))*2. Suppose -54*q**2 - z*q**3 - 4*q**4 + 6*q + 66*q**2 + 9*q + 8 + 5*q = 0. What is q?
-1, 2
Let m be 1/2*0/(-46). Let -5/8*f**5 + m + 0*f + 0*f**2 + 1/4*f**3 + 3/8*f**4 = 0. Calculate f.
-2/5, 0, 1
Factor -33*z**2 + 102*z - 72 + 14*z**2 - 3*z**3 - 6*z**2 - 2*z**2.
-3*(z - 2)*(z - 1)*(z + 12)
Solve -16*p**5 - 7 + 2*p + 8*p**2 - 4*p**3 - 4*p**4 + 6*p**5 + 3 + 12*p**5 = 0 for p.
-1, 1, 2
Let x(t) = -5*t**4 + 24 + 4*t**4 - 10*t**3 - t**4 - 57*t + 36*t**2. Let l(a) = 3*a**4 + 10*a**3 - 36*a**2 + 58*a - 23. Let u(h) = -3*l(h) - 4*x(h). Factor u(c).
-(c - 3)**3*(c - 1)
Let l be -3 + (-4 - -7) + 2. Factor -11*r**2 - 4*r**2 + l*r**2 + 8*r + r**2.
-4*r*(3*r - 2)
Let l(t) = -t + 3. Let s(a) = -5*a**2 + 73*a - 74. Let g(n) = 3*l(n) + s(n). Solve g(u) = 0.
1, 13
Let l(v) be the first derivative of -1/4*v**2 + 7*v + 8 - 1/6*v**3 - 1/24*v**4. Let i(a) be the first derivative of l(a). Determine b, given that i(b) = 0.
-1
Factor 2*m**3 + 21*m + 313*m - 132*m - 144 + 62*m + 47*m**2.
(m + 12)**2*(2*m - 1)
Let q be (30/(-25))/(42/(-2240)*18). Factor 0 - 4/9*y**2 + q*y.
-4*y*(y - 8)/9
Suppose -22*y - 130*y**2 - 21*y - 78*y**3 - 34*y**3 + 58*y - 29*y + 4 = 0. What is y?
-1, -2/7, 1/8
Suppose 81*t = 110*t - 87. Factor 21/4*h + 15/4*h**t + 27/4*h**2 + 3/4*h**4 + 3/2.
3*(h + 1)**3*(h + 2)/4
Let y(s) be the second derivative of 1/10*s**6 - 3/2*s**4 + 0 - 15*s + 4*s**3 - 9/2*s**2 + 0*s**5. Factor y(m).
3*(m - 1)**3*(m + 3)
Let v(y) be the second derivative of 3*y**5/20 + 9*y**4/4 - 6*y**3 - 30*y**2 - 9*y + 2. Factor v(s).
3*(s - 2)*(s + 1)*(s + 10)
Factor 84*z - 42*z**2 - 38*z**2 + 29 + 84*z**2 - 11 + 62.
4*(z + 1)*(z + 20)
Let s(w) = -6*w + 6*w**2 - 8 - 2*w - 5*w**2 - w. Let p be s(10). Factor q + 12*q**3 - 15*q**3 + p*q + 3*q**2 - 3*q**4.
-3*q*(q - 1)*(q + 1)**2
Let c(n) be the third derivative of 53/6*n**4 - 3*n + 0 - 1/10*n**6 + 28/15*n**5 + 13*n**2 + 44/3*n**3. Suppose c(y) = 0. What is y?
-1, -2/3, 11
Let r(o) be the first derivative of o**4/24 + o**3/3 + 3*o**2/4 + 2*o/3 - 103. Factor r(d).
(d + 1)**2*(d + 4)/6
Let y = 12 - 1. Suppose -2 - 12 = -3*g + 2*u, 0 = -4*g - 5*u + y. Suppose -3*l**2 + 0 - 3/4*l**g + 3*l**3 + 0*l = 0. What is l?
0, 2
Let h(v) = -v**3 + 4*v**2 + 4*v + 9. Let n be h(5). Factor 7*y**2 + 3*y**2 - 5*y**5 + 14*y**4 + 6*y**n - 25*y**3.
-5*y**2*(y - 2)*(y - 1)**2
Factor 0 + 115/2*l - 5/2*l**4 + 125/2*l**3 - 235/2*l**2.
-5*l*(l - 23)*(l - 1)**2/2
Suppose 2*w + 2 - 6 = 0. Suppose -5*x + 5*k = -3*x + 4, 0 = x - 5*k + 7. Factor -m**x - m**2 + 2*m - 3*m + 2*m**w + m**2.
-m*(m - 1)**2
Suppose 9*o - 39 = -21. Let t(p) be the third derivative of -1/180*p**5 + 1/9*p**3 + 1/72*p**4 + 0 + 0*p - 8*p**o. Find j, given that t(j) = 0.
