 = 0 for w.
0, 1
Let k(h) = h**4 + h**3 + h**2. Let t(d) = d**4 - d**3 + 3*d**2 + 4*d + 2. Let a(f) = 3*k(f) - t(f). Factor a(y).
2*(y - 1)*(y + 1)**3
Let v(g) = -4*g**3 + 2*g**2 - 6*g + 6. Let n(z) = z**2 - z + 1. Let h(k) = -6*n(k) + v(k). Factor h(c).
-4*c**2*(c + 1)
Let -5*p - 4*p**4 + p**3 + 7*p**3 + 4*p**2 + p - 4*p = 0. What is p?
-1, 0, 1, 2
Suppose -3*s - 2*s - 4*q - 20 = 0, 5*q = -3*s - 25. Let p(j) be the third derivative of -1/20*j**5 + s*j**3 - 4*j**2 + 0 + 1/8*j**4 + 0*j. Factor p(r).
-3*r*(r - 1)
Let v(g) be the third derivative of g**7/42 - g**6/24 - g**5/3 + 5*g**4/6 + 7*g**2. Let v(s) = 0. What is s?
-2, 0, 1, 2
Let y(c) be the third derivative of 0*c + 1/80*c**6 + 1/140*c**7 + 1/672*c**8 + 2*c**2 + 0*c**3 + 1/120*c**5 + 0*c**4 + 0. Let y(u) = 0. What is u?
-1, 0
Let d(g) be the third derivative of g**8/3360 - g**7/630 + g**6/360 + g**4/24 - g**2. Let u(o) be the second derivative of d(o). What is a in u(a) = 0?
0, 1
Suppose -4*c + 4 = 0, -2*b - c + 3 = 2*c. Let s(i) be the first derivative of 0*i**5 - 1 + 0*i**3 + b*i + 1/10*i**4 - 1/10*i**2 - 1/30*i**6. Factor s(y).
-y*(y - 1)**2*(y + 1)**2/5
Factor -1/5 - 1/5*s**2 - 2/5*s.
-(s + 1)**2/5
Let u be 0 + 5 - 72/16. Factor 2*z + u*z**2 + 2.
(z + 2)**2/2
Let j(g) be the second derivative of 1/25*g**5 - 1/15*g**3 - 1/105*g**7 + 0*g**2 + 0 + 0*g**4 - 5*g + 0*g**6. Suppose j(f) = 0. Calculate f.
-1, 0, 1
Let a = 8/79 + -209/2844. Let f(x) be the second derivative of 0 + 0*x**2 - a*x**4 + x + 1/18*x**3. Factor f(m).
-m*(m - 1)/3
Let i(g) = g**2 - 5*g + 4. Let n be 47/7 + 2/7. Let q(h) = 3*h**2 - 11*h + 8. Let j(v) = n*i(v) - 3*q(v). Factor j(m).
-2*(m - 1)*(m + 2)
Let z(n) be the second derivative of -n**7/147 + n**6/105 - 12*n. Let z(q) = 0. Calculate q.
0, 1
Let f be (3/(-5))/(16/(-300)). Suppose 2 = -3*i + 4*i. Determine y so that -93/4*y**i - f*y - 3/2 - 9*y**3 = 0.
-2, -1/3, -1/4
Factor 4/13*f - 2/13*f**3 + 2/13*f**2 + 0.
-2*f*(f - 2)*(f + 1)/13
Let n be (-5)/(-3 - 140/24). Let m = n + 1122/265. What is w in 112/5*w**3 - 138/5*w**4 - 8/5 + 54/5*w**2 + 36/5*w**5 - m*w = 0?
-1/3, 1/2, 2
Let d(i) be the first derivative of -i**7/525 - i**6/150 - i**5/150 - 3*i**2/2 + 1. Let t(m) be the second derivative of d(m). Factor t(n).
-2*n**2*(n + 1)**2/5
Let x(q) be the third derivative of 0 + 0*q**4 + 1/30*q**5 + 0*q**3 + 0*q - 2*q**2. Factor x(r).
2*r**2
Let l be (-1)/2*10*-1. Let n(z) be the third derivative of -1/60*z**l + 0*z**3 + 0*z**4 + 0*z + 1/120*z**6 + 0 - 2*z**2. Factor n(w).
w**2*(w - 1)
Factor 0 - k**4 + 1/2*k + k**2 - 1/2*k**5 + 0*k**3.
-k*(k - 1)*(k + 1)**3/2
Let c(i) be the first derivative of -i**3/21 - 2*i**2/7 - 4*i/7 - 10. Factor c(r).
-(r + 2)**2/7
Suppose 4 = -3*o - 2*h + 3*h, -5*h + 20 = 5*o. Factor o + 0*v - 2/7*v**4 - 4/7*v**2 + 6/7*v**3.
