1
Let f be (-49)/42*(-8)/14. Factor -f*i**4 + 0*i + 0 - 2/3*i**3 + 0*i**2.
-2*i**3*(i + 1)/3
Suppose 0 + 1/2*d**5 - 1/4*d**4 + 1/4*d - 3/4*d**3 + 1/4*d**2 = 0. Calculate d.
-1, -1/2, 0, 1
Let r(n) be the third derivative of n**6/600 + n**5/300 - 3*n**2. Suppose r(h) = 0. What is h?
-1, 0
Suppose 5*p - 2*p = 9. Factor -3*r**2 + 2*r**p - 4*r**3 + 4*r**2 - 3*r**2.
-2*r**2*(r + 1)
Suppose 7*r = 10*r - 12. Let -8/5*o**5 + 4/5*o**3 + 16/5*o**2 - 14/5*o**r + 4/5*o - 2/5 = 0. What is o?
-1, 1/4, 1
Let w(v) = -v**5 + 15*v**4 + 26*v**3 + 27*v**2 + 11*v. Let x(b) = -b**5 + 29*b**4 + 52*b**3 + 53*b**2 + 21*b. Let f(j) = 5*w(j) - 3*x(j). Factor f(t).
-2*t*(t + 1)**2*(t + 2)**2
Let v(t) = 6*t**4 - 6*t**2 - 6*t. Let w(d) = d**4 - d**3 - d**2 - d. Let q(a) = v(a) - 3*w(a). Suppose q(y) = 0. Calculate y.
-1, 0, 1
Let l(t) = -t**3 - 2*t**2 + 2*t - 1. Let b be l(-3). Factor 0 - 4*v**b + 2 - 2*v**3 - 2 - 2*v.
-2*v*(v + 1)**2
Suppose 5*y - 21 = 4. Determine q so that 5*q**5 + q**y + 2*q**2 - 6*q**3 + 2*q**5 + 0*q**5 = 0.
-1, 0, 1/2
Let m(n) = -n - 1. Suppose -2*j = -2 - 0. Let r(o) = -3*o**2 + o + 4. Let d(a) = j*r(a) + 4*m(a). Solve d(w) = 0 for w.
-1, 0
Let y(b) = b**3 - b**2. Let p(r) = r**3 + 11*r**2 + 14*r + 6. Let o(v) = p(v) + y(v). Solve o(k) = 0.
-3, -1
Let j(o) be the second derivative of -o**5/120 + o**4/24 - o**3/12 - o**2/2 - 2*o. Let a(d) be the first derivative of j(d). Find w, given that a(w) = 0.
1
Let g(q) be the third derivative of q**5/480 - q**4/48 + q**3/12 - 7*q**2. Factor g(s).
(s - 2)**2/8
Let f be (27/(-20))/(-3) + (-3)/15. Let v = -2 + 4. Factor f*c + 1/2 - 1/4*c**v.
-(c - 2)*(c + 1)/4
Let m be -2 + (-1)/4*34. Let k = m + 11. Factor 3*y - 9/2 - k*y**2.
-(y - 3)**2/2
Let x(o) = -10*o - 397. Let f be x(-40). Let 0*y - 1/2*y**f + 0 - y**2 = 0. Calculate y.
-2, 0
Let d = 87 + -87. Let m(l) be the second derivative of -1/60*l**6 + 1/20*l**5 + d - 1/12*l**3 + 2*l - 1/4*l**2 + 1/12*l**4 - 1/84*l**7. Factor m(k).
-(k - 1)**2*(k + 1)**3/2
Let -3*m**2 + 30*m**3 - 12*m**3 - 21*m**3 = 0. Calculate m.
-1, 0
Let p(o) be the second derivative of -1/2*o**2 - 5/6*o**4 - 1/2*o**5 + 0 - 5*o - 1/6*o**6 - 5/6*o**3 - 1/42*o**7. Factor p(z).
-(z + 1)**5
Let f(h) be the first derivative of -h**3 + 9*h**2/2 - 6*h + 16. Solve f(l) = 0 for l.
1, 2
Let l be ((-16)/4)/(-2) - 0. Suppose l*s = 4*s. Suppose 0*u + 0*u**2 + 0*u**3 + s + 1/3*u**5 - 1/3*u**4 = 0. Calculate u.
0, 1
Let w(n) be the first derivative of 4/15*n**5 - 1/3*n**3 + 1/3*n**4 - 2/3*n**2 - 1/3*n + 2. Factor w(v).
(v - 1)*(v + 1)*(2*v + 1)**2/3
Let c(r) = -r**3 - 5*r**2 - 6*r + 3. Let b be c(-3). Suppose -3 = -l - 0. Factor b*s**2 + l*s**2 - 1 - 5*s**2.
(s - 1)*(s + 1)
Let s = -29 - -34. Let o be 4 + -7 + 17/s. Factor 2/5*z**2 - 2/5 - 2/5*z**3 + o*z.