-1, 2
Let b(y) be the first derivative of y**6/360 - y**5/40 + y**4/12 + 6*y**3 - 15. Let o(v) be the third derivative of b(v). Factor o(z).
(z - 2)*(z - 1)
Let k be (-15)/(-9) + 11/33. Let f(i) be the first derivative of 2/3*i + 0*i**k - 4 - 2/9*i**3. Factor f(v).
-2*(v - 1)*(v + 1)/3
Find b, given that -3/5*b**5 - 6/5*b**2 + 9/5*b**3 + 0 + 0*b**4 + 0*b = 0.
-2, 0, 1
Let c(f) = -9*f**2 + 204*f + 4. Let n(m) = 3*m**2 - 1. Let u(i) = -c(i) - 4*n(i). Factor u(l).
-3*l*(l + 68)
Let b(y) be the second derivative of y**7/231 + 4*y**6/165 + 3*y**5/110 - 2*y**4/33 - 4*y**3/33 + 207*y. Solve b(k) = 0.
-2, -1, 0, 1
Let p(j) be the third derivative of j**5/3 + 23*j**4/6 - 20*j**3/3 - 95*j**2 + 1. Factor p(i).
4*(i + 5)*(5*i - 2)
Suppose -20 = 5*t, l + 3*t = -7 - 4. Suppose 0 = -j + l, 5*q + 9*j - 6*j - 18 = 0. Factor 4/5*b**2 + 2/5*b**5 - 6/5*b**q + 0*b**4 + 0*b + 0.
2*b**2*(b - 1)**2*(b + 2)/5
Suppose 13*n - 23*n - 40 = 0. Let m = n + 13/3. Factor -m*t**4 + 1/3*t**5 - t**3 + 0 - 2/3*t + 5/3*t**2.
t*(t - 1)**3*(t + 2)/3
Let c = 1850 - 20332/11. Let z = 1/195 + 379/2145. Suppose -8/11*d**3 - 4/11*d**2 + 24/11*d + z*d**4 + c = 0. Calculate d.
-1, 3
Let p(a) be the second derivative of a**4/54 + a**3/9 - 2*a**2 - a - 39. Suppose p(f) = 0. What is f?
-6, 3
Let o(x) be the third derivative of -2*x**7/525 - x**6/24 - x**5/50 + 16*x**4/15 + 16*x**3/15 + 251*x**2. Let o(j) = 0. Calculate j.
-4, -1/4, 2
Suppose -2*m = -5*m + 3. Let p(x) be the first derivative of m + 0*x + 2/15*x**5 + 10/9*x**3 + 2/3*x**2 + 2/3*x**4. Factor p(j).
2*j*(j + 1)**2*(j + 2)/3
Suppose x - 4 = -1. Let r(o) = -x*o - 8*o**2 - 3*o - 13 + o**2. Let b(y) = y**2 + y + 2. Let f(j) = 39*b(j) + 6*r(j). Solve f(p) = 0.
0, 1
Let g(c) be the third derivative of -3*c**8/784 + 151*c**7/245 - 3697*c**6/140 - 2626*c**5/35 + 2397*c**4/56 + 2601*c**3/7 - c**2 - 14. What is p in g(p) = 0?
-1, 2/3, 51
Let g be (-3)/9 + 0 - 20/(-6). Let t(h) be the first derivative of -3/5*h**5 - 4 - 1/3*h**g + 0*h**2 - 3/4*h**4 - 1/6*h**6 + 0*h. Factor t(x).
-x**2*(x + 1)**3
Let g(l) = l**4 + l**3 - 11*l**2 - l + 7. Let j(o) = o**3 + 2*o**2 - o + 1. Let w(h) = 3*g(h) + 3*j(h). Determine n so that w(n) = 0.
-4, -1, 1, 2
Factor -266 - 39*k**2 + 19*k**2 - 88*k + 750 + 24*k**2.
4*(k - 11)**2
Let y(r) be the third derivative of 0*r**5 + 0*r**6 + 1/105*r**7 + 0*r**4 + 0*r**3 + 1/336*r**8 - 8*r**2 + 0 + 0*r. Factor y(a).
a**4*(a + 2)
Suppose -l + 33 - 27 = 0. Factor -12*c**3 + 15*c**4 + 5 - l*c + 22*c**3 + 6*c - 20*c**2 - 10*c.
5*(c - 1)*(c + 1)**2*(3*c - 1)
Factor -216/5*d + 0 + 0*d**3 - 4/5*d**4 + 108/5*d**2.
-4*d*(d - 3)**2*(d + 6)/5
Let k(h) = h**2 - 7*h + 12. Let z be k(5). What is l in 8*l - 6 + 0 + 0 + l**2 - 3*l**z = 0?
1, 3
Suppose 147 + 1/3*v**2 + 14*v = 0. Calculate v.
