 4)**2
Let w(u) be the third derivative of u**8/112 + 3*u**7/70 + u**6/20 - u**5/10 - 3*u**4/8 - u**3/2 + 4*u**2. Solve w(a) = 0 for a.
-1, 1
Let h be 2/(68/(-20) - -3). Let w = 8 + h. Factor 3/4*p**2 - 3/4 + 3/4*p - 3/4*p**w.
-3*(p - 1)**2*(p + 1)/4
Let o(h) = 2*h - 8. Let p be o(5). Suppose l**3 - 3*l**2 + l**p + l**3 = 0. What is l?
0, 1
Let r be 6/(-5)*5 - -6. Factor -4/7*z**3 + 1/7*z**2 + 0*z + 3/7*z**4 + r.
z**2*(z - 1)*(3*z - 1)/7
Suppose 4 = 4*r - 12. Let o be r/((-16)/(-9)) + -2. What is c in -o - 1/4*c + 1/4*c**3 + 1/4*c**2 = 0?
-1, 1
Suppose -2/9*l**2 - 2/3 - 8/9*l = 0. What is l?
-3, -1
Let u = 4 - 2. Factor 4*p**2 - 4 - u*p**2 - 4 + 6.
2*(p - 1)*(p + 1)
Let k be 9*((-30)/75 - 18/(-20)). Find m, given that -k*m**3 - 15*m**2 - 27/2*m - 3 = 0.
-2, -1, -1/3
Let l(b) be the first derivative of -6 + 0*b - 12/5*b**3 - 21/20*b**4 + 6/5*b**2. Factor l(n).
-3*n*(n + 2)*(7*n - 2)/5
Let c(r) be the first derivative of -3*r**4/8 + 3*r**3/2 - 6*r - 8. Solve c(l) = 0.
-1, 2
Let k(d) = 10*d**3 + 3*d**2 - 5*d. Let i(o) = 11*o**3 + 2*o**2 - 4*o. Let p(x) = 5*i(x) - 4*k(x). Suppose p(n) = 0. What is n?
0, 2/15
Let b(m) be the first derivative of m**3/12 + 3*m**2/8 + m/2 + 7. Factor b(x).
(x + 1)*(x + 2)/4
Let n be ((-24)/4 - 0) + 8. Factor c**n + 0*c**3 - 1/3*c**4 + 0 - 2/3*c.
-c*(c - 1)**2*(c + 2)/3
Let l be 80/44 - 4/(-22). Let t(p) be the third derivative of 0*p**4 + 3*p**l + 0*p - 1/120*p**6 + 0 + 0*p**3 + 1/60*p**5. Factor t(x).
-x**2*(x - 1)
Let h = 24 - 21. Determine s, given that s**2 + 0 - 5/2*s**h + 0*s = 0.
0, 2/5
Let c(n) be the first derivative of n**6/3 - 4*n**5/5 - n**4 + 16*n**3/3 - 7*n**2 + 4*n - 4. Find o, given that c(o) = 0.
-2, 1
Let b = -2817/4 + 705. What is v in -1/2 - 1/4*v**2 - b*v = 0?
-2, -1
Determine n, given that -1/5*n**3 + 0 - 1/5*n**4 + 0*n + 0*n**2 = 0.
-1, 0
Let t(p) be the first derivative of 1/12*p**4 + 1/6*p**3 - p + 2 + 0*p**2. Let g(b) be the first derivative of t(b). Factor g(n).
n*(n + 1)
Determine p so that 3/5*p**3 - 6/5*p**2 - 3/5*p + 6/5 = 0.
-1, 1, 2
Let w(f) = -f + 9. Let v be w(7). Let u = -71/21 - -26/7. Determine j so that 0*j + 1/3 - u*j**v = 0.
-1, 1
Suppose 3*l**2 - l**2 + 0*l**2 - l**2 = 0. Calculate l.
0
Let q(c) = 7*c**3 - c**2 + 7*c + 3. Let n(r) = -20*r**3 + 2*r**2 - 21*r - 9. Let b(l) = -6*n(l) - 17*q(l). Factor b(v).
(v + 1)**2*(v + 3)
Suppose 0 = 45*n - 50*n + 60. Let p = 14 - n. Factor 0 - 2/9*v**p + 0*v.
-2*v**2/9
Let g(f) be the second derivative of -f**6/15 + f**5/5 - f**4/6 + f. Suppose g(r) = 0. What is r?
0, 1
Let y(c) be the first derivative of 3/8*c**2 - 1/2*c + 2 - 1/12*c**3. Let y(v) = 0. What is v?
1, 2
Let u(f) = -16*f - 8. Let b(i) = i**2 - 17*i - 8. Let h = -19 + 15. Let o(n) = h*b(n) + 5*u(n). Factor o(v).
-4*(v + 1)*(v + 2)
Let g(x) be the second derivative of 0*x**3 + 0 + 1/8*x**4 - 9/80*x**5 + 0*x**2 - 1/8*x**6 - x. Factor g(t).