-2*v**2*(v - 2)*(v - 1)/7
Let d be 5/5 - 4/(-3 + 1). Let j(g) be the third derivative of 0 + 1/3*g**d + 1/6*g**4 + 4*g**2 + 1/30*g**5 + 0*g. Factor j(a).
2*(a + 1)**2
Let l(t) be the second derivative of -t**8/840 - t**7/525 + t**6/300 + t**5/150 - t**2 + 3*t. Let a(s) be the first derivative of l(s). Factor a(i).
-2*i**2*(i - 1)*(i + 1)**2/5
Let t(k) be the first derivative of 2*k**3/3 + 8*k**2 + 32*k + 19. Factor t(l).
2*(l + 4)**2
Let k(c) be the third derivative of -c**10/15120 - c**9/3780 + c**7/630 + c**6/360 + c**4/12 - 2*c**2. Let f(l) be the second derivative of k(l). Factor f(i).
-2*i*(i - 1)*(i + 1)**3
Let n be 3 - 1/(-3)*-3. Suppose 0 = 16*y - 14*y - 6. Find w, given that -2*w**2 + 0*w**n - w + 1 - w + 2*w**y + 1 = 0.
-1, 1
Factor 6 - 9 - 13 + 4*x**2 + 0 + 2*x**3 - 8*x.
2*(x - 2)*(x + 2)**2
Suppose 4 + 14 = l. Suppose -5*p + 3*w + l = 0, p - 2 = -5*w - 4. Let -7*b**p + 4*b**3 + 4*b**2 - 2*b**2 = 0. Calculate b.
0, 2/3
Let c(s) = -1. Let k(r) = -35*r**5 - 185*r**4 - 365*r**3 - 335*r**2 - 140*r - 15. Let d(h) = 5*c(h) + k(h). Let d(b) = 0. What is b?
-2, -1, -2/7
Let q be 2/(-3) - 224/(-120). Determine t so that 6/5*t**2 + q*t + 2/5 + 2/5*t**3 = 0.
-1
Let t(m) be the first derivative of 4*m**5/5 + 6*m**4 - 64*m**2 + 46. Find y such that t(y) = 0.
-4, 0, 2
Let j(a) = -7*a**2 + 6*a + 1. Let m(n) = -6*n**2 + 6*n. Let z(t) = 4*j(t) - 5*m(t). Suppose z(p) = 0. What is p?
1, 2
Suppose 3*z = 4*z. Let m(b) be the third derivative of 0*b**4 + 1/270*b**5 + 0 + 2*b**2 + 0*b**3 + z*b. Solve m(p) = 0.
0
Let u(f) = f**4 - f**2 + f - 1. Let r(n) = n**3 + 3 + 0*n**4 - 3*n - 2*n**4 + 5*n**2 - n**3 - 3*n**3. Let c(j) = -4*r(j) - 12*u(j). Factor c(y).
-4*y**2*(y - 2)*(y - 1)
Let p be (-57)/76*15*4. Let x be ((-4)/p)/((-3)/(-30)). Factor -4/3*t**4 + x*t + 2/9*t**5 - 8/3*t**2 + 0 + 26/9*t**3.
2*t*(t - 2)**2*(t - 1)**2/9
Let n(k) be the second derivative of 5*k - 3/20*k**5 - 3/2*k**3 - 3/2*k**2 - 3/4*k**4 + 0. Factor n(b).
-3*(b + 1)**3
Suppose 4*m - 8 = -0. Suppose -m*k**2 - 30 + 30 = 0. Calculate k.
0
Let m(z) be the second derivative of -z**4/6 - 4*z**3/3 - 4*z**2 - 5*z. Suppose m(c) = 0. Calculate c.
-2
Let b = -1 - -6. Let l = b + -3. Factor 0 - 1/4*k**3 + 1/4*k - 1/4*k**l + 1/4*k**4.
k*(k - 1)**2*(k + 1)/4
Suppose 17*n - 13*n = 8. Suppose 0 = -q - 5*f + 9, 5*q + n*f - 18 = q. Find u, given that -1/4 + 0*u**3 - 1/4*u**q + 1/2*u**2 + 0*u = 0.
-1, 1
Let p(i) be the third derivative of i**10/75600 - i**9/7560 + i**8/2016 - i**7/1260 - i**5/60 - 4*i**2. Let n(a) be the third derivative of p(a). Factor n(u).
2*u*(u - 2)*(u - 1)**2
Let h = -1109/11 + 101. Find g such that -2/11*g**5 + 6/11*g**4 + h*g**2 - 6/11*g**3 + 0 + 0*g = 0.