-21
Solve 53*o + 60*o + 3*o**2 - 98*o = 0.
-5, 0
Let l be -5*(-3)/39 + (-1 - -1). Let f = -2/39 + l. Factor 2/3*u**4 + 0 - 2/3*u**2 - f*u**5 + 1/3*u + 0*u**3.
-u*(u - 1)**3*(u + 1)/3
Let d(g) be the third derivative of -g**8/336 - g**7/210 + g**6/120 + g**5/60 - 5*g**2 + 22. Factor d(w).
-w**2*(w - 1)*(w + 1)**2
Let z(l) be the first derivative of -4*l**3/3 + 176*l**2 - 7744*l - 392. Solve z(v) = 0.
44
Let r = 26/269 + 4174/1345. Factor r - 4/5*c**2 - 2/5*c**3 + 8/5*c.
-2*(c - 2)*(c + 2)**2/5
Suppose -12*a + 14*a = -60. Let h be ((-1)/a*3)/(2/5). Factor -3/8*z + h + 1/8*z**2.
(z - 2)*(z - 1)/8
Let w(j) be the first derivative of 2 - 69/4*j**4 + 24*j**2 + 7/2*j**6 - 12*j - j**3 + 3*j**5. Determine q so that w(q) = 0.
-2, -1, 2/7, 1
Let w(p) be the first derivative of p**3/4 + 507*p**2/4 + 85683*p/4 - 100. What is x in w(x) = 0?
-169
Let d be (108/1323)/((-18)/(-1155)). Factor -d*w**2 - 26/21*w - 2/21 - 50/7*w**3.
-2*(3*w + 1)*(5*w + 1)**2/21
Let s = 27 - 24. Suppose -6 - 1 = b - 3*m, 1 = 2*b - m. Factor -4*o + s*o - 3*o**2 + 2*o**b.
-o*(o + 1)
Let p(g) = 26*g**4 - 16*g**3 - 32*g**2 + 16*g + 33. Let k(h) = -6*h**4 + 4*h**3 + 8*h**2 - 4*h - 8. Let n(l) = 9*k(l) + 2*p(l). Factor n(z).
-2*(z - 3)*(z - 1)*(z + 1)**2
Let q(c) be the third derivative of -c**5/48 + 55*c**4/96 + 85*c**3/4 + c**2 - 35. Factor q(v).
-5*(v - 17)*(v + 6)/4
Let t be (-2)/10 + 315/75. Determine l, given that -10*l - 2 - 15*l**2 + 11*l**3 - 12*l + 31*l - 3*l**t = 0.
2/3, 1
Let w(f) be the first derivative of 6/5*f**2 - 34 + 0*f - 2/15*f**3. Solve w(p) = 0 for p.
0, 6
Let m(z) be the third derivative of z**6/24 + 5*z**5/4 + 105*z**4/8 + 245*z**3/6 + 183*z**2. Factor m(o).
5*(o + 1)*(o + 7)**2
Let u(q) be the second derivative of -q**7/28 + q**6/15 + q**5/40 - q**4/12 + 54*q. Suppose u(t) = 0. Calculate t.
-2/3, 0, 1
Let k be (-25 - -11)/(0 - 2). Let c be k/21*(0 + 0). Factor 6/13*y**4 + c + 0*y**2 + 0*y + 8/13*y**5 - 2/13*y**3.
2*y**3*(y + 1)*(4*y - 1)/13
Let t be 108/(-8)*-3*8/18. Suppose 3*c**2 - 53*c + 65*c - 6 + t = 0. Calculate c.
-2
Let 86*d**2 + 5*d**4 + 38*d**3 + 30*d**3 + 24*d**2 - 420*d - 8*d**3 + 245 = 0. What is d?
-7, 1
Suppose -9*z = -6*z + 3*q - 24, q + 12 = 3*z. Let m(a) be the second derivative of -a + 0 + 3/20*a**z - 1/4*a**4 + 0*a**2 + 0*a**3. Factor m(r).
3*r**2*(r - 1)
Let w = 6 + -5. Suppose -5 = -a + w. Suppose 7 + 12*j + 3*j**2 - 1 + a = 0. Calculate j.
-2
Factor -1/5*q**3 + 0*q + 16/5*q**2 + 0.
-q**2*(q - 16)/5
Let w = -431/107 - 301612/749. Let d = w - -408. What is y in 69/7*y**2 - d + 15/7*y + 57/7*y**3 + 12/7*y**4 = 0?
-3, -1, 1/4
Find r such that 1/2*r**3 + 3/8*r + 7/8*r**2 + 0 = 0.
-1, -3/4, 0
Let u(n) = n**2 - 3*n - 10. Let k be u(5). Suppose 0*b + 3*b - 9 = k. Find h such that 6*h**b + 2*h**3 - 24*h**4 + 12*h**4 + 4*h**5 = 0.
0, 1, 2
