6*g**4 - 32*g**3 + 86*g**2 - 92*g + 32. Let o(k) = -19*k**4 + 96*k**3 - 259*k**2 + 278*k - 96. Let p(a) = 7*m(a) + 2*o(a). Factor p(z).
4*(z - 4)*(z - 2)*(z - 1)**2
Let b be 0/((12/4)/(-3)). Let y(o) be the third derivative of 0*o - 1/240*o**5 + b*o**3 + 6*o**2 + 0 + 1/32*o**4. Find k, given that y(k) = 0.
0, 3
Let p(t) be the second derivative of -t**9/756 + t**8/420 + t**7/210 - t**6/90 - t**3/3 - 6*t. Let s(j) be the second derivative of p(j). Factor s(g).
-4*g**2*(g - 1)**2*(g + 1)
Let x(p) = 10*p**4 - 20*p**3 + 36*p - 26. Let q be 9/2*10/(-15). Let r(b) = 2*b**4 - 4*b**3 + 7*b - 5. Let y(k) = q*x(k) + 16*r(k). Factor y(a).
2*(a - 1)**3*(a + 1)
Suppose -50*o + 13*o**4 + 42*o**3 - 2*o + 14249 + 9*o**2 - 14261 = 0. Calculate o.
-2, -3/13, 1
Let v(t) be the third derivative of t**6/660 + 17*t**5/330 - t**4/132 - 17*t**3/33 + 8*t**2 - 1. Factor v(m).
2*(m - 1)*(m + 1)*(m + 17)/11
Suppose -14*m - 308 = -336. Let t(b) be the first derivative of -20*b**m + 12 + 16*b**3 + 12*b - 6*b**4 + 4/5*b**5. Factor t(u).
4*(u - 3)*(u - 1)**3
Let z(i) be the first derivative of i**6/60 + 3*i**5/20 + 3*i**4/8 - 53*i - 6. Let b(j) be the first derivative of z(j). Factor b(h).
h**2*(h + 3)**2/2
Let s be 0 - -1 - (-1)/(-1). Let m = 11 + s. Factor 10*t**3 - t**4 + 6*t**2 - m*t**3 + t**5 - 5*t**2.
t**2*(t - 1)**2*(t + 1)
Suppose 2 = 149*u - 148*u. Let g(p) be the second derivative of -9*p + 0 + 1/12*p**3 + 1/40*p**5 - 1/12*p**4 + 0*p**u. Let g(m) = 0. What is m?
0, 1
Let t = -1040 + 1044. Let v(d) be the second derivative of 1/24*d**3 - 1/24*d**t - 6*d + 0*d**2 + 1/80*d**5 + 0. Factor v(w).
w*(w - 1)**2/4
Suppose 1/2*y**2 + 17298 - 186*y = 0. What is y?
186
Let l(m) be the second derivative of m**5/480 + m**4/96 + m**3/48 - m**2/2 + 19*m. Let f(r) be the first derivative of l(r). Solve f(v) = 0.
-1
Let s(u) = -u**3 + 20*u + 20. Let x be s(-7). Determine v, given that 4*v**3 - x + 223 - 4*v**5 = 0.
-1, 0, 1
Suppose 0 = -6*u + 7 + 23. Determine l so that -5*l**5 + 38*l**3 - u*l**4 + 5*l**2 + 32*l**3 - 65*l**3 = 0.
-1, 0, 1
Let a be (-7)/(7/(-3)) - 1. Find p such that 24*p + 4 - 6*p - 7 - 12 - 3*p**a = 0.
1, 5
Suppose -4*k = -13 - 35. Factor k*a**3 + 63*a**2 - 1 + 4*a**3 - 4*a**3 + 19 + 87*a.
3*(a + 2)*(a + 3)*(4*a + 1)
Let n(s) = 54*s + 1083. Let r be n(-20). Find o such that -1/3*o**5 + 0*o**2 - 1/3*o**4 + 0*o**r + 0*o + 0 = 0.
-1, 0
Suppose 0*x + 0 + 2/5*x**4 - 2/15*x**5 + 2/15*x**3 - 2/5*x**2 = 0. What is x?
-1, 0, 1, 3
Let q(w) be the second derivative of w**6/120 - w**5/48 + w**4/96 - 3*w**2 + 5*w. Let t(h) be the first derivative of q(h). What is m in t(m) = 0?
0, 1/4, 1
Factor -2*j - 6 + 1/2*j**2.
(j - 6)*(j + 2)/2
Let m = 147 - 145. Let u(a) be the first derivative of -1/15*a**3 - 1/10*a**m + 1/20*a**4 - 2 + 1/5*a. Factor u(q).
