y + 1)/3
Determine q, given that 4 - 11*q**4 + 37*q**3 + 39*q + 28*q**4 + 3*q**5 - 70*q + 39*q**2 + 51*q = 0.
-2, -1, -2/3
Let d(m) be the first derivative of -6*m - 7 + 1/2*m**3 + 3/16*m**4 - 3/2*m**2. Factor d(w).
3*(w - 2)*(w + 2)**2/4
Let p(f) be the second derivative of f**6/5 - 13*f**5/10 + 13*f**4/6 - f**3 - 4*f. Factor p(d).
2*d*(d - 3)*(d - 1)*(3*d - 1)
Solve 4/5*q + 8/5 - 4/5*q**3 + 4/5*q**4 - 12/5*q**2 = 0.
-1, 1, 2
Let b(f) be the third derivative of f**6/360 - f**5/20 + 3*f**4/8 - 3*f**3/2 - 10*f**2. Factor b(v).
(v - 3)**3/3
Let m(a) = a + 1. Let g be m(1). Let r(v) be the first derivative of -1/3*v**g - 1/3*v**3 - 3 - 1/12*v**4 + 0*v. Let r(q) = 0. What is q?
-2, -1, 0
Factor -1 + 1/5*y**2 + 4/5*y.
(y - 1)*(y + 5)/5
Let r = 5 + 2. Suppose -i**4 - 14*i**3 - 3*i**2 + 4*i**3 - i + r*i**3 = 0. What is i?
-1, 0
Let o(v) be the third derivative of -2197*v**6/660 - 169*v**5/55 - 13*v**4/11 - 8*v**3/33 + 3*v**2. Factor o(d).
-2*(13*d + 2)**3/11
Let v(b) be the second derivative of 21*b**5/100 - 43*b**4/60 + 2*b**2/5 + 2*b. Factor v(c).
(c - 2)*(3*c - 1)*(7*c + 2)/5
Let m(a) = -a**3 + a - 1. Let p(b) = -3*b**2 + 3*b - 3. Let r be 2/(-10) - 6/(-5). Let h(o) = r*p(o) - 3*m(o). Determine u so that h(u) = 0.
0, 1
Let g = -13 + 16. Let o be 4/12 + 1/3. Factor -2/9*z**4 + 0 + 2/3*z**g + 2/9*z - o*z**2.
-2*z*(z - 1)**3/9
Suppose 5*h - 16 = 2*p, p + 0*h - 18 = -4*h. Let d(v) be the first derivative of -14/9*v**3 - 4/3*v - 2 + 3*v**p. Factor d(c).
-2*(c - 1)*(7*c - 2)/3
Let u(y) be the first derivative of y**5/10 + 3*y**4/8 + y**3/2 + y**2/4 - 23. Factor u(b).
b*(b + 1)**3/2
Let d(h) = 2*h**3 + 4*h**2 - 5*h - 4. Let x(p) = 3*p**3 + 7*p**2 - 8*p - 7. Let n(z) = -5*d(z) + 3*x(z). Solve n(t) = 0.
-1, 1
Let j(f) be the second derivative of f**6/105 + 3*f**5/70 + f**4/42 - f**3/7 - 2*f**2/7 + 14*f. Find r, given that j(r) = 0.
-2, -1, 1
Let i(l) be the third derivative of l**6/300 + l**5/50 - 4*l**3/15 + 11*l**2. Factor i(f).
2*(f - 1)*(f + 2)**2/5
Let x(p) be the first derivative of -p**3/9 + p/3 - 1. Find q such that x(q) = 0.
-1, 1
Let o(v) = -v**2 - v + 1. Let x(a) = 2*a**2 - 6*a + 9. Let k(j) = o(j) + x(j). Determine f, given that k(f) = 0.
2, 5
Let k(d) = -d**2 + 15*d + 4. Let r be k(15). Let j(c) be the first derivative of 0*c**3 + 0*c + 0*c**r + 0*c**2 + 1/21*c**6 - 1 - 2/35*c**5. Factor j(u).
2*u**4*(u - 1)/7
Let u(z) be the first derivative of z**6/100 - z**5/30 + z**4/30 + 4*z**2 + 6. Let a(t) be the second derivative of u(t). Determine k, given that a(k) = 0.
0, 2/3, 1
Factor -5*s**3 + 157 - 225*s + 2*s**3 + 0*s**3 + 45*s**2 + 218.
-3*(s - 5)**3
Let h(a) = -a - 1. Let t(g) = -4*g**3 + 4*g**2 - 3*g - 3. Let p(f) = 3*h(f) - t(f). Find v such that p(v) = 0.
