1)**2
Suppose 2*i - 4 = u, 4 = 2*i + 3*u - 0*u. Let s = i + -1. Find q such that 3*q + q - 3*q**2 + q**3 - s - q = 0.
1
Suppose o + 1 - 2 = 0. Let i be (((-21)/6)/(-7))/o. Factor n**3 + 0*n**2 + i - n - 1/2*n**4.
-(n - 1)**3*(n + 1)/2
Factor 3*g**3 + 1/2*g**4 + 6*g**2 + 5*g + 3/2.
(g + 1)**3*(g + 3)/2
Suppose 5*l - 10 + 0 = 0. Suppose 4*j = l*d + 4, -7*j - 2*d + 17 = -4*j. What is r in 20*r**2 + 2 - 15*r**j - 8*r**3 + 10*r**4 + 3*r**3 - 10*r - 2*r**5 = 0?
1
Let g = 4/49 - -233/147. Factor -g*b + 1/3 - b**3 + 7/3*b**2.
-(b - 1)**2*(3*b - 1)/3
Let g(k) be the third derivative of -k**7/735 - k**6/210 + k**4/42 + k**3/21 + 13*k**2. Determine x, given that g(x) = 0.
-1, 1
Let f(z) be the third derivative of -z**6/60 - z**5/30 + z**4/12 + z**3/3 - 15*z**2. Suppose f(b) = 0. Calculate b.
-1, 1
Let p(m) be the second derivative of -5*m**7/42 + 3*m**5/4 + 5*m**4/6 - 22*m. Solve p(u) = 0 for u.
-1, 0, 2
Suppose -8*p + 9 = -5*p. Let c(a) be the first derivative of -2/15*a**p - 1 + 4/5*a**2 - 8/5*a. Factor c(j).
-2*(j - 2)**2/5
Let k(u) = 6*u**2 - 12*u + 9. Let f(d) = d**2. Let a(y) = 3*f(y) - k(y). Factor a(v).
-3*(v - 3)*(v - 1)
Let a = 18 + -6. Suppose -6 = 2*d + 2*l, 2*d - a = -3*d + 4*l. Factor -y**4 - 7/3*y**2 - 2/3*y - 8/3*y**3 + d.
-y*(y + 1)**2*(3*y + 2)/3
Factor 4*d**4 - 5*d**2 + 8*d**3 + 2*d**5 + d**2 - 10*d**3.
2*d**2*(d - 1)*(d + 1)*(d + 2)
Let v be ((-16)/(-24))/((-2)/(-6)). Suppose -4*z + 14 = -w, -3*w + 5*z - v = 3*z. Factor -2*x**3 - 4*x**2 + 4*x**2 - x - 5*x**2 - w*x**3.
-x*(x + 1)*(4*x + 1)
Let u = -16 + 23. Suppose 3*y = -2*v + 3, -2*y - 5 = -4*v - u*y. Solve 0 + v*k**2 + 1/2*k**3 - 1/2*k = 0 for k.
-1, 0, 1
Factor -23*y + 3 - y**2 - 2*y**2 + 23*y.
-3*(y - 1)*(y + 1)
Let p(h) = 7*h**3 - 10*h**2 + 9*h - 6. Let k(w) = 13*w**3 - 19*w**2 + 17*w - 11. Let d(f) = -6*k(f) + 11*p(f). Factor d(t).
-t*(t - 3)*(t - 1)
Let h(c) be the second derivative of 0 + 1/2*c**4 + 2/5*c**5 - 4/3*c**3 + 1/15*c**6 - 4*c**2 - 5*c. Factor h(v).
2*(v - 1)*(v + 1)*(v + 2)**2
Let t(z) be the second derivative of 1/90*z**6 - 2*z - 1/18*z**4 + 0*z**5 + 0*z**3 + 0 + 1/6*z**2. Determine p so that t(p) = 0.
-1, 1
Suppose 0 = 3*n + 4*n - 28. Let k(g) be the first derivative of 1/18*g**6 + 1 - 1/6*g**n + 0*g + 1/6*g**2 + 0*g**5 + 0*g**3. Suppose k(p) = 0. What is p?
-1, 0, 1
Suppose -3*p = -p - 4. What is o in o**3 - 35*o**p + 2*o**3 + 29*o**2 = 0?
0, 2
Let m be (-2)/(-6) + 4/(-18). Let c(t) be the first derivative of -m*t**3 - 1/3*t + 1 + 1/3*t**2. Factor c(y).
-(y - 1)**2/3
Suppose 3*k = 5*u - 27, 3*k + 10 = -2*u - k. Let x be -2*2 + 5 + -1. Factor x*n + 0 - n**u + 0*n**4 + 1/3*n**5 - 2/3*n**2.
n**2*(n - 2)*(n + 1)**2/3
Suppose 5*r = y - 22, -14 = y - 0*y + 4*r. Let g(p) be the second derivative of 3*p + 0 + 0*p**4 - 1/30*p**6 + 1/20*p**5 + 0*p**3 + 0*p**y. Factor g(x).