-3*t**2*(t + 1)*(5*t - 2)/4
Let w(g) be the first derivative of 1/9*g**3 - 2/3*g + 1/6*g**2 + 3. Factor w(p).
(p - 1)*(p + 2)/3
Factor -4/5 - 26/5*d - 18/5*d**3 - 8*d**2.
-2*(d + 1)**2*(9*d + 2)/5
Let f(d) = 3*d + 3. Let r be f(7). Suppose r*j = 23*j. Factor j + 2/9*z**2 - 2/9*z.
2*z*(z - 1)/9
Let j = -1275 + 1277. Find d such that 0 + 2/5*d - 1/5*d**3 + 1/5*d**j = 0.
-1, 0, 2
Let p = -3 - -3. Suppose 5*u + i + 13 = 7*u, 5*u - 15 = -i. Factor -21/2*t**u + 0 + p*t - 15/2*t**3 + 3*t**2.
-3*t**2*(t + 1)*(7*t - 2)/2
Let y = 9/13 + -7/13. Factor y*h + 2/13*h**2 - 2/13*h**3 - 2/13.
-2*(h - 1)**2*(h + 1)/13
Let b(z) = z**3 - 1. Let w be b(2). Suppose 0 = -3*i - 2*s + w, -i = 2*s + 1 - 2. Solve -1/2*q**2 + 0 + 0*q**i + 0*q + 1/2*q**4 = 0.
-1, 0, 1
Let x(d) be the first derivative of d**4/30 - 4*d**3/45 + 23. Factor x(w).
2*w**2*(w - 2)/15
Let a(i) = i**3 + i**2 + 1. Let z(m) = -5*m**5 - 5*m**4 + 6*m**3 + 6*m**2 + 1. Let f(s) = -a(s) + z(s). Factor f(c).
-5*c**2*(c - 1)*(c + 1)**2
Suppose 3*r - 1 = 8. Suppose o**2 - r*o**3 - 5*o**3 - 2*o**4 - 9*o**2 = 0. What is o?
-2, 0
Let r be 9/(-12)*6/(-9). Factor -1/2*t**3 + 1/2*t**2 + r*t - 1/2.
-(t - 1)**2*(t + 1)/2
Suppose -6*u = -4*u - 6. Suppose -16 = -7*s + u*s. Factor -m**3 - 1/3*m + 0 - m**2 - 1/3*m**s.
-m*(m + 1)**3/3
Let a be 3 + 0 - (20 + -19). Factor 0*f**3 - 2/7*f**5 + 4/7*f**a + 2/7*f + 0 - 4/7*f**4.
-2*f*(f - 1)*(f + 1)**3/7
Let b be (2/64)/1*4/15. Let p(y) be the third derivative of 2*y**2 - 1/48*y**4 + 0 + 1/240*y**6 + 0*y - b*y**5 + 1/12*y**3. Suppose p(z) = 0. Calculate z.
-1, 1
Let h(m) be the second derivative of 2/25*m**5 + 0*m**2 + 2*m + 0 - 1/15*m**3 + 1/10*m**4. Factor h(k).
2*k*(k + 1)*(4*k - 1)/5
Let c be ((-5)/(10/(-24)))/2. Factor l**4 - 4*l**5 + l**5 - 3*l - l**4 + c*l**3.
-3*l*(l - 1)**2*(l + 1)**2
Let x be (0/(-17))/(1 - -1). Solve x + 1/3*b**5 - b**3 - 1/3*b**4 + 5/3*b**2 - 2/3*b = 0.
-2, 0, 1
Let j be (-39)/(-9) - 1/3. Let l = 2 + j. Factor -l*d**2 + 0 - 9*d + 3*d**2 - 6.
-3*(d + 1)*(d + 2)
Let r(t) = 7*t**5 + 12*t**4 + 8*t**3 - 5*t**2 - 15*t - 4. Let j(k) = 8*k**5 + 12*k**4 + 8*k**3 - 4*k**2 - 16*k - 4. Let o(v) = 3*j(v) - 4*r(v). Factor o(l).
-4*(l - 1)*(l + 1)**4
Let i(r) = -6*r**2 - r + 10*r - 7 + 7. Let g(j) = 5*j**2 - 8*j. Let a(h) = -7*g(h) - 6*i(h). Factor a(n).
n*(n + 2)
Let p = -5 - -10. Let k(c) be the second derivative of 1/18*c**4 - 1/30*c**6 + 0 + 1/6*c**2 + 1/6*c**3 - 1/126*c**7 - 1/30*c**p + 3*c. Factor k(h).
-(h - 1)*(h + 1)**4/3
Let d = -9 - -9. Suppose y - 4*j - 16 = 0, -5*y - 4*j = 16 - d. Factor 7/5*n**3 + y + 4/5*n + 16/5*n**2.
n*(n + 2)*(7*n + 2)/5
Let g(o) be the third derivative of o**7/2940 + o**6/1260 - o**5/210 - 5*o**3/6 + 2*o**2. Let q(k) be the first derivative of g(k). What is u in q(u) = 0?
