**3 - 8*f**2 + 2*f + 23. Let r(n) = 2*y(n) - 5*z(n). Factor r(w).
3*w*(w + 1)*(w + 6)
Let m(b) be the first derivative of -b**5/210 - b**4/14 - 3*b**3/7 - b**2 - 11. Let z(v) be the second derivative of m(v). Solve z(s) = 0 for s.
-3
Let y be ((-3)/(-12))/(4/448*-218 - -2). Factor 0*f**2 - y*f - 4 + 2/3*f**3.
2*(f - 3)*(f + 1)*(f + 2)/3
Let 2 - 5/4*w**2 - 9/2*w = 0. Calculate w.
-4, 2/5
Suppose 7 = -3*m - j, -14*j + 14 = -16*j. Let 2/9*a**5 + m*a**2 - 2/9*a**3 + 0 + 0*a**4 + 0*a = 0. What is a?
-1, 0, 1
Let s(t) be the second derivative of -4/9*t**3 + 4/3*t**2 + 0 + 12*t + 1/18*t**4. Factor s(i).
2*(i - 2)**2/3
Let s be 4/144*12*4. Factor 14/3*m + 6*m**2 + s + 2/3*m**4 + 10/3*m**3.
2*(m + 1)**3*(m + 2)/3
Factor -728*w**3 - 88*w - 88*w + 169*w**4 + 888*w**2 + 2*w - 50*w + 16.
(w - 2)**2*(13*w - 2)**2
Let b(y) = y**2 - y + 1. Let w = -15 + 18. Suppose 4 - 7 = w*f. Let m(i) = i**2 + 11*i + 4. Let u(j) = f*m(j) - 2*b(j). Determine z, given that u(z) = 0.
-2, -1
Suppose -5*a - 2 = -4*u, -3*a - 4*u + 18 = -0*u. Suppose a*g + 12 = 4*z, g + 1 = 4*z - 13. Determine y, given that 9*y**3 - 9*y**3 + z*y**3 = 0.
0
Let k be -1 - 4 - (-74 - 1). Let g be k/3 + (24 - 26). Suppose -4/3*p**2 - 32/3*p - g = 0. What is p?
-4
Let o(l) be the second derivative of 5*l + 0*l**2 + 1/3*l**3 + 0 + 1/6*l**4. Find f, given that o(f) = 0.
-1, 0
Let o(j) be the second derivative of -43*j**4/108 - 217*j**3/54 - 5*j**2/9 + 17*j - 6. Find c, given that o(c) = 0.
-5, -2/43
Let o(i) be the first derivative of -3/5*i**5 + 0*i + 3*i**4 + 3*i**2 - 5*i**3 + 14. Find y, given that o(y) = 0.
0, 1, 2
Let r(a) be the first derivative of 2*a**6/3 - 6*a**5/5 - 9*a**4/2 - 2*a**3/3 + 3*a**2 + 60. Let r(k) = 0. Calculate k.
-1, 0, 1/2, 3
Let d(s) be the first derivative of -s**6/15 + s**4 + 8*s**3/3 + 3*s**2 + s - 6. Let g(b) be the first derivative of d(b). What is m in g(m) = 0?
-1, 3
Let y(g) be the first derivative of 5*g**4/8 + 25*g**3/6 + 15*g**2/4 - 45*g/2 + 474. Factor y(p).
5*(p - 1)*(p + 3)**2/2
Let v(o) be the second derivative of -5*o**7/42 + 17*o**6/6 - 63*o**5/4 - 135*o**4/4 - 150*o. Find j, given that v(j) = 0.
-1, 0, 9
Let t(s) be the first derivative of -5/2*s**2 + 0*s**3 + 3 - 1/70*s**5 + 0*s**4 + 0*s - 1/280*s**6. Let q(c) be the second derivative of t(c). Factor q(l).
-3*l**2*(l + 2)/7
Let z = -1103 + 1105. Factor 1/3*m**z - 2/3 - 1/3*m.
(m - 2)*(m + 1)/3
Let d be 2/7 - 0 - (-66)/14. Factor -3*z**3 + 61*z**5 + 4*z**4 + 5*z**2 - 60*z**d - 23*z**2.
z**2*(z - 2)*(z + 3)**2
Suppose -4*z = -z - 9. Suppose -15 = z*k - 8*k. Solve -1 + 10*t - 3*t - k*t**2 - 5 + 2*t = 0.
1, 2
Let t = 18316/45 + -407. Let f = t - -8/45. Suppose f*l**3 + 0 + 1/5*l**2 - 2/5*l = 0. What is l?
-2, 0, 1
Let p = -1703 + 66421/39. Let v = p + 97/195. Factor -3/5*y**2 + 0*y + v.