-x**3*(x - 1)
Suppose 36 = 4*o - 0*o. Let n(q) = 4*q**3 + 4*q**2 + 8*q. Let d(c) = 17*c**3 + 15*c**2 + 33*c - 1. Let p(s) = o*n(s) - 2*d(s). Find v such that p(v) = 0.
-1
Factor -4/3*a**3 - 4/3*a**2 + 4/3*a**4 + 4/3*a**5 + 0*a + 0.
4*a**2*(a - 1)*(a + 1)**2/3
Let q(h) be the third derivative of -2/15*h**4 + 1/60*h**6 - 1/150*h**5 + 0*h - 4/15*h**3 - 7*h**2 - 1/840*h**8 + 0 + 1/525*h**7. Factor q(l).
-2*(l - 2)**2*(l + 1)**3/5
Let r(a) = -a**3 - 8*a**2 - a. Let k(o) = -o**3 - 16*o**2 - o. Let c(g) = 3*k(g) - 7*r(g). Suppose c(j) = 0. Calculate j.
-1, 0
Let u be (-4)/(-26) - (-35)/26. Let 0 + 3/2*h**3 - u*h**2 + 1/2*h - 1/2*h**4 = 0. What is h?
0, 1
Solve -2*n**2 - 1/2*n**3 - 1 - 5/2*n = 0.
-2, -1
Suppose -8*b = -14*b. Let i(a) be the first derivative of 0*a**2 + 4/15*a**5 + b*a - 2/9*a**3 - 4 - 1/6*a**4. Factor i(m).
2*m**2*(m - 1)*(2*m + 1)/3
Let l(a) = 8*a**4 + 21*a**3 - 15*a**2 - 32*a + 7. Let x(c) = -3*c**4 - 7*c**3 + 5*c**2 + 11*c - 2. Let r(p) = 4*l(p) + 11*x(p). Factor r(t).
-(t - 6)*(t - 1)**2*(t + 1)
Suppose 0 = 3*w + 5*q + 5, 0 = 2*w + 2*q + 2. Factor -8/9*s**3 + w*s + 0 - 2/3*s**5 + 16/9*s**4 + 0*s**2.
-2*s**3*(s - 2)*(3*s - 2)/9
Let y(z) = -z + 3*z**3 + z - 7*z**4 + 5 + 2*z**2 + 7*z. Let w(x) = -3*x**4 + x**3 + x**2 + 3*x + 2. Let u(b) = -5*w(b) + 2*y(b). Solve u(t) = 0.
-1, 0, 1
Let f(r) = -2*r**3 - 13*r**2 - 3*r + 5. Suppose -17 = -4*o + 7. Let d(t) = -2*t**3 - 14*t**2 - 2*t + 6. Let q(n) = o*f(n) - 5*d(n). Factor q(s).
-2*s*(s + 2)**2
Let m be (-8)/(-36) - 205/(-9). Let i = 12 + m. Determine d so that -8*d - 4/5 - 49/5*d**5 - i*d**4 - 29*d**2 - 47*d**3 = 0.
-1, -2/7
Let s(n) be the third derivative of n**8/1680 - n**6/360 - n**3/2 - 3*n**2. Let d(i) be the first derivative of s(i). Find q such that d(q) = 0.
-1, 0, 1
Let s(m) = -2*m**3 + 12*m + 20. Suppose -j + 6 - 1 = 0. Let g(r) = -2*r**3 + r**2 + 13*r + 21. Let y(w) = j*s(w) - 4*g(w). Factor y(u).
-2*(u - 2)*(u + 2)**2
Let q(j) = -8*j**2 + 8. Let w(p) = p**2 - 1. Let z(c) = -q(c) - 6*w(c). Factor z(x).
2*(x - 1)*(x + 1)
Suppose -15 = 5*m - 8*m. Let c(k) be the third derivative of 1/540*k**6 - k**2 + 0*k**3 - 1/108*k**4 - 1/270*k**m + 0*k + 1/945*k**7 + 0. Solve c(a) = 0 for a.
-1, 0, 1
Let y(p) be the second derivative of -1/54*p**4 - 1/90*p**5 + 0*p**2 + 1/27*p**3 - 5*p + 0 + 1/135*p**6. What is u in y(u) = 0?
-1, 0, 1
Suppose -6 = -4*r - 14. Let d be 2 + 1 + 0/r. Factor 3*j**3 + 2*j**2 - 2*j**d + 0*j**3 + j.
j*(j + 1)**2
Let r(u) be the first derivative of u**6/10 - 3*u**4/10 + 3*u**2/10 + 13. Suppose r(t) = 0. Calculate t.