-2*(z - 1)**2*(z + 1)/5
Let l(x) be the second derivative of 0 - 1/10*x**2 - 1/4*x**4 - 6*x + 7/30*x**3 + 9/100*x**5. Factor l(o).
(o - 1)*(3*o - 1)**2/5
Factor 0*o + 2/7*o**5 - 8/7*o**2 + 0*o**3 + 6/7*o**4 + 0.
2*o**2*(o - 1)*(o + 2)**2/7
Let c(x) be the third derivative of -9*x**6/10 - 19*x**5/20 + 15*x**4/8 - x**3 + 17*x**2. Factor c(d).
-3*(d + 1)*(4*d - 1)*(9*d - 2)
Let i(c) = 8*c**2 + 2*c + 14. Let r(y) = y**2 - y + 4 - 1 - 2. Let z be 0 - (-1 - 0 - -2). Let l(m) = z*i(m) + 6*r(m). Let l(v) = 0. What is v?
-2
Suppose -3*g = k + g - 2, 0 = -2*g. Suppose -12 = -k*u - 2. Determine q so that -1/2*q - 1/2*q**u + 1/4*q**4 - 1/2*q**2 + 1/4 + q**3 = 0.
-1, 1/2, 1
Let a(w) be the first derivative of w**6/33 + 2*w**5/11 + 9*w**4/22 + 14*w**3/33 + 2*w**2/11 + 2. Solve a(k) = 0 for k.
-2, -1, 0
Suppose 7*m = 3*m. Let z be m + 1/(-1 - -3). Let -z - 1/4*i + 1/4*i**2 = 0. What is i?
-1, 2
Let s(q) be the first derivative of 3*q**6/10 - 3*q**5/20 - q**4/2 - 3*q + 10. Let y(z) be the first derivative of s(z). Factor y(v).
3*v**2*(v - 1)*(3*v + 2)
Let k(h) be the third derivative of -h**4/24 - h**2. Let w(l) = -l**2 - 2*l - 2. Let o(b) = -k(b) - w(b). What is g in o(g) = 0?
-2, -1
Let l(z) be the first derivative of 2*z**5/25 - 3*z**4/10 - 2*z**3/15 + 3*z**2/5 - 5. What is q in l(q) = 0?
-1, 0, 1, 3
Let r be -2 - 9 - (-3 - -3). Let i = 11 + r. Factor 0*v**2 - 6/5*v**5 + 0 + i*v + 4/5*v**4 + 2/5*v**3.
-2*v**3*(v - 1)*(3*v + 1)/5
Let s(i) = -i**5 - 5*i**4 - 3*i**3 + 5*i**2 + 4*i. Let f(t) = -t**4 - t**3 + t**2 + t. Let k(m) = 6*f(m) - 2*s(m). Factor k(r).
2*r*(r - 1)*(r + 1)**3
Suppose 0 = -7*o + 4*o + 9. Suppose 4*c**5 + o*c**5 + 3*c**2 + 2*c + 5*c - 2 - 2*c**4 - 14*c**3 + c**2 = 0. Calculate c.
-1, 2/7, 1
Let s = 1 + 1. Factor v + 3*v - 4*v + s*v**2.
2*v**2
Let q(v) = v**3. Let l(r) = 15*r**3 + 7*r**2 - 14*r + 3. Let o(s) = 2*l(s) - 22*q(s). Let o(z) = 0. Calculate z.
-3, 1/4, 1
Suppose -5*h + 14 + 1 = 0. Find j such that h*j + 9*j - j**2 + 5*j**2 = 0.
-3, 0
Factor -11*z**2 - 1/3*z**4 - 16/3 + 10/3*z**3 + 40/3*z.
-(z - 4)**2*(z - 1)**2/3
Let i(h) = -h**2 - 5*h + 5. Let q be i(-6). Let f = q + 2. Factor -u**5 + f - u - 1 + 2*u**3.
-u*(u - 1)**2*(u + 1)**2
Suppose -4*v = -5*o + 40, 3*v - v = -o - 6. Let k(g) be the second derivative of -g - 1/2*g**2 + 1/3*g**3 + 1/30*g**6 + 0 - 1/10*g**5 + 0*g**o. Factor k(r).
(r - 1)**3*(r + 1)
Let u(g) be the second derivative of 3/20*g**5 - 6*g - 5/4*g**4 - 6*g**2 + 0 + 4*g**3. Let u(w) = 0. What is w?
1, 2
Suppose 3*y - 3*l = 9, -1 = -3*y - l - 4. Let g(r) be the second derivative of -2*r - 1/48*r**4 + y*r**3 + 0*r**2 + 0. Factor g(h).
-h**2/4
Suppose -4*l + l = 3*l. Solve 1/3*d**3 + 0*d**2 + 0*d + l = 0.