-3*(y - 1)*(y + 1)/5
Let k(h) = h**2 + h. Let l be k(3). Let s(y) = -11*y**2 + 13*y + 5. Let q(n) = -27*n**2 + 33*n + 12. Let z(r) = l*s(r) - 5*q(r). Factor z(a).
3*a*(a - 3)
Suppose 2*t = 3*t. Let z(m) = -m**3 + m**2 + m + 3. Let g be z(0). Factor t*r - 2/3*r**4 + 0 - 2/3*r**g + 4/3*r**2.
-2*r**2*(r - 1)*(r + 2)/3
Let i(t) be the second derivative of -3*t**5/10 + 5*t**4/3 + 71*t**3/3 + 42*t**2 + 14*t + 7. Let i(x) = 0. What is x?
-3, -2/3, 7
Let o be (59 - (1 - -53)) + -5 + 0/1. Factor 30/19*y**3 + o + 98/19*y - 126/19*y**2 - 2/19*y**4.
-2*y*(y - 7)**2*(y - 1)/19
Suppose 2*y - 5*c - 25 = 0, 2 = 4*y + 2*c - 12. Factor -3*w**4 + 4*w**3 + 4*w**3 - 4*w**y - w**4.
-4*w**3*(w - 1)*(w + 2)
Suppose -2*b - 3*p + 4 = 0, -11 + 3 = -4*b - 5*p. Suppose 3*k = 10 + b. Factor -2*l**k + 18*l**2 - l**4 + 6*l - 30*l + 9.
-3*(l - 1)**3*(l + 3)
Let s = -23 + 27. Solve 311*r**4 + 5*r**5 - 326*r**s - 3*r**3 - 3*r**3 + r**3 - 20 + 35*r**2 = 0 for r.
-1, 1, 2
Let k = -63 - -63. Let n(l) = l**3 + l**2 - 2*l + 4. Let o be n(k). Factor 2/5 - 4/5*j**3 - 2/5*j**o + 4/5*j + 0*j**2.
-2*(j - 1)*(j + 1)**3/5
Let y(c) be the third derivative of c**6/30 + 16*c**5/5 + 128*c**4 + 8192*c**3/3 - c**2 - 39*c. Factor y(n).
4*(n + 16)**3
Let i(s) be the third derivative of s**7/16380 + s**6/936 + s**5/195 - 13*s**4/24 + 4*s**2. Let n(y) be the second derivative of i(y). Factor n(x).
2*(x + 1)*(x + 4)/13
Suppose 19 = 3*z + r - 6*r, -r + 1 = z. Factor 4/9*h**2 + 0 + 8/9*h**4 + 2/9*h**5 + 0*h + 10/9*h**z.
2*h**2*(h + 1)**2*(h + 2)/9
Suppose -3*s - 20 = -5*p, -5*s - 3 = -3*p + 25. Suppose -4*h + 11 = -p. Solve 2/7*z**h + 0 - 4/7*z**2 + 0*z + 2/7*z**4 = 0.
-2, 0, 1
Let f(o) be the second derivative of o**8/840 + o**7/105 + o**6/36 + o**5/30 + 13*o**3/6 - 10*o. Let j(r) be the second derivative of f(r). Factor j(a).
2*a*(a + 1)**2*(a + 2)
Let z(b) be the third derivative of b**6/160 + 3*b**5/20 + 41*b**4/32 + 15*b**3/4 + 15*b**2 - b. Factor z(t).
3*(t + 1)*(t + 5)*(t + 6)/4
Let i = -1665 + 11667/7. Factor 6*u - i*u**3 - 3*u**2 - 9/7.
-3*(u - 1)*(u + 3)*(4*u - 1)/7
Suppose -3*m + 4*m = -2*y + 1, 4*y - 17 = 3*m. Let j(f) = f**2. Let z(k) = -3*k**3 - 8*k**2 - 3*k. Let r(t) = y*j(t) + z(t). Determine v so that r(v) = 0.
-1, 0
Let g(d) be the third derivative of d**7/2100 + 23*d**6/1200 - 13*d**5/40 + 147*d**4/80 - 9*d**3/2 + 8*d**2 + 23*d. Factor g(f).
(f - 3)**2*(f - 1)*(f + 30)/10
Let y(g) be the third derivative of -g**8/1344 + g**6/144 + 25*g**4/24 + 8*g**2. Let r(c) be the second derivative of y(c). Factor r(o).
-5*o*(o - 1)*(o + 1)
Let w(d) be the first derivative of -d**6/33 - 6*d**5/55 + 2*d**4/11 + 32*d**3/33 - 32*d/11 - 41. Suppose w(r) = 0. What is r?
-2, 1, 2
Let o(v) = v**3 + 10*v**2 + 14*v - 47. Let i be o(-7). Solve -4/3*c**i + 2/3*c**5 - 4/3*c**3 + 2/3*c + 2/3 + 2/3*c**4 = 0 for c.