0, 1
Determine o so that -479 + 16*o**4 + 4*o**5 + 12*o**3 - 12*o**2 - 16*o + 479 - 4*o**2 = 0.
-2, -1, 0, 1
Let d(j) be the third derivative of 1/33*j**3 + 1/132*j**4 + 0 - 1/660*j**6 + 2*j**2 + 0*j - 1/330*j**5. Factor d(r).
-2*(r - 1)*(r + 1)**2/11
Let f = 5/18 - 1/18. Let 0*k + f*k**3 + 0 - 2/9*k**2 = 0. What is k?
0, 1
Factor 24/7*i - 2/7*i**2 - 72/7.
-2*(i - 6)**2/7
Let w(y) = y**2 + y - 9. Let g(a) = a**2 + a - 8. Let x(q) = q**3 - 7*q**2 + 8*q - 6. Let f be x(6). Let m(l) = f*w(l) - 7*g(l). Solve m(s) = 0 for s.
-2, 1
Let d = 16645/12 - 1386. Let q(u) be the first derivative of -d*u**4 - 1/3*u**5 + 2/3*u + 1/6*u**2 - u**3 - 1. Suppose q(v) = 0. What is v?
-1, 2/5
Suppose 0 = 4*y - 8, 2*y + 0 = 2*z - 2. Factor 0*j - z*j + j**2 + 2*j.
j*(j - 1)
Let k(n) be the first derivative of 0*n - 1/12*n**3 + 1/20*n**5 + 0*n**2 - 1/24*n**6 - 1 + 1/16*n**4. Determine w, given that k(w) = 0.
-1, 0, 1
Let k(t) be the second derivative of 0 - 1/6*t**4 - t**3 + 5*t - 2*t**2. Determine d so that k(d) = 0.
-2, -1
Let p(v) be the third derivative of 1/180*v**5 + 0*v + 2*v**2 + 0 + 0*v**3 + 1/72*v**4. Factor p(q).
q*(q + 1)/3
Let f = 13 + -157. Let g be (-1)/4 - 84/f. What is d in 1/3*d + g*d**3 - 2/3*d**2 + 0 = 0?
0, 1
Let x(t) be the second derivative of -1/72*t**4 + 1/180*t**5 - 2*t + 0 - 1/9*t**3 + t**2. Let n(h) be the first derivative of x(h). Factor n(y).
(y - 2)*(y + 1)/3
Let h(y) be the first derivative of y**7/21 - y**5/5 + y**3/3 + 3*y + 1. Let s(v) be the first derivative of h(v). Let s(j) = 0. Calculate j.
-1, 0, 1
Let c(l) be the first derivative of 2*l**5/25 - 11*l**4/10 + 14*l**3/3 - 5*l**2 - 12. Suppose c(s) = 0. Calculate s.
0, 1, 5
Let h(v) = v**2 + 2*v - 4. Let n(l) = -1. Suppose -47 = 5*f + 3*z - 2*z, 9 = 3*z. Let u be (-17)/(-3) + f/15. Let k(b) = u*n(b) - h(b). Factor k(d).
-(d + 1)**2
Let i(v) be the second derivative of -7*v**5/50 - v**4/15 + 7*v**3/15 + 2*v**2/5 + 15*v. Factor i(c).
-2*(c - 1)*(c + 1)*(7*c + 2)/5
Let u(y) be the first derivative of -y**7/14 + y**6/5 + 3*y**5/20 - y**4/2 + 5*y - 3. Let f(k) be the first derivative of u(k). Find g such that f(g) = 0.
-1, 0, 1, 2
Let q = 1997/1870 - 18/17. Let x(l) be the second derivative of 1/33*l**3 + 0 + 0*l**2 - 1/165*l**6 - 2*l + 1/66*l**4 - q*l**5. Factor x(j).
-2*j*(j - 1)*(j + 1)**2/11
Let j(t) = -t**2 + 15*t + 57. Let n be j(18). Factor 0*c - 1/5*c**n - 1/5*c**5 - 2/5*c**4 + 0*c**2 + 0.
-c**3*(c + 1)**2/5
Let o(t) = -2*t + 11. Let s be o(6). Let g be -1 + (5 - 2 - s). Factor 8/3*r**2 + 2/3*r**g + 10/3*r + 4/3.
2*(r + 1)**2*(r + 2)/3
Let b(u) be the second derivative of -1/135*u**6 - 3*u - 1/90*u**5 + 1/189*u**7 + 0 + 0*u**3 + 1/54*u**4 + 0*u**2. Factor b(l).
2*l**2*(l - 1)**2*(l + 1)/9
Suppose 3*z + z - 12 = 4*b, 2*z + b = 3. Factor 15*s**5 + z*