s(i) = 0. Calculate i.
0, 1
Let m be (1/(-15))/(-25 - 7). Let s(x) be the third derivative of m*x**6 + 0*x + 0 - 1/840*x**7 - x**2 + 0*x**4 + 0*x**5 + 0*x**3. Factor s(w).
-w**3*(w - 1)/4
Let v(l) be the first derivative of -l**6/90 - l**5/60 + l**4/18 + 2*l - 3. Let s(b) be the first derivative of v(b). Factor s(u).
-u**2*(u - 1)*(u + 2)/3
Let g be (-14)/21 + 114/63. Factor -8/7*o - g*o**3 + 2/7*o**4 + 2/7 + 12/7*o**2.
2*(o - 1)**4/7
Let j(c) = 2*c**5 + 2*c**3 + 9*c**2 + 5*c - 3. Let b(x) = -3*x**5 + x**4 - 4*x**3 - 19*x**2 - 11*x + 5. Let z(y) = 6*b(y) + 10*j(y). Let z(m) = 0. Calculate m.
-2, -1, 0, 2
Solve 45*o**2 + 13*o - 133*o**3 + 14*o + 154*o**3 + 3*o**4 = 0 for o.
-3, -1, 0
Factor 12*x**4 + 2*x**2 + 10*x**3 + 3*x**4 - 17*x**2 - 11*x + x.
5*x*(x - 1)*(x + 1)*(3*x + 2)
Suppose 0*i + 6*i - 12 = 0. Let f(x) be the third derivative of 0 + 1/180*x**5 + 0*x + 1/24*x**4 - 2*x**i + 1/9*x**3. Factor f(l).
(l + 1)*(l + 2)/3
Let m(t) be the second derivative of 2*t**6/45 - t**5/5 + t**4/3 - 2*t**3/9 + 3*t. Let m(q) = 0. What is q?
0, 1
Let c be (-5)/(-10)*(0 - -6). Factor d**3 - 2*d + 4*d - c*d**3 - 2*d**2 + 2*d**4.
2*d*(d - 1)**2*(d + 1)
Let t = 352 + -4506/13. Find q such that 40/13*q**3 + 22/13*q**4 - t*q**5 + 0*q + 8/13*q**2 + 0 = 0.
-2/5, -2/7, 0, 1
Suppose -4*s = -16, 4*w - 4*s = -0*s - 8. Let y(z) be the first derivative of -z**w + 2 - 3/2*z**4 - 2*z + 10/3*z**3. Factor y(n).
-2*(n - 1)**2*(3*n + 1)
Let u(c) = 2*c**2 - 4*c + 4. Suppose l + 0 = -3. Suppose -2*f = -3*f + 4. Let j(p) = 2*p**2 - 3*p + 3. Let v(i) = f*j(i) + l*u(i). Factor v(h).
2*h**2
Let v be -1 + 3 + 8/4. Let l(c) = c**2 - 5*c + 6. Let o be l(v). Find p such that -8/3 - 2/3*p**4 - 26/3*p**o - 8*p - 4*p**3 = 0.
-2, -1
Let p(i) = -i**3 + 4*i**2 - 2*i - 1. Let s be p(2). Suppose -5 - 1 = -s*b. Suppose 2/3*f + 2*f**3 + 2/3*f**4 + 0 + 2*f**b = 0. What is f?
-1, 0
Let q(i) be the first derivative of 2*i**3/3 - 20*i**2/9 + 8*i/9 - 4. Factor q(x).
2*(x - 2)*(9*x - 2)/9
Suppose 5*t - 13 = -d + 11, 0 = 2*d + 5*t - 28. Suppose 4*m + 8 + 12 = 0, p - m - 7 = 0. Let -5*u**d + u**5 + u**2 + u**3 + 4*u**4 - p*u**3 = 0. What is u?
-1, 0, 1
Let d(j) be the first derivative of 2*j**3 + 3*j**2 + 2*j + 1 + 1/2*j**4. Factor d(w).
2*(w + 1)**3
Let o(z) = z**2 + z - 1. Let b(v) = 4*v**3 - 2*v**2 - 10*v + 2. Let m(n) = -b(n) - 6*o(n). Let m(p) = 0. What is p?
-1, 1
Let r = 23/44 + -1/44. Let v(b) be the first derivative of 4/3*b**3 - 4*b - b**2 + r*b**4 - 1. Solve v(h) = 0.
-2, -1, 1
Factor -4/3*i - 2/3*i**3 - 2*i**2 + 0.
-2*i*(i + 1)*(i + 2)/3
Factor -1/2*n**2 - 225/2 - 15*n.
-(n + 15)**2/2
Let b(f) be the second derivative of 0 - f + 0*f**3 + 1/18*f**4 + 0*f**2 + 1/30*f**5. Factor b(w).
