ative of -7 + 2/21*q**3 + 4/7*q**2 + r*q. What is y in w(y) = 0?
-3, -1
Let g(n) be the second derivative of -21/2*n**2 + 3*n**3 + 2*n + 0 + 1/4*n**4. Factor g(m).
3*(m - 1)*(m + 7)
Let r be ((-585)/60)/(9/(-6)) + -5. Determine p, given that -r*p**3 - 2 - 11/2*p**2 - 6*p = 0.
-2, -1, -2/3
Let c = -32 + 24. Let i be (-1 - (-11)/8)*c/(-6). Factor -i*w + 1 - 1/2*w**2.
-(w - 1)*(w + 2)/2
Let h be (2 - 0) + 5/((-30)/(-18)). Let -b**5 + 5*b**4 - 25*b**2 - 35*b**3 + 0*b**h - 16*b**4 = 0. What is b?
-5, -1, 0
Let b = 27218/15 + -1814. Factor -2/15*u**3 + 0 + 0*u + b*u**5 + 0*u**4 + 0*u**2.
2*u**3*(2*u - 1)*(2*u + 1)/15
Suppose -5*c - 995*j + 47 = -997*j, -2*j + 43 = 5*c. What is b in 21/2*b**2 - c - 57/2*b = 0?
-2/7, 3
Suppose 0*m = 4*m - 40. Suppose -2*x - 5*i = m - 0, 0 = x + 5*i + 15. Factor 7*s**2 + s - 4*s - x*s - s + 2.
(s - 1)*(7*s - 2)
Let i(k) be the first derivative of 7 + 1/6*k**2 + 0*k**3 - 5*k - 1/36*k**4. Let p(r) be the first derivative of i(r). Factor p(m).
-(m - 1)*(m + 1)/3
Let a(r) be the second derivative of 7*r - 1/35*r**5 - 2/7*r**2 + 0 + 2/21*r**3 + 1/21*r**4. Factor a(q).
-4*(q - 1)**2*(q + 1)/7
Let z(b) = 14*b**3 + 7*b**2 - 12*b - 10. Let l(g) = 3*g**3 - 2. Let q(r) = 5*l(r) - z(r). Suppose q(j) = 0. What is j?
0, 3, 4
Let r(p) be the first derivative of -7*p**6/3 - 4*p**5/5 + 21*p**4/2 + 40*p**3/3 + 4*p**2 - 37. Determine o so that r(o) = 0.
-1, -2/7, 0, 2
Let m(s) = -s**2 - 10*s - 12. Let h be m(-8). Suppose -5 = -h*i + 11. Factor -d**4 - 3*d**4 + d**2 + d**5 + 3*d**i + 0*d**4 - d**3.
d**2*(d - 1)**2*(d + 1)
Let i = -1131327/35 - -163761/5. Let y = 432 - i. Factor -y*k**3 - 4/7*k + 0 + 8/7*k**4 + 18/7*k**2.
2*k*(k - 2)*(2*k - 1)**2/7
Determine m so that -138*m**4 + 141*m**4 + 6*m**2 - 9*m**2 = 0.
-1, 0, 1
Let c(a) be the first derivative of 0*a**2 - 2/3*a**3 + 4 + 1/6*a**4 + 0*a. Factor c(w).
2*w**2*(w - 3)/3
Let o(i) = -i**3 + 3*i**2 + 5*i - 1. Let y be o(4). Suppose x = -y*x - 3*h + 10, -h = -5*x + 22. Factor 0 + 1 - x*v - 1 + 14*v**2.
2*v*(7*v - 2)
Let z be 70/20*160/980. Determine p, given that -28*p**3 - z*p - 8*p**2 + 0 = 0.
-1/7, 0
Let s(a) = 2*a**2 - 47*a + 45*a**2 - 3 + 18*a**2. Let z(d) = -66*d**2 + 46*d + 2. Let w(c) = -6*s(c) - 5*z(c). Factor w(i).
-4*(i - 1)*(15*i + 2)
Let r(k) = -k**4 + 29*k**3 - 39*k**2 + 7*k + 6. Let o(t) = 4*t**4 - 145*t**3 + 194*t**2 - 35*t - 29. Let d(w) = -2*o(w) - 11*r(w). Factor d(l).
(l - 8)*(l - 1)**2*(3*l + 1)
Let r be 7/(-1)*(-28)/98. What is y in 0 - 1/5*y**4 + 0*y + 2/5*y**3 - 1/5*y**r = 0?
0, 1
Let w(p) be the third derivative of 2*p**7/105 - p**6/10 + 2*p**5/15 + 78*p**2. Let w(r) = 0. Calculate r.
0, 1, 2
Let z(c) = c + 10. Let y be z(-8). What is l in -3*l**3 - y*l**3 - 3*l**3 + 4*l**4 + 4*l**5 = 0?