(q - 1)**2*(q + 1)/5
Let j be 25/10*(-3 - 27/(-5)). Determine v so that 14*v + j + 10 + v**2 - 22*v = 0.
4
Let i(m) be the second derivative of -1/18*m**5 + 1/135*m**6 + 31*m + 4/27*m**4 - 4/27*m**3 + 0 + 0*m**2. Suppose i(c) = 0. What is c?
0, 1, 2
Let z(f) be the first derivative of 5*f**6/6 + 23*f**5 + 475*f**4/2 + 3290*f**3/3 + 4165*f**2/2 + 1715*f + 13. Determine x so that z(x) = 0.
-7, -1
Let s(a) be the third derivative of -1/33*a**4 - 1/330*a**5 - 6*a**2 + 0 + 0*a - 1/11*a**3. Factor s(v).
-2*(v + 1)*(v + 3)/11
Let x(f) be the third derivative of f**7/945 - 11*f**6/540 - 3*f**2 + 5*f. Determine k, given that x(k) = 0.
0, 11
Let m = -1460 + 1466. Let d(b) be the third derivative of -1/140*b**5 + 0*b + 1/840*b**m + 0*b**4 - b**2 + 0 + 0*b**3. Let d(u) = 0. What is u?
0, 3
Let w(y) be the first derivative of 11/8*y**4 + 0*y - 8 + y**2 - 2*y**3 - 3/10*y**5. Solve w(t) = 0 for t.
0, 2/3, 1, 2
Suppose 2*v - 14 = 2*b, -33 = -5*v + 3*b - 0*b. Let r be 116/24 - 2/v. Suppose -1/2*u**3 + 7/2*u**2 + r - 15/2*u = 0. Calculate u.
1, 3
Let l(a) be the third derivative of -a**7/210 + a**6/20 - a**5/15 - a**4/4 + 5*a**3/6 + 33*a**2. Factor l(f).
-(f - 5)*(f - 1)**2*(f + 1)
Let v(a) be the first derivative of a**4/26 - 3*a**2/13 + 4*a/13 - 146. Solve v(r) = 0 for r.
-2, 1
Suppose 41/2*b - 1/2*b**2 + 0 = 0. Calculate b.
0, 41
Let k(w) = -w**3 + 9*w**2 - 2*w + 12. Let j be k(9). Let r(t) = -t**2 - 6*t + 5. Let x be r(j). Factor 7*m**5 + 10*m**5 + 2*m**3 - 19*m**x.
-2*m**3*(m - 1)*(m + 1)
Let u(c) = 22*c**3 + 16*c**2 + 30*c - 68. Let p(i) = -2*i**3 + i**2 - i + 2. Let m(g) = -20*p(g) - 2*u(g). Factor m(a).
-4*(a - 1)*(a + 2)*(a + 12)
Let n be -1 + 10*4/10. Factor 6*w**4 + 6 - n*w**3 - 6*w**2 - 6 + 3*w**5 + 0*w**3.
3*w**2*(w - 1)*(w + 1)*(w + 2)
Let s be -1*2/(-9) - 75/(-27). Factor 18 - a**3 + 14*a**2 + 2*a**3 - 3*a**s + 0*a**3 - 30*a.
-2*(a - 3)**2*(a - 1)
Let a(v) = -15*v**4 - 20*v**3 + 270*v**2 - 245*v. Let o(d) = 13*d**4 + 20*d**3 - 271*d**2 + 246*d. Let n(u) = 4*a(u) + 5*o(u). Factor n(k).
5*k*(k - 5)*(k - 1)*(k + 10)
Let b(f) be the first derivative of -f**5/10 + 5*f**4/8 + 7*f**3/2 - 53*f**2/4 + 14*f - 584. Factor b(i).
-(i - 7)*(i - 1)**2*(i + 4)/2
Let f be (119/(-4))/(-17) - (-3)/12. Factor -1 - 1/4*x**f - x.
-(x + 2)**2/4
Suppose 4*m**2 + 1/2*m**4 - 5/2*m**3 + 0 - 2*m = 0. Calculate m.
0, 1, 2
Let d(q) be the third derivative of q**6/15 - 3*q**5/10 + q**4/2 - q**3/3 - 91*q**2. Determine c so that d(c) = 0.
1/4, 1
Let x(p) be the third derivative of -p**9/5040 + p**8/280 - 2*p**7/105 + 7*p**4/8 + 14*p**2. Let v(g) be the second derivative of x(g). Factor v(j).
-3*j**2*(j - 4)**2
Let v(n) be the second derivative of n**6/20 + n**5/4 + n**4/8 - n**3 + 5*n**2/2 - 26*n. Let w(s) be the first derivative of v(s). Factor w(c).