2*w**2*(w + 1)/3
Suppose -5*x + 3 = -7. Solve 0 + 6*q**x + 4/3*q = 0.
-2/9, 0
Factor 0*p**3 + 4/5*p**4 + 0*p**2 + 2/5*p**5 + 0*p + 0.
2*p**4*(p + 2)/5
Let a(j) be the third derivative of 2/15*j**3 - 1/60*j**6 - 3/20*j**4 + 0 + 2*j**2 + 2/25*j**5 + 0*j. Solve a(v) = 0 for v.
2/5, 1
Let z(m) = 2*m - 6. Let i be z(4). Let g(v) be the second derivative of -i*v + 0*v**2 + 1/60*v**4 + 0 + 0*v**3. Suppose g(o) = 0. What is o?
0
Let p(n) be the third derivative of n**5/12 + 5*n**4/8 - 3*n**2. Factor p(a).
5*a*(a + 3)
Let w = 32/7 - 40/21. Find u such that 8/3 - w*u + 2/3*u**2 = 0.
2
Let d(b) be the first derivative of b**3/2 + 21*b**2/2 + 147*b/2 - 21. Suppose d(p) = 0. Calculate p.
-7
Let z(q) be the third derivative of -q**5/750 + q**4/100 - 2*q**3/75 - 16*q**2. Factor z(d).
-2*(d - 2)*(d - 1)/25
Let x(r) = -13*r**2 + 6*r. Let c(d) = 13*d**2 - 25*d**2 + 11*d**2. Let u(h) = -22*c(h) + 2*x(h). What is i in u(i) = 0?
0, 3
Let o(m) be the second derivative of m**6/180 + m**5/20 + m**4/8 + m**3/9 + 2*m - 22. Suppose o(q) = 0. Calculate q.
-4, -1, 0
Factor 16/3*a**2 + 20/3*a**4 + 32/3*a**3 + 4/3*a**5 + 0 + 0*a.
4*a**2*(a + 1)*(a + 2)**2/3
Suppose 4*d - v - 7 = 0, -v = -0 - 1. Suppose 3*i - 5 = 4. Solve d*s**2 - 3*s**4 + 5*s**4 + 4*s**i + 0*s**3 = 0.
-1, 0
Let j(d) = d. Let o(l) = -4*l + 13. Let s(t) = 3*j(t) + o(t). Let m be s(9). Factor -2*b**5 - 3*b + b + m*b**3 + 0*b.
-2*b*(b - 1)**2*(b + 1)**2
Let q(s) be the second derivative of s**6/15 - s**5/2 + 33*s. Find b such that q(b) = 0.
0, 5
Let m(l) be the third derivative of -l**5/30 - l**4/2 - 3*l**3 - 4*l**2. Factor m(s).
-2*(s + 3)**2
Let i = -65 + 587/9. Solve 2/9*f**3 + i*f**2 - 2/9*f - 2/9 = 0.
-1, 1
Determine n so that 6*n**4 - 2*n**3 + 2*n**2 + n**3 - 7*n**4 = 0.
-2, 0, 1
Suppose 0 = -2*b + 3*b - 3*b. Factor 0*f - 2/5*f**4 - 2/5*f**5 + b*f**3 + 0*f**2 + 0.
-2*f**4*(f + 1)/5
What is m in -2*m**2 + 1/2*m**5 + 0*m + 1/2*m**4 + 0 - 2*m**3 = 0?
-2, -1, 0, 2
Let q(i) be the second derivative of 0*i**2 - 4*i + 0*i**3 - 1/60*i**5 + 1/90*i**6 + 0*i**4 + 0. Factor q(p).
p**3*(p - 1)/3
Factor 4/5*a - 2/5*a**4 + 0 - 4/5*a**3 + 2/5*a**2.
-2*a*(a - 1)*(a + 1)*(a + 2)/5
Let r be -1 - -4 - 25/10. Let q(l) = l**3 + 16*l**2 - 17*l + 2. Let p be q(-17). Find a such that 0*a - r*a**p + 0 + 1/4*a**3 = 0.
0, 2
Let g = 7/2 - 43/12. Let c = 1/3 + g. Factor -1/2*w + 0 + c*w**2.
w*(w - 2)/4
Let i(x) be the first derivative of x**3/3 - 9*x**2/2 + 3*x + 3. Let r be i(9). Suppose -2*o**2 - 3*o**2 + 3*o**2 + r*o**2 + o = 0. Calculate o.
-1, 0
Let w(r) be the third derivative of r**7/1260 - r**6/720 - r**5/120 + 5*r**4/144 - r**3/18 + 11*r**2. Factor w(q).
(q - 1)**3*(q + 2)/6
Let f(l) be the first derivative of -2 + 1/12*l**3 + 1/2*l**2 + l. Solve f(h) = 0.
-2
Let m(t) = -t + 8. Let o be m(6). Let w be (-7)/(63/12) + o. Factor 0 - 7/3*n**2 - w*n.
