 2/3
Suppose -5*d = -10, -2*s + 5*d + 0 = 10. Factor s - 48/5*c**2 + 6/5*c.
-6*c*(8*c - 1)/5
Let k = 1634/9 - 181. Let a(s) be the second derivative of -1/9*s**4 - 3*s + 2/15*s**5 - k*s**3 + 1/63*s**7 + 4/45*s**6 - 2/3*s**2 + 0. Factor a(t).
2*(t - 1)*(t + 1)**3*(t + 2)/3
Let d(i) be the first derivative of 1/2*i**4 + 0*i + 1/5*i**5 - i**2 - 1/3*i**3 + 21. Determine y, given that d(y) = 0.
-2, -1, 0, 1
Let u = -8 - -10. Suppose 0 = -3*h + r + 10, -10 = 2*r - u. Suppose -v - 2*v**3 + v**2 - 3*v - 3*v**2 + 8*v**h = 0. Calculate v.
0, 1, 2
Let d(o) be the first derivative of -o**4/10 - 16*o**3/15 - 16*o**2/5 + 117. Determine r so that d(r) = 0.
-4, 0
Let a(g) = g**2 + g. Let v be a(-1). Factor 4*p**2 + 0*p**2 + v*p**3 - 2*p**2 + 2*p**3.
2*p**2*(p + 1)
Factor -2*c**3 - 9 - 2*c - 3*c**2 + 30*c - c**3 - 13*c.
-3*(c - 1)**2*(c + 3)
Factor 66/7*g**2 - 141/7*g - 9/7*g**3 + 12.
-3*(g - 4)*(g - 1)*(3*g - 7)/7
Let q(u) = -3*u**5 + 7*u**4 - 7*u**3 - 13*u**2 + 6*u + 5. Let w(s) = s**5 - 3*s**4 + 4*s**3 + 6*s**2 - 4*s - 2. Let y(t) = 2*q(t) + 5*w(t). Factor y(b).
-b*(b - 2)*(b - 1)*(b + 2)**2
Let a(j) be the first derivative of j**5/240 - j**4/96 + 9*j**2/2 + 18. Let y(l) be the second derivative of a(l). Factor y(h).
h*(h - 1)/4
Let g(w) be the third derivative of 4*w**2 + 0*w + 0*w**3 - 1/120*w**6 - 1/210*w**7 + 0*w**4 + 1/30*w**5 + 0. Determine v, given