- 4*b**3 + 2*b**c - 4*b**2 - b**4.
-b**2*(b + 1)*(b + 2)
Let y = -2519/3 - -840. Factor 0 + y*s**2 - 1/3*s.
s*(s - 1)/3
Suppose -g = -3*a + 4*a + 2, 3*g - a + 2 = 0. Let d(m) = 2*m**2 - m. Let v be d(g). Factor 2*l + 2*l**2 + 5*l**2 + 2*l**3 - v*l**2.
2*l*(l + 1)**2
Let b = -28 - -31. Let n(g) be the first derivative of 1/3*g**2 + 2/9*g**3 + b - 2/3*g - 1/6*g**4. Solve n(c) = 0 for c.
-1, 1
Let z be (-10)/6*((-230)/25 + 9). Let 1/3*v - 1/3*v**3 + 1/3*v**2 + 0 - z*v**4 = 0. Calculate v.
-1, 0, 1
Factor 4/7*q**5 + 4/7*q**4 + 0*q**2 - 8/7*q**3 + 0*q + 0.
4*q**3*(q - 1)*(q + 2)/7
Let c(m) be the first derivative of 74/9*m**3 - 4*m**2 - 8/3*m + 6 + 49/9*m**6 + 143/6*m**4 + 98/5*m**5. What is r in c(r) = 0?
-1, -2/7, 2/7
Let z(x) be the second derivative of -x**4/15 + 2*x**2/5 + 7*x. Let z(f) = 0. What is f?
-1, 1
Let u(g) be the third derivative of 0*g - 5*g**2 + 1/180*g**6 + 0 + 0*g**3 + 0*g**5 - 1/36*g**4. Factor u(k).
2*k*(k - 1)*(k + 1)/3
Let t(a) be the second derivative of -25*a**7/21 - a**6/6 + 3*a**5 + 5*a**4/12 - 5*a**3/3 - 6*a. Find b such that t(b) = 0.
-1, -1/2, 0, 2/5, 1
Suppose 22 = 4*m - 5*c, -17 = -5*m - 2*c + 3*c. Let b(v) = v**2 - v - 4. Let s be b(m). Solve 2*f**3 + f**2 + 3*f**2 - 2*f**s - 2*f - 2 = 0 for f.
-1, 1
Let t(i) be the third derivative of i**6/480 + i**5/60 + i**4/24 - 18*i**2. Factor t(p).
p*(p + 2)**2/4
Let q be 8/72 - (-1)/(-9). Let b(l) be the third derivative of 1/48*l**4 + 1/80*l**5 + 1/480*l**6 + 3*l**2 + q*l + 0*l**3 + 0. Suppose b(u) = 0. What is u?
-2, -1, 0
Let w(d) be the second derivative of -d**2 + 0*d**3 - 1/210*d**7 + 0 + 0*d**6 - d + 1/60*d**5 + 0*d**4. Let b(h) be the first derivative of w(h). Factor b(x).
-x**2*(x - 1)*(x + 1)
Let c be (-10)/44 - (-2)/4. Let q = 26/55 - c. Let 1/5*z + 0 - q*z**2 = 0. What is z?
0, 1
Let x(s) be the first derivative of 0*s**2 + 3 + 0*s + 0*s**3 + 1/18*s**4. Solve x(l) = 0.
0
Suppose -1 + 2 + 3 + 7*f + f + 4*f**2 = 0. Calculate f.
-1
Factor 8/7*j + 8/21 + 26/21*j**2 + 2/21*j**4 + 4/7*j**3.
2*(j + 1)**2*(j + 2)**2/21
Factor 228 + 9*i - 228 - 3*i**2.
-3*i*(i - 3)
Let q(s) = -s**2 + 1. Let x(u) = -u**3 + 3*u**2 - 2. Let a(o) = 2*q(o) + x(o). Solve a(c) = 0 for c.
0, 1
Let h(f) be the first derivative of 5*f**3/9 + f**2/2 - 2*f/3 + 2. Factor h(a).
(a + 1)*(5*a - 2)/3
Let g(r) = 5*r**2 - 2. Let k(m) = m**2 + 4*m - 2. Let z be k(-4). Let s(n) = 4*n**2 - 2. Let f(i) = z*g(i) + 3*s(i). Factor f(o).
2*(o - 1)*(o + 1)
Let r(l) be the second derivative of l**5/40 + l**4/12 + 15*l. Factor r(o).
o**2*(o + 2)/2
Let z(n) = -n**3 - 6*n**2 - 6*n - 2. Let v be z(-5). Factor -c**5 - 2*c**v + 1 + 4*c**3 - c + 0*c**2 - 2*c**2 + c**4.
-(c - 1)**3*(c + 1)**2
Let i(n) be the first derivative of -n**5/20 - n**4/6 - n**3/6 + n + 2. Let b(z) be the first derivative of i(z). Factor b(y).