-n*(7*n + 2)/3
Suppose 8 = 2*i + 4. Suppose 1 = -3*m - 5, 2*u + 4*m = -8. What is c in 0 + 2/3*c**5 + 2/3*c**2 + 2*c**4 + i*c**3 + u*c = 0?
-1, 0
Let s(h) be the third derivative of 5*h**8/336 - h**7/21 + h**5/6 - 5*h**4/24 + 9*h**2. Find a, given that s(a) = 0.
-1, 0, 1
Let u(r) be the third derivative of r**6/160 - 3*r**4/32 - r**3/4 + r**2. Factor u(a).
3*(a - 2)*(a + 1)**2/4
Factor 2/5*h**3 + 0 + 6/5*h**2 - 8/5*h.
2*h*(h - 1)*(h + 4)/5
Let y(h) be the first derivative of h**7/2940 + h**6/315 + h**5/84 + h**4/42 - 4*h**3/3 + 3. Let a(q) be the third derivative of y(q). Factor a(u).
2*(u + 1)**2*(u + 2)/7
Let n be ((-3)/(-10))/((-4)/5 - -2). Factor -n*s**2 + 0 - 1/4*s.
-s*(s + 1)/4
Let c(l) be the third derivative of 0*l - 2*l**2 - 1/336*l**8 + 0 + 1/30*l**5 + 1/24*l**4 - 1/105*l**7 + 0*l**6 + 0*l**3. Factor c(y).
-y*(y - 1)*(y + 1)**3
Let z(j) be the first derivative of -j**5/2 + 25*j**4/8 - 5*j**3/6 - 105*j**2/4 + 45*j - 8. Find t such that z(t) = 0.
-2, 1, 3
Let d(h) = h**2 - 6*h + 4. Let b be d(6). Determine s so that 15*s**b - 2*s**2 + 2*s**3 - 16*s**4 + s**2 = 0.
0, 1
Suppose -2*q - u = 5, 0 = q - u + 4. Let p be (q/9)/((-3)/18). Find f, given that -1 - 1/2*f**p + 3/2*f = 0.
1, 2
Let n(s) = s**4 - s**3 - s**2 - 1. Let b(y) = 15*y**4 - 24*y**3 - 9*y**2 + 24*y - 6. Let u(t) = -b(t) + 18*n(t). Factor u(x).
3*(x - 2)*(x + 1)**2*(x + 2)
Let m = 0 - -3. Factor -8*d**5 + 2*d**4 + 0*d**3 + 4*d**5 + 2*d**m.
-2*d**3*(d - 1)*(2*d + 1)
Let m(s) be the third derivative of -s**5/60 + s**4/12 - s**3/6 - 3*s**2. Let v(k) = -5*k**2 + 10*k - 5. Let g(z) = 11*m(z) - 2*v(z). Factor g(a).
-(a - 1)**2
Let m(j) be the third derivative of -j**6/120 + j**5/20 - j**4/8 + j**3/2 - 5*j**2. Let f(c) be the first derivative of m(c). Factor f(d).
-3*(d - 1)**2
Factor 3*j**3 - 5*j**3 - 4*j**5 + 2*j**5 - 4*j**4.
-2*j**3*(j + 1)**2
Let 4/3 - 2*p + 2/3*p**2 = 0. Calculate p.
1, 2
Let m be 14/3*6/8 + -3. Solve -1/2*q + 1 - m*q**2 = 0.
-2, 1
Let g = -5 + 7. Let v(o) = o**3 - o**2 + o + 2. Let h be v(0). Factor -3*q**h + 2*q**2 + 4*q**2 - q - 4*q**g.
-q*(q + 1)
Solve 15*c - 12*c**4 - 9*c**3 + 48*c**3 - 45*c**2 + 6*c - 3 = 0.
1/4, 1
What is k in -2/5*k + 4/5 - 2/5*k**2 = 0?
-2, 1
Let f be 1203/(-1572) + 12/16. Let h = f + 401/524. Factor 3/2 - 3/4*b - h*b**2.
-3*(b - 1)*(b + 2)/4
Suppose 0 = 3*s - 5*k - 20, 3*k = 3*s - 0*s - 12. Factor -2/5*t**5 - 2/5*t**4 + 0*t**2 + 0*t + s + 0*t**3.
-2*t**4*(t + 1)/5
Let l(d) be the third derivative of d**5/90 - d**4/9 + 4*d**3/9 - 2*d**2 - 17. Factor l(w).
2*(w - 2)**2/3
Let r(k) = 2*k**2 - 3*k - 5. Let c(u) = u**2 - 3*u - 4. Suppose -2*b + 6 - 2 = 0. Let g be 1/b + (-6)/(-4). Let i(h) = g*r(h) - 3*c(h). Solve i(n) = 0.
-2, -1
Let h = 8 - 4. Let