-2, 0, 1
Suppose 0 = -3*q - 2*r + r + 6, 0 = 5*q + 5*r. What is f in -5*f**4 + 6*f**2 - 3*f**5 + 6*f**q + 9 + 2*f**4 - 12 - 3*f = 0?
-1, 1
Let q be 1/(-2)*(-8)/1. Factor q - 66*m**3 + 74*m**3 - m**2 - 11*m**2.
4*(m - 1)**2*(2*m + 1)
Let m(b) = 9*b**3 - 57*b**2 - 15*b - 12. Let r(c) = 2*c**3 - 14*c**2 - 4*c - 3. Let j(d) = 5*m(d) - 21*r(d). What is w in j(w) = 0?
-1
Let v(r) be the second derivative of 1/9*r**3 - 1/18*r**4 - r + 0 - 1/30*r**5 + 1/3*r**2. Solve v(n) = 0.
-1, 1
Suppose 0 = -k - 4*q + 7, k - 4 = -3*q + 3. Let b = -5 + k. Suppose b*s**4 - 2*s**2 - 5 + 5 = 0. Calculate s.
-1, 0, 1
Let o be ((-4)/(-6))/((-39)/(-9)). Let c(h) = -h**3 - 2*h + 3. Let i be c(0). Factor -2/13*t**4 + o*t - 2/13*t**i + 2/13*t**2 + 0.
-2*t*(t - 1)*(t + 1)**2/13
Let 0 + 0*r**3 - 6/7*r**2 + 0*r + 6/7*r**4 = 0. Calculate r.
-1, 0, 1
Let t(w) be the second derivative of -3/10*w**5 - 1/6*w**4 + 2*w**2 - 1/15*w**6 - w + 0 + w**3. Factor t(d).
-2*(d - 1)*(d + 1)**2*(d + 2)
Suppose 7*i - 27 = 1. Let o(v) be the second derivative of 1/4*v**4 - 1/2*v**2 + 0 - 1/3*v**3 + i*v. Find g such that o(g) = 0.
-1/3, 1
Let p = -19/84 + 10/21. Factor 0*s + 1 - p*s**2.
-(s - 2)*(s + 2)/4
Let m(i) be the second derivative of 0*i**2 + 0 + 0*i**3 - 4*i + 1/16*i**4. Factor m(d).
3*d**2/4
Suppose 3*q - 3*f - 2 - 10 = 0, -2*q + 5*f = -8. Suppose -2*g + 11 + 1 = 4*t, -q*g + 6 = -t. Factor 2*w**2 - t*w + 4*w**4 - 6*w**4 + 0*w**3 + 2*w**3.
-2*w*(w - 1)**2*(w + 1)
Let u(k) be the first derivative of 5*k**4/2 - 8*k**3/3 - 11*k**2 - 4*k - 11. Factor u(p).
2*(p - 2)*(p + 1)*(5*p + 1)
Let y be 2/6*0/4. Let b(l) be the first derivative of -2 + 0*l + y*l**2 + 1/4*l**4 + 2/3*l**3 - 1/5*l**5. Let b(d) = 0. What is d?
-1, 0, 2
Let m(v) be the second derivative of -v**5/5 + v**4/3 - 12*v. Suppose m(y) = 0. Calculate y.
0, 1
Let t(z) = 2*z**2 + z - 4. Let y(p) = -10*p**2 - 4*p + 20. Let w(n) = 14*t(n) + 3*y(n). Find h such that w(h) = 0.
-1, 2
Let p be (3 - 116/16)*4. Let s(f) = -9*f**4 + 26*f**3 + 27*f**2 - 45*f + 1. Let n(r) = 3*r**4 - 9*r**3 - 9*r**2 + 15*r. Let j(d) = p*n(d) - 6*s(d). Factor j(z).
3*(z - 1)**3*(z + 2)
Let r = 2/1325 - -59621/2650. Suppose -2 + 4*f + r*f**2 = 0. Calculate f.
-2/5, 2/9
Suppose 13*y = 20*y. Factor -4/7*v - v**2 + y.
-v*(7*v + 4)/7
Factor 0 + 0*z - 1/4*z**2 + 1/4*z**3.
z**2*(z - 1)/4
Factor 2927 - 2927 + 2*n**4.
2*n**4
Factor 0 - 4/5*z**2 + 0*z.
-4*z**2/5
Let g(s) be the third derivative of -1/20*s**5 + 1/120*s**6 + 1/8*s**4 - 1/6*s**3 + 0*s - 2*s**2 + 0. Solve g(o) = 0.
1
Suppose 22 = 5*p - 4*p. Let -60*q - 18*q**4 + 3*q**2 + 87*q**3 - 7*q**2 - p*q**5 - 5*q**5 + 24 - 2*q**2 = 0. C