-2, 0, 1
Let b(r) = 101*r**3 - 55*r**2 + 499*r + 578. Let a(v) = -9*v**3 - v**2 + v. Let h(t) = 22*a(t) + 2*b(t). Factor h(z).
4*(z - 17)**2*(z + 1)
Let s = -7/18 + 1/2. Let x(t) be the second derivative of s*t**3 + 0 + 0*t**2 - 1/54*t**4 - 6*t. Determine z so that x(z) = 0.
0, 3
Let o = 383/61 - 2559/427. What is t in o*t - 5/7*t**3 - 9/7*t**2 + 0 = 0?
-2, 0, 1/5
Let p(o) be the second derivative of o**7/21420 - o**5/255 + o**4/2 - 11*o. Let h(s) be the third derivative of p(s). Factor h(w).
2*(w - 2)*(w + 2)/17
Let g(d) = -d**3 + 6*d**2 - 2*d + 15. Let p be g(6). Let b = -2/31 + 35/62. Solve -q**p - 1/2 + q + b*q**2 = 0 for q.
-1, 1/2, 1
Factor 2 + 2/3*m**2 - 8/3*m.
2*(m - 3)*(m - 1)/3
Let k(g) = g**2 - g + 11. Let p be k(-8). Let j = 85 - p. Suppose 32/3*z**j + 2/3 - 16/3*z = 0. Calculate z.
1/4
Let t(d) be the third derivative of 0*d**3 + 8*d**2 + 2/27*d**4 + 0 + 8/135*d**5 + 0*d - 2/105*d**7 - 1/90*d**6. Factor t(o).
-4*o*(o - 1)*(3*o + 2)**2/9
Let k(o) be the second derivative of 1/540*o**6 + 0 - 5/6*o**3 + 1/180*o**5 + 0*o**2 + 4*o - 1/18*o**4. Let s(x) be the second derivative of k(x). Factor s(g).
2*(g - 1)*(g + 2)/3
Factor 178*b - 13*b**2 - 33*b**2 + 52*b**2 - 66*b**2 + 6.
-2*(b - 3)*(30*b + 1)
Determine u so that -4*u**5 - 55*u**3 + 50*u - 265 + 9*u**5 - 15*u**4 + 145 + 135*u**2 = 0.
-3, -1, 1, 2, 4
Factor -258*t - 128*t + 3*t**2 + 33282 - t**2 - 130*t.
2*(t - 129)**2
Let a = 12 - -15. Suppose 4*c = -c + 75. What is n in 3*n**3 - 81 - a*n**2 + 71*n - 2*n + 27*n - c*n = 0?
3
Suppose -9*u = 12*u - 630. Let m be (u/105)/((-6)/14*-1). Suppose 2/9*f + 2/3*f**2 + 0 + 2/9*f**4 + m*f**3 = 0. Calculate f.
-1, 0
Let z(k) be the first derivative of 4/15*k**3 + 3 + 0*k**2 + 1/10*k**4 - 2/25*k**5 + 0*k. Suppose z(m) = 0. What is m?
-1, 0, 2
Let k be 2757/12 - 4/(-32)*2. Let l = -228 + k. Factor -2*q - 4/3 - 2/3*q**l.
-2*(q + 1)*(q + 2)/3
Let y be (-2 - 0/1) + (-13)/((-819)/666). Suppose 16*c**5 + 0 - 8/7*c - 104/7*c**3 - y*c**2 + 60/7*c**4 = 0. Calculate c.
-1, -2/7, -1/4, 0, 1
Suppose 3*q - k = 11, 2*q - 3*k + 1 = 13. Factor -1/2*c**2 - 1/4*c**5 + 1/2 + c**q + 0*c**4 - 3/4*c.
-(c - 1)**3*(c + 1)*(c + 2)/4
Suppose -20*a + 14*a = -12. Let k(y) be the first derivative of 8*y + 4 + 4*y**a + 2/3*y**3. Factor k(h).
2*(h + 2)**2
Let v be (-4)/(-1) - -6*2. Suppose 2*b = -5*i + 4*b + v, -4*i + 17 = -3*b. Let -1/3*x**4 + 0 - 1/3*x + 1/3*x**3 + 1/3*x**i = 0. What is x?
-1, 0, 1
Let x(k) be the third derivative of -k**6/780 - 2*k**5/195 + 11*k**4/156 - 2*k**3/13 + 118*k**2. Factor x(a).
-2*(a - 1)**2*(a + 6)/13
Let y(d) = -13*d**4 - 19*d**3 + 6*d**2 + 25*d + 7. Let p(t) = -11*t**4 - 18*t**3 + 5*t**2 + 22*t + 6. Let w(v) = -6*p(v) + 4*y(v). Find j, given that w(j) = 0.