0, 1
Let g(v) = 2*v**3 + 17*v**2 - 3*v. Let a(k) = -5*k**3 - 50*k**2 + 8*k. Let b(u) = 3*a(u) + 8*g(u). Solve b(r) = 0 for r.
0, 14
Let y(n) be the first derivative of n**4 - 10*n**2 + 4*n**3 - 4/5*n**5 + 8*n + 7. Factor y(a).
-4*(a - 1)**3*(a + 2)
Let -y**4 + y**2 - 1/3*y**5 + 1/3*y**3 + 0*y + 0 = 0. Calculate y.
-3, -1, 0, 1
Let l be ((-6)/5)/((-2)/5). Solve -4*o**l - 4*o**2 - 5*o**5 - 5*o**3 + o - 13*o**4 + o + 5*o**2 = 0.
-1, 0, 2/5
Suppose -22*x = 40*x - 124. Factor -4/9*n**3 + 10/9*n**x - 4/9*n + 0.
-2*n*(n - 2)*(2*n - 1)/9
Factor 2/5*o**4 - 8/5*o + 16/5 + 2/5*o**3 - 12/5*o**2.
2*(o - 2)*(o - 1)*(o + 2)**2/5
Let k(j) be the second derivative of -j**6/120 + j**4/8 + j**3/3 + 2*j**2 - 6*j. Let i(h) be the first derivative of k(h). Determine p, given that i(p) = 0.
-1, 2
Let v be (-10)/15 - 64/(-6). Let q be ((-3)/v)/((-1)/5). What is t in -4*t**4 + q*t**5 + 0 + 0*t**2 - 1/2*t + 3*t**3 = 0?
-1/3, 0, 1
Let o(y) = -y**2 + 7*y. Let z(w) = w**2 - 8*w. Let t(v) = v**3 - 5*v**2 + v - 4. Let d be t(5). Let s be d*6*(-3 - -2). Let m(q) = s*z(q) - 7*o(q). Factor m(x).
x*(x - 1)
Let u(l) be the second derivative of l**6/120 + l**5/80 - l**4/48 - l**3/24 - 4*l. Solve u(t) = 0 for t.
-1, 0, 1
Factor 12*f**2 - 4*f + 18*f**3 - 22*f**3 - 5*f + f.
-4*f*(f - 2)*(f - 1)
Let x(s) be the third derivative of s**6/540 + s**5/18 + 25*s**4/36 + 125*s**3/27 + s**2. Let x(r) = 0. What is r?
-5
Let z be 6/(-9) + (-5)/(-5). Let f(k) be the first derivative of 2/9*k**3 - z*k**2 - 1 + 0*k. Find q such that f(q) = 0.
0, 1
Factor -48/13*r**3 - 2/13*r + 0 - 20/13*r**2.
-2*r*(4*r + 1)*(6*r + 1)/13
Suppose 0 = -488*x + 485*x + 9. Solve -8/11*v - 2/11*v**4 + 0 + 0*v**2 + 6/11*v**x = 0.
-1, 0, 2
Let i = 2158/7 - 308. Factor i*s**2 + 4/7 + 6/7*s.
2*(s + 1)*(s + 2)/7
Let v = 41 + -41. Let g = 64 + -190/3. Solve v + 0*n**2 - 2/3*n**4 + 0*n - g*n**3 = 0 for n.
-1, 0
Let b(d) = d**3 + 4*d**2 - 10*d + 12. Let l be b(-6). Let k(o) be the first derivative of 0*o**3 + 0*o - 1/7*o**4 - 2 + l*o**2 - 2/5*o**5. Factor k(n).
-2*n**3*(7*n + 2)/7
Let p(h) be the first derivative of -h**4/4 + h**3/3 - 2. Let v(g) = -8*g**3 + 9*g**2 - g. Let q(o) = -14*p(o) + 2*v(o). Find l such that q(l) = 0.
0, 1
Let o(p) be the first derivative of -2*p**5/35 + 5*p**4/14 - 2*p**3/3 + 3*p**2/7 - 6. Factor o(t).
-2*t*(t - 3)*(t - 1)**2/7
Let c(r) be the third derivative of r**5/60 + r**4/8 + r**3/3 + 25*r**2. Solve c(q) = 0 for q.
-2, -1
Let i(b) = 10 + 17*b**3 + 4*b**2 - 31*b - 15 - b**4 + b**2 - 20. Let m(t) = t**4 - 8*t**3 - 2*t**2 + 16*t + 13. Let k(q) = -4*i(q) - 7*m(q). Factor k(u).
-3*(u - 1)*(u + 1)**2*(u + 3)
Suppose 5*s + 36 = 4*r, 2*s = -4*r - 2*s. Suppose -2*i + r*y = 8, -5 = 5*i - 5*y - 0*y. Factor u**3 + 2*u**2 + 3*u**3 - i*u**3.