3*(c + 1)*(c + 2)*(2*c - 1)
Factor -7*p + 1 + 7*p - 10 + 12*p**2 - 3*p.
3*(p - 1)*(4*p + 3)
Let o(h) be the first derivative of -1/3*h**3 + 0*h**2 - 1/4*h**4 + 18 + 0*h. Factor o(y).
-y**2*(y + 1)
Let m(c) be the second derivative of 4/5*c**5 - 2/5*c**6 + 33*c + 0 + 0*c**3 - 2/21*c**7 + 4*c**4 + 0*c**2. Solve m(g) = 0.
-3, -2, 0, 2
Let q(c) be the first derivative of 1/30*c**6 + 0*c - 3/35*c**5 - 10 + 0*c**3 - 11/2*c**2 + 1/21*c**4. Let m(l) be the second derivative of q(l). Factor m(d).
4*d*(d - 1)*(7*d - 2)/7
Suppose 0 = -3*i + 3*f - 12, 11*i + 3*f - 12 = 6*i. What is u in 0*u + 2/7*u**3 - 2/7*u**5 + 0*u**4 + 0*u**2 + i = 0?
-1, 0, 1
Let t = -239 - -239. Let x(g) be the third derivative of t*g**3 + 0*g - 1/20*g**5 - 3*g**2 + 0 + 1/4*g**4. Determine j, given that x(j) = 0.
0, 2
Let k(p) be the second derivative of p**4/8 - 2*p**3/9 - p**2/12 + 239*p. Factor k(f).
(f - 1)*(9*f + 1)/6
Factor 4/7*t - 1/7*t**2 - 3/7.
-(t - 3)*(t - 1)/7
Let f(n) = -n**3 + 67*n**2 + 70*n - 134. Let d be f(68). Solve 0*q + 4/5*q**4 + 0 + 8/5*q**3 + 4/5*q**d = 0.
-1, 0
Let t = 10634 + -95698/9. Solve -22/9*i**2 - 2/9*i**5 + 0 + 2*i**3 + t*i - 2/9*i**4 = 0 for i.
-4, 0, 1
Let r be (-12)/22 - (-1127)/1078. Let y(d) be the first derivative of 2 + 2*d**2 + 0*d - 2/3*d**3 - r*d**4. What is n in y(n) = 0?
-2, 0, 1
Let n(m) be the second derivative of -m**4/90 - m**3/15 + 4*m**2/15 - 2*m - 31. Factor n(p).
-2*(p - 1)*(p + 4)/15
Let p be 30/7 - 6/21. Determine j so that -j**p + 2*j**3 - 8*j**5 + 7*j**5 + 0*j**5 = 0.
-2, 0, 1
Suppose 5*d - 3*f = 24, 4*d - d = -5*f + 28. Factor -d*h**2 + 23*h**3 - 7*h**3 + 108*h**5 - 108*h**4 + 2*h**2 + 20*h**3.
4*h**2*(3*h - 1)**3
Let s(j) be the third derivative of -j**7/70 - 2*j**6/5 - 23*j**5/10 + 18*j**4 - 81*j**3/2 - 57*j**2 - 2*j. Solve s(u) = 0 for u.
-9, 1
Let l(c) = c**3 - 3*c**2 - c + 9. Let t be l(3). Suppose 9*z = t*z + 9. Solve 15/2*a**4 - z*a + 0 - 3/2*a**5 - 27/2*a**3 + 21/2*a**2 = 0 for a.
0, 1, 2
Let z(c) be the third derivative of 0*c**3 + 1/42*c**6 + 0*c + 0 + 8*c**2 - 2/105*c**5 - 2/245*c**7 + 0*c**4. Let z(h) = 0. Calculate h.
0, 2/3, 1
Let w(b) = 75*b + 432. Let a(c) = -3*c**3 - 2*c**2 - 3*c - 1. Let n be a(-1). Let g(i) = i**2 + 74*i + 432. Let u(f) = n*g(f) - 2*w(f). Factor u(r).
3*(r + 12)**2
Let n be (2 + (-1 - -1))/1. Let k(z) = -z**2 - 10*z + 5. Let y be k(-8). Factor -6*b + 3*b**3 + y*b + 6 + 4*b**3 + 12*b**n - 4*b**3.
3*(b + 1)**2*(b + 2)
Let i(c) = c**2 - 8*c + 11. Let n be i(7). Suppose -377*s**n + 3*s + 36*s**2 - 391*s**4 - 3*s**3 + 3*s**3 = 0. What is s?
-1/8, 0, 1/4
Let z(p) be the second derivative of p**6/195 - p**5/13 + 7*p**4/26 - 461*p. Solve z(k) = 0.
0, 3, 7
Let k(o) be the se