-2, -1, -2/7, 1
Let z(m) = -m**3 - m**2 - 2*m + 11. Let y be z(0). Find a such that 4 + 4*a**2 + 6*a**2 + 3*a - y*a - 6*a**2 = 0.
1
Let k = -24902 - -24907. Factor 3/4*l**k + 12 + 42*l**2 + 36*l + 27/4*l**4 + 24*l**3.
3*(l + 1)*(l + 2)**4/4
Suppose -10*t - 12 = -6*t. Let m(r) = -2*r**2 - 6*r + 2. Let n be m(t). Solve 4/15*i**n - 2/15 - 2/15*i = 0 for i.
-1/2, 1
Let p be (-180)/72*4*-1. Suppose 0 = 21*t - 18*t - 4*x + 2, -t = 4*x - p. Determine a so that 0 - 2/5*a**t - 8/5*a**4 + 3/5*a**5 + 7/5*a**3 + 0*a = 0.
0, 2/3, 1
Let h = 1285 + -1282. Find w such that 0 + 3/2*w**h - 3/2*w**2 + 0*w = 0.
0, 1
Let o(h) be the second derivative of -h**5/60 + h**4/6 - h**3/2 - 12*h**2 + 30*h. Let a(n) be the first derivative of o(n). Solve a(u) = 0 for u.
1, 3
Let q(m) = -11*m**3 - 64*m**2 + 299*m + 364. Let u(g) = -24*g**3 - 129*g**2 + 597*g + 729. Let h(w) = 9*q(w) - 4*u(w). Factor h(z).
-3*(z - 5)*(z + 1)*(z + 24)
Let s(a) be the third derivative of 1/84*a**4 - a**2 - 1/735*a**7 - 1/21*a**3 + 1/105*a**5 - 1/210*a**6 + 1/1176*a**8 + 0 + 0*a. Factor s(p).
2*(p - 1)**3*(p + 1)**2/7
Let b(h) = -h**3 - 2*h**2 + 8*h. Let g be b(2). Factor g + 0*v**2 - 1/5*v**3 + 1/5*v**4 + 0*v.
v**3*(v - 1)/5
Let s(t) be the first derivative of 2*t**3/27 - t**2 + 28*t/9 + 129. What is x in s(x) = 0?
2, 7
Let u be (-2 - -5)*2*(-3)/(-9). Find d such that -6*d**4 - 9/2*d**3 + 0 + 6*d**u - 3/2*d**5 + 6*d = 0.
-2, -1, 0, 1
Let d(u) be the second derivative of -3/2*u**4 - 5/2*u**2 - 1/30*u**6 + 0 - 8/3*u**3 - 2/5*u**5 + 48*u. Find j, given that d(j) = 0.
-5, -1
Let f(d) = 3*d - 4. Let v be f(3). Suppose -4*x + v*t + 22 = -4, -3*t - 26 = -5*x. Determine r so that 2 + 0 - 4*r**3 + 2*r**x + 4*r - 4 = 0.
-1, 1
Let g(l) be the second derivative of 32/7*l**2 - 1/21*l**7 - 76/35*l**5 - 88/21*l**4 - 2*l - 16/7*l**3 + 0 - 18/35*l**6. Factor g(m).
-2*(m + 2)**4*(7*m - 2)/7
Let z be (38/(-7) + 4)*-14. Factor -10*h**2 + 25*h**3 - 110*h + z*h**3 + 5*h**5 + 25*h**4 + 45*h**2 + 120*h.
5*h*(h + 1)**3*(h + 2)
Let n(f) be the third derivative of -f**6/360 - 167*f**5/180 + 337*f**4/72 - 169*f**3/18 - 3*f**2 + 244. Determine t, given that n(t) = 0.
-169, 1
Let g(q) = 4*q - 4. Let p be g(3). Let m be 1/5 - p/(320/(-52)). Factor 0*d**4 + 0 + 3/2*d + m*d**5 + 0*d**2 - 3*d**3.
3*d*(d - 1)**2*(d + 1)**2/2
Find r such that 1458*r + 1/6*r**3 + 26244 + 27*r**2 = 0.
-54
Let r(a) be the first derivative of -8*a**3/57 - 3*a**2/19 + 2*a/19 - 118. Factor r(w).
-2*(w + 1)*(4*w - 1)/19
Let b(a) be the third derivative of -a**5/180 + 11*a**4/24 + 17*a**3/9 - 13*a**2 + 2*a. Factor b(w).
-(w - 34)*(w + 1)/3
Factor -4 - 1/8*v**3 - 9/2*v - 3/2*v**2.
-(v + 2)**2*(v + 8)/8
Let u(b) be the second derivative of -2 - 1/39*b**3 - 6/13*b**2 + 5*b + 1/78*b**4. Factor u(r).
2*(r - 3)*(r + 2)/13
Let i(w) be the seco