-1, 0, 1
Let a be (26/(-9) - -3) + 1. Let z(o) be the first derivative of -2/5*o**5 - 1 - a*o**3 + 1/3*o**2 + 0*o + 7/6*o**4. Factor z(i).
-2*i*(i - 1)**2*(3*i - 1)/3
Let d(f) be the first derivative of 3/4*f**2 - 1 + 1/4*f**3 + 3/4*f. Suppose d(o) = 0. What is o?
-1
Let q(p) be the third derivative of 0*p**4 + 0 - 1/168*p**8 + 1/30*p**5 - 1/105*p**7 + 0*p**3 + 1/60*p**6 + 0*p - 4*p**2. Determine s, given that q(s) = 0.
-1, 0, 1
Let w(v) = v**2 + 4. Let u be w(0). Determine n, given that n**u - 3*n + n + n**2 - 4*n**2 = 0.
-1, 0, 2
Let h = -2267/21 - -108. Let j(p) be the third derivative of 1/210*p**5 + 0*p + 0 - h*p**3 + 1/420*p**6 - 2*p**2 - 1/84*p**4. Suppose j(d) = 0. What is d?
-1, 1
Let n(t) = -t**3 + 4*t**2 - t - 2. Let m be n(2). Let p = -2 + m. Suppose 0*b**2 - b**2 + 0*b**p + 1 = 0. What is b?
-1, 1
Let y(h) be the first derivative of 0*h**2 - 1/5*h**3 + 0*h + 1. Factor y(r).
-3*r**2/5
Suppose -5*u = -4*f - 25, -5*f - 2*u + 9 = -1. Suppose f*z - 24 = -4*z. Factor z*q - 4 + 1/2*q**3 - 3*q**2.
(q - 2)**3/2
Let b(m) be the first derivative of m**5/30 - m**4/12 + m**3/18 + 43. Solve b(w) = 0.
0, 1
Solve -1/2*d**2 - 3/2 + 2*d = 0 for d.
1, 3
Let m(x) = 5*x**2 - 3 + 1 - 13*x + 4*x + x**3 - 12. Let u be m(-6). Let 3/4*l**3 + 0*l**2 + 1/4*l**u - l + 0 = 0. Calculate l.
-2, 0, 1
Let g(s) be the first derivative of s**4/10 + 2. What is l in g(l) = 0?
0
Suppose 0 = -4*f + 3*f + 5. Factor -a**4 - a**5 - 4*a**4 + 6*a**4 + 0*a**f.
-a**4*(a - 1)
Let r(g) = 20*g**2 + 149*g + 138. Let b(x) = -5*x**2 - 37*x - 34. Let j(m) = -9*b(m) - 2*r(m). Let j(w) = 0. What is w?
-6, -1
Let s(a) be the first derivative of -1/2*a**4 + a**2 - 2 + 4/9*a**3 - 4/3*a. Determine y, given that s(y) = 0.
-1, 2/3, 1
Let g(q) be the first derivative of q**4/4 - 7*q**3/3 + 5*q + 2. Let w be g(7). Factor -u**2 - 9*u**3 + 2 + 4*u**2 + w*u**3 + 9*u.
-(u - 2)*(u + 1)*(4*u + 1)
Let f be (-20)/5 - (1 + -8 - 0). Let s(y) be the second derivative of 0*y**3 + 1/24*y**4 - f*y + 0 + 0*y**2. Let s(o) = 0. Calculate o.
0
Let s be ((-2)/3)/((-52)/(-18)). Let t = s - -41/65. Solve -2/5 + 0*i + t*i**2 = 0.
-1, 1
Let f be 21/18 + 2/(-3). Suppose 0*k - 3 = -k. Determine u so that 0*u + f*u**k + 0 + 1/2*u**2 = 0.
-1, 0
Let l = -10 - -8. Let r be 3/36 + l/(-8). Factor -r*q**2 - 1/3*q + 0.
-q*(q + 1)/3
Let y(g) = 2*g - 10. Let j be y(7). Suppose 0 = -2*f + j*f - 24. Suppose -f*c + 2*c**2 + 1 + 1 + 14 + 2 = 0. Calculate c.
3
Let y(q) be the second derivative of 1/2*q**2 - 7*q - 1/5*q**5 + 0 + 1/30*q**6 - 2/3*q**3 + 1/2*q**4. What is m in y(m) = 0?
1
Suppose 0*q - 2*q = 0. Let h(p) be the first derivative of 3 + 0*p**2 + q*p + 1/12*p**3 + 1/16*p**4. Suppose h(g) = 0. Calculate g.
-1, 0
Let n(f) be the first derivative of f**5/30 + f**4/24 - f**3/18 - f**2/12 + 20. Let n(m) = 0. Calculate m.
-1, 0, 1
Let j(s) be the third derivative of -s**6/60 - s**5/10 - s**4/4 - s