-y*(y + 1)**2
Let c be ((-6)/3)/(-2)*(2 - -2). Factor -76/11*g**2 - 16/11 - 16/11*g**c + 50/11*g**3 + 2/11*g**5 + 56/11*g.
2*(g - 2)**3*(g - 1)**2/11
Suppose 0 = 4*k - 18 - 34. Factor 3 + k*p**2 - 14*p**2 + p**3 - 3.
p**2*(p - 1)
Let k(q) be the third derivative of q**8/3360 - q**7/1680 - q**6/720 + q**5/240 - q**3/6 + q**2. Let v(m) be the first derivative of k(m). Factor v(c).
c*(c - 1)**2*(c + 1)/2
Let q(k) = -k**3 - 10*k**2 - 2*k - 15. Let f be q(-10). Let -3*l**3 - 3*l + l**3 + 4*l - 7*l**5 + 8*l**f = 0. Calculate l.
-1, 0, 1
Let p(y) be the third derivative of y**7/4620 - y**5/660 + y**3/3 - y**2. Let s(r) be the first derivative of p(r). Solve s(x) = 0 for x.
-1, 0, 1
Let t(c) be the second derivative of c**6/30 - 3*c**5/20 + c**4/4 - c**3/6 + 27*c. Suppose t(a) = 0. Calculate a.
0, 1
Suppose 2*c + 5*n - 47 = 0, 0 = 4*c + 5*n - 17 - 52. Suppose 0 = m - 5*q + c, -m = -2*m - 2*q + 10. Factor -3*r - r**m + 3*r**2 - 2 + 2*r + 3*r**3 - 2*r**3.
-(r - 2)*(r - 1)*(r + 1)**2
Let d(s) be the first derivative of 0*s - 9/8*s**4 + s**3 + 0*s**2 + 4 + 3/10*s**5. Factor d(t).
3*t**2*(t - 2)*(t - 1)/2
Let m(n) be the second derivative of -n**4/72 + n**2/12 + 6*n. Factor m(h).
-(h - 1)*(h + 1)/6
Let j = 8/9 + -2/3. Determine w so that 0 - 2/9*w**3 - j*w**2 + 0*w = 0.
-1, 0
Suppose -14 = -s - 4*h, s - h + 22 = 4*h. Let a = s + 4. Determine u so that -2*u + 1 + 0 - 2 - u**2 + 0*u**a = 0.
-1
Let n(i) = i**4 - i**3 - i**2 - i + 1. Let x(c) = 1 - 6*c**3 - 2*c**2 - 5 + 8 + c**4. Let q(p) = 3*n(p) - x(p). Factor q(h).
(h - 1)*(h + 1)**2*(2*h + 1)
Let k(m) = -m**2 - m. Let s(n) = 6*n**2 + 2. Let u(l) = 4*k(l) + s(l). Let h(i) = 4*i**2 - 8*i + 4. Let r(o) = -2*h(o) + 5*u(o). Factor r(d).
2*(d - 1)**2
Let m(d) be the first derivative of 1 - 2/5*d**5 - 2/5*d**2 + 4/5*d**4 - 2/15*d**3 + 0*d. Find s, given that m(s) = 0.
-2/5, 0, 1
Let y be 2/(-12) + (-66)/(-360). Let l(o) be the third derivative of -2*o**2 + y*o**5 + 0*o + 1/18*o**3 - 1/360*o**6 - 1/24*o**4 + 0. Let l(g) = 0. Calculate g.
1
Let g be 2*3/(1 + 2). Suppose 0 = -g*t - 2*t. Find j, given that 2/7*j**5 + 0 + 0*j**2 - 2/7*j**3 + t*j**4 + 0*j = 0.
-1, 0, 1
Let j = -1 + 3. Factor 4*t**3 - 3*t**j + t**2 - 2*t**4 + 0*t**3.
-2*t**2*(t - 1)**2
Factor -6*w - 48*w**2 + 243/2*w**4 + 0 - 135/2*w**3.
3*w*(w - 1)*(9*w + 2)**2/2
Let o(s) be the third derivative of 1/36*s**4 - 1/90*s**5 - 5*s**2 + 0*s - 1/180*s**6 + 0*s**3 + 0 + 1/315*s**7. Suppose o(u) = 0. What is u?
-1, 0, 1
Let b(u) = 2*u**2 + 10*u. Let h(o) be the third derivative of o**5/60 + o**4/8 - 5*o**2. Let m(j) = -2*b(j) + 7*h(j). Let m(v) = 0. What is v?
-1/3, 0
Factor 3*s**2 - 6*s + 9*s - 10*s**3 - 9*s**2 + s.