2*u**2*(u + 1)
Let b(x) be the second derivative of -x**4/4 + x**3 - 3*x**2/2 + 2*x. Factor b(j).
-3*(j - 1)**2
Let b(d) be the third derivative of 0*d**4 - 1/105*d**7 - 1/168*d**8 + 1/30*d**5 + 1/60*d**6 + 0 - d**2 + 0*d + 0*d**3. Factor b(u).
-2*u**2*(u - 1)*(u + 1)**2
Solve -1/5*u**2 - 1/5*u + 2/5 = 0 for u.
-2, 1
Let v = -3 - -7. Suppose 3*y - 2*y - 2*n = 10, 2*y = -2*n - v. Solve -4/3*b + 1/3*b**y + 4/3 = 0 for b.
2
Let y(s) be the third derivative of s**7/525 + s**6/450 + 14*s**2. Let y(i) = 0. Calculate i.
-2/3, 0
Let b(f) be the second derivative of -f**5/40 + f**4/48 + f**3/12 - f**2/8 + 22*f. Determine q, given that b(q) = 0.
-1, 1/2, 1
Let h(r) be the third derivative of 0*r + 1/60*r**5 - r**2 + 0 + 1/6*r**4 + 1/2*r**3. Determine g, given that h(g) = 0.
-3, -1
Let g be 1 + -1 - 0 - (37 - 40). Factor g*v**2 + 15/4*v + 3/4.
3*(v + 1)*(4*v + 1)/4
Let o(q) be the second derivative of -q**6/120 + q**5/16 - q**4/8 - q**3/6 + q**2 - 14*q. Factor o(i).
-(i - 2)**3*(i + 1)/4
Suppose 5*n - 4*c + 0*c = 3, 3*c = -n + 12. Solve -2*x + n*x**2 + 4*x + 3*x**2 + 1 - 5*x**2 = 0 for x.
-1
Let i(l) be the first derivative of l**5/20 + l**4/4 + l**2 - 1. Let g(n) be the second derivative of i(n). Determine y, given that g(y) = 0.
-2, 0
Let v = -118 - -118. Let a(f) be the third derivative of 0*f + 0*f**3 + 1/40*f**4 + 1/100*f**5 + v + 3*f**2. Factor a(w).
3*w*(w + 1)/5
Let w(v) be the third derivative of 2*v**7/315 + v**6/90 - v**5/45 - v**4/18 - 12*v**2. Factor w(h).
4*h*(h - 1)*(h + 1)**2/3
Suppose -43 = -2*i - o, -i + 11 = 2*o - 5*o. Let z be ((-2)/i)/((-4)/32). Factor z + 2/5*t**2 - 6/5*t.
2*(t - 2)*(t - 1)/5
Let n be (-14)/2*(-6)/7. Let u(j) be the second derivative of 3/10*j**5 + 0 - 2*j + 1/5*j**n + 0*j**3 + 0*j**2 + 1/6*j**4 + 1/21*j**7. Factor u(d).
2*d**2*(d + 1)**3
Factor 28 - 2*k - 30*k - 44*k**2 - 43*k**2 + 91*k**2.
4*(k - 7)*(k - 1)
Let a be -4 + 1 - (76/(-12) + 3). Let h(z) be the second derivative of a*z**4 + z**2 - 3/2*z**3 + 0 - 3*z. Suppose h(m) = 0. What is m?
1/4, 2
Suppose 6 = 4*t - 5*y, 0*t = -2*t - 3*y + 14. Factor -7*f**t + 11/2*f - 1 - 12*f**2 + 13*f**3 + 3/2*f**5.
(f - 1)**4*(3*f - 2)/2
Let j = -59 + 64. Let l(z) be the third derivative of 1/6*z**3 - z**2 + 1/60*z**j - 1/12*z**4 + 0*z + 0. Suppose l(y) = 0. What is y?
1
Let k(a) be the first derivative of a**3/3 + 2*a**2 + 4*a + 12. Suppose k(z) = 0. What is z?
-2
Let i(y) be the second derivative of -2*y**6/15 - y**5/5 + y**4 + 2*y**3/3 - 4*y**2 - 9*y. Factor i(z).
-4*(z - 1)**2*(z + 1)*(z + 2)
Let a = 6/19 + 110/133. Suppose 0 = -6*j + 11*j. What is d in -2/7*d**3 + 8/7*d**2 - a*d + j = 0?
0, 2
Factor -136 - 10*l**3 - 40*l**2 + 216 + 5*l**4 + 10*l**3.
5*(l - 2)**2*(l + 2)**2
Let u(j) be the second derivative of j**7/3780 + j**6/540 + j**5/180 +