-1, 1
Let h(f) = f**3 + 6*f**2 + 4*f - 1. Let y be h(-5). Factor 8*s**4 - 18*s**4 + 3*s**2 + 7*s**y.
-3*s**2*(s - 1)*(s + 1)
Let p(u) = -u**3 + 5*u**2 - 2*u - 7. Let b be p(3). Suppose -b*z - 4*q + 12 = -12, 3*z = 5*q + 7. Factor 0 - 1/4*d**z - 3/4*d**3 + 0*d - 1/2*d**2.
-d**2*(d + 1)*(d + 2)/4
Suppose -2*o + o = -r + 2, -4*o + 13 = 3*r. Suppose 15 = 7*n + 1. Solve -13 + 13 + 2*d**n - d**r - 2*d**4 - d + 2*d = 0.
-1, -1/2, 0, 1
Let s(f) be the third derivative of -11*f**8/84 - 34*f**7/105 + 9*f**6/10 + 73*f**5/15 + 26*f**4/3 + 8*f**3 + 3*f**2 + 11. Determine w, given that s(w) = 0.
-1, -6/11, 2
Let g = 130/81 - -14/81. Determine i so that -g*i + 10/9*i**2 - 2/9*i**3 + 8/9 = 0.
1, 2
Let 0*l + 0 - 2*l**2 - 1/3*l**3 + 1/3*l**4 = 0. What is l?
-2, 0, 3
Determine c, given that 0 + 2/17*c**4 - 54/17*c**2 + 24/17*c**3 + 28/17*c = 0.
-14, 0, 1
Let l = 1670/63 - 184/7. Let b = -603 - -5429/9. Factor -b*i**3 + 2/9 - 2/9*i**2 + l*i.
-2*(i - 1)*(i + 1)**2/9
Let f(b) be the second derivative of b**6/6 - 5*b**5/4 - 15*b**4/2 + 50*b**3/3 + 140*b**2 + 4*b + 43. Determine q so that f(q) = 0.
-2, 2, 7
Let f = 19 - 17. Suppose q - 6*q + 2*p = 4, -3*p = -f*q - 6. Factor 0 + q*m + 4/13*m**2 + 6/13*m**3.
2*m**2*(3*m + 2)/13
Let f be -12*(5 + 466/(-93)). Let j = f - -18/341. Solve 0 - 2/11*d + j*d**2 = 0.
0, 1
Factor 8/3*f + 0 + 6*f**3 + 40/3*f**2.
2*f*(f + 2)*(9*f + 2)/3
Suppose 4*c = -3*i + 25, -4*c + 8*i = 10*i - 26. Suppose -5 - 5 = -5*q + 3*m, q - 2 = -3*m. Factor 17/2*b**2 - 9/4*b**3 - q - c*b.
-(b - 2)**2*(9*b + 2)/4
Let f(i) be the second derivative of 0*i**2 + 3/16*i**3 - 1/16*i**4 + 0 - 3/160*i**5 + 9*i. Factor f(n).
-3*n*(n - 1)*(n + 3)/8
Suppose -51/8*n**4 + 0 + 9*n**3 + 3/2*n**5 + 3/4*n - 39/8*n**2 = 0. Calculate n.
0, 1/4, 1, 2
Let k(q) be the third derivative of q**7/1470 - q**5/140 - q**4/84 + 6*q**2 + 2*q. Factor k(x).
x*(x - 2)*(x + 1)**2/7
Suppose 18/7*l**4 - 228/7*l**2 + 0 + 64/7*l - 274/7*l**3 = 0. Calculate l.
-1, 0, 2/9, 16
Suppose 2*a - 1 = 3. Factor 110 + 2*p + 4*p**4 - 4*p**a - 2*p**5 - 110.
-2*p*(p - 1)**3*(p + 1)
Let j(u) be the first derivative of -8 + 2/3*u**3 + 0*u + 4*u**2. Factor j(t).
2*t*(t + 4)
Let m be (-295)/(-575) - (-10)/115. Find y, given that -y**2 + m*y + 2/5 = 0.
-2/5, 1
Let v(t) = t**4 - 3*t**3 - t**2 + 3*t - 6. Let l(r) = 10*r**2 - 20*r**2 + 11*r**2 - r**4 - 3*r + 5 + 3*r**3. Let q(x) = -6*l(x) - 5*v(x). Factor q(d).
d*(d - 3)*(d - 1)*(d + 1)
Let o(q) be the third derivative of -q**5/270 + q**4/9 - 11*q**3/27 + 30*q**2. Factor o(g).
-2*(g - 11)*(g - 1)/9
Let f(c) = 2*c**2 + 4*c + 2. Let b(j) = j**3 - 3*j**2 + 4*j - 6. Let g be b(2). Let a be f(g). Factor -8/5*o**