-2*s*(s + 1)*(5*s - 2)
Suppose 0 = 3*w - 0*w - 6. Let t(y) be the first derivative of 0*y - 2/3*y**3 + 1/3*y**6 + 0*y**w + 3/2*y**4 - 6/5*y**5 + 2. Find g such that t(g) = 0.
0, 1
Let f = 107/3 - 746/21. Factor -1/7*j**4 - f*j**5 + 0 + 0*j**2 + 0*j + 0*j**3.
-j**4*(j + 1)/7
Let w(x) be the second derivative of -x**4/30 + 2*x**3/15 - x**2/5 - 6*x. Factor w(p).
-2*(p - 1)**2/5
Suppose 53*b = 49*b + 8. Suppose 3/4*c**3 - 3/4*c - 3/4*c**b + 3/4*c**4 + 0 = 0. What is c?
-1, 0, 1
Let k(l) = -l**2 + 31*l - 11. Let g(a) = 6*a - 2. Let z be 6/(-2 + -1) + 0. Let c(y) = z*k(y) + 11*g(y). Factor c(f).
2*f*(f + 2)
Let d(c) be the third derivative of c**7/630 - c**6/120 + c**5/60 - c**4/72 + 6*c**2. Determine a so that d(a) = 0.
0, 1
Let r(k) = 6*k**2 + 6*k - 3. Let d(x) = -x**3 - 19*x**2 - 18*x + 8. Let b(c) = 3*d(c) + 8*r(c). Determine g, given that b(g) = 0.
-2, -1, 0
Solve -2*u - 4 - 1/4*u**2 = 0.
-4
Suppose 4*g - 44 = -7*g. Solve 4/11 - 6/11*j**5 - 6/11*j + 4/11*j**g - 8/11*j**2 + 12/11*j**3 = 0.
-1, 2/3, 1
Let u(b) be the second derivative of -b**5/10 - 5*b**4/6 - 8*b**3/3 - 4*b**2 + 10*b. Solve u(y) = 0 for y.
-2, -1
Let o = 32 + -29. Let i(r) be the first derivative of 0*r**o - 2/5*r - 1/5*r**4 + 2/25*r**5 + 1 + 2/5*r**2. Suppose i(g) = 0. Calculate g.
-1, 1
Let m(c) be the second derivative of -c**5/80 - c**4/16 + c**2/2 + 5*c. Factor m(t).
-(t - 1)*(t + 2)**2/4
Let c be -3 + -2 - 155/(-30). Let c*r**5 - 7/6*r - 1/3*r**4 - 1/3*r**3 + 4/3*r**2 + 1/3 = 0. What is r?
-2, 1
Determine z, given that -4*z + 5*z + 7 + 11*z**3 - 5 - 7*z**2 - 3*z**4 - 4*z**2 = 0.
-1/3, 1, 2
Let o(k) be the second derivative of k**4/24 - 5*k**3/48 + k**2/16 - 8*k. Suppose o(r) = 0. Calculate r.
1/4, 1
Let v be (-9 - (5 + -1 + -10))/(-2). Suppose -3/4*o**2 + v - 3/4*o = 0. Calculate o.
-2, 1
Let v(k) be the third derivative of 0*k**4 + 1/10*k**6 + 1/5*k**5 + 1/70*k**7 - 3*k**2 + 0*k + 0*k**3 + 0. Let v(x) = 0. Calculate x.
-2, 0
Factor -4*x**5 - 222 + 222 - 4*x**4.
-4*x**4*(x + 1)
Let b(n) = 14*n**5 - 20*n**4 + 20*n**2 + 2*n - 8. Let w(j) = 9*j**5 - 13*j**4 + 13*j**2 + j - 5. Let y(t) = -5*b(t) + 8*w(t). Factor y(i).
2*i*(i - 1)**3*(i + 1)
Let y(x) be the second derivative of -7*x + 0 + 0*x**3 - 4/45*x**6 + 1/10*x**5 + 1/18*x**4 + 0*x**2. Factor y(c).
-2*c**2*(c - 1)*(4*c + 1)/3
Let j(l) = -2*l + 1 + 10*l - 4*l - 4*l**3 + 2*l**2. Let h(m) = -9*m**3 + 5*m**2 + 8*m + 1. Let t(y) = 3*h(y) - 7*j(y). Factor t(v).
(v - 2)*(v + 1)*(v + 2)
Let r(d) be the third derivative of -d**7/105 + d**6/15 + d**5/10 - 3*d**4/2 + 11*d**2. Solve r(f) = 0 for f.
-2, 0, 3
Let m(y) be the first derivative of y**6/180 - 2*y**5/45 + y**4/9 + y**2 - 2. Let c(q) be the second derivative of m(q). Determine f, given that c(f) = 0.
0, 2
Suppose 0 = 15*h - 21*h + 18. Suppose 8/