0
Let u(l) = -l**4 - l**3 - l - 1. Let p(f) = -10*f**4 - 16*f**3 + 7*f**2 - 14*f - 11. Let w(t) = 2*p(t) - 22*u(t). Factor w(y).
2*y*(y - 3)*(y - 1)**2
Let u be -1 - -5 - (0 - (-4)/2). Let w(q) be the first derivative of -4/3*q**u - 2 + 2/9*q**3 + 8/3*q. Suppose w(i) = 0. Calculate i.
2
Let x(k) be the third derivative of k**10/529200 - k**8/35280 + k**6/2520 - k**5/30 + 3*k**2. Let h(d) be the third derivative of x(d). Solve h(b) = 0 for b.
-1, 1
What is l in -10*l**4 + 14*l**5 + 13*l**3 + 10*l**2 + 9*l - 31*l**3 - 2*l - 3*l = 0?
-1, -2/7, 0, 1
Let v be (30/(-9) + 3)*-9. Find j such that 3 - j**v + 6*j - 2*j**3 + j**3 - 3*j**4 - 4*j**3 = 0.
-1, 1
Let n(d) be the third derivative of -d**8/10080 + d**7/3780 - d**4/6 - 3*d**2. Let l(u) be the second derivative of n(u). Factor l(r).
-2*r**2*(r - 1)/3
Suppose -2*g**4 - 2*g + 5*g**2 - 3*g**2 - 3*g**3 + 5*g**3 = 0. What is g?
-1, 0, 1
Let v = 27 + -24. Let g(z) be the first derivative of 1/3*z**2 + 2 - 2/3*z + 2/9*z**v - 1/6*z**4. Factor g(d).
-2*(d - 1)**2*(d + 1)/3
Factor -2/3*o**2 - 2/9*o**4 + 0 - 10/9*o**3 + 0*o + 2/9*o**5.
2*o**2*(o - 3)*(o + 1)**2/9
Let s(w) be the first derivative of -24*w**5/25 - 7*w**4/5 + 12*w**3/5 - 4*w**2/5 + 14. Solve s(z) = 0 for z.
-2, 0, 1/3, 1/2
Let i(q) be the first derivative of q**4/4 + 3*q**3/2 + 3*q**2 + 7*q - 6. Let h(x) be the first derivative of i(x). Factor h(n).
3*(n + 1)*(n + 2)
Suppose 18 = 5*s + 48. Let v = s - -6. Let -1/4*q**2 - 1/4*q + v = 0. Calculate q.
-1, 0
Suppose -2*q - q + 57 = -3*a, 4*q - 22 = a. Let l be 3/(a/(-4))*3. Factor -2/5*i**3 + 4/5 - l*i + 8/5*i**2.
-2*(i - 2)*(i - 1)**2/5
Let a(k) be the second derivative of 0*k**2 - 1/35*k**5 + 0 + 0*k**3 - 1/42*k**4 + 2*k - 1/105*k**6. What is v in a(v) = 0?
-1, 0
Factor -5*d**3 + 2*d**3 - 27*d + 39*d**2 + 12 - 21*d**2.
-3*(d - 4)*(d - 1)**2
Let h(x) be the first derivative of -x**6/3 + 4*x**5/5 + 2*x**4 - 4*x**3/3 - 3*x**2 - 15. Determine t, given that h(t) = 0.
-1, 0, 1, 3
Let j(i) = 18*i**3 - 8*i**2 + 26*i - 26. Let x(w) = -2*w**3 + w**2 - 3*w + 3. Let l be 4/(-10)*1*130. Let z(q) = l*x(q) - 6*j(q). Factor z(u).
-4*u**2*(u + 1)
Suppose -30 = -5*b + 4*n, 0*b = -4*b + n + 13. Find w such that 2/3*w**b + 0 + 2/3*w = 0.
-1, 0
Suppose 14*c**3 - 11 + 0 + 23*c**4 + 34*c - 24*c**4 - 36*c**2 = 0. What is c?
1, 11
Let x(i) = -i**2 + 12*i + 28. Let v be x(14). Suppose 0*l**2 - 2/3*l**5 + 0*l + 0 + 2/3*l**4 + v*l**3 = 0. Calculate l.
0, 1
Let y(q) be the third derivative of -q**6/40 + q**5/20 + q**4/8 - q**3/2 - 3*q**2. Factor y(r).
-3*(r - 1)**2*(r + 1)
Solve 0*z**4 - 2/5*z**5 + 0 + 6/5*z**3 - 4/5*z**2 + 0*z = 0.
-2, 0, 1
Let q(b) be the first derivative of b**4 + 4*b**3/3 - 2*b**2 - 4*b + 10. Let q(p) = 0. Calculate p.
-1, 1
Let z(k) = 17*k**3 + k**2 - k - 4. Let j(x) = -8*x**3 + 2. Let 