i - 1)*(i + 1)**2
Suppose 3*r + 18 = 9*r. Determine p so that 4/5*p + 0 - 6/5*p**r - 2*p**2 = 0.
-2, 0, 1/3
Suppose 11 = -3*m - 3*r + 26, -r = -2. Factor 5 + n + m*n**2 - 3 - 1 - 2 - 2*n**4 - n**3.
-(n - 1)*(n + 1)**2*(2*n - 1)
Suppose 3*a = 4*u + 29, 4*a - u + 0 = 17. Suppose -15 = -3*i - 3*r, 0*r + r + a = i. Solve -2*p**3 - p**4 + 0*p**5 - 3*p**i - 2*p**5 = 0.
-1, 0
Factor -6 + 4 - 6 - 12*x**2 - 2*x**3 - 18*x.
-2*(x + 1)**2*(x + 4)
Let i(r) be the second derivative of 2*r + 0*r**5 + 1/45*r**6 + 0 + 1/3*r**2 + 0*r**3 - 1/9*r**4. Determine k, given that i(k) = 0.
-1, 1
Let q(a) = 5*a**4 - 5*a**3 + 6*a + 6. Let c(f) = -4*f**4 + 4*f**3 - 5*f - 5. Let h(d) = 6*c(d) + 5*q(d). Find x such that h(x) = 0.
0, 1
Let h(a) be the third derivative of -a**8/2184 + 2*a**7/1365 + a**6/260 - 2*a**5/195 - a**4/39 + 16*a**2. Factor h(c).
-2*c*(c - 2)**2*(c + 1)**2/13
Let g(z) be the first derivative of 8*z**3/3 - z**2 - 7*z + 3. Let c(q) = 4*q**2 - q - 4. Let l(i) = -7*c(i) + 4*g(i). Factor l(f).
f*(4*f - 1)
Let q be ((1 + -1)/5)/(-1). Find c, given that 1/2*c**5 + 2*c + 2*c**2 + q - 3/2*c**3 - c**4 = 0.
-1, 0, 2
Let g(y) = y**2 - 2. Let l be g(2). Let t be -2 + l + 2 + -2. Factor t*w**3 + w**3 - 2*w**2 - 2*w**3 - w.
-w*(w + 1)**2
Let f(h) be the first derivative of h**7/70 - h**5/10 + h**3/2 - 3*h**2/2 - 3. Let n(b) be the second derivative of f(b). Solve n(i) = 0.
-1, 1
Let o be (-626)/(-1113) + 2/(-6). Let r = o + 3/53. Factor 6/7*n - r*n**2 - 4/7.
-2*(n - 2)*(n - 1)/7
Let b(p) be the third derivative of -p**6/480 + p**5/240 + p**4/48 + 18*p**2. Determine f so that b(f) = 0.
-1, 0, 2
Let f(o) be the third derivative of -o**6/540 + o**5/270 - 41*o**2. Factor f(l).
-2*l**2*(l - 1)/9
Let h(u) be the third derivative of u**8/840 + u**7/420 - u**3/2 - 3*u**2. Let t(o) be the first derivative of h(o). Solve t(r) = 0 for r.
-1, 0
Let z(d) be the first derivative of 3/5*d**5 + d**3 + 0*d**2 + 3/2*d**4 - 5 + 0*d. Solve z(a) = 0 for a.
-1, 0
Suppose 0 = -4*g - 10*p + 5*p - 25, 15 = -3*p. Solve u**3 - 4*u - 2 + g + u = 0.
-1, 2
Let j(y) = -y + 1. Let h be j(-4). Suppose -16*l = -17*l + h. Factor -1/4*c**2 + 1/4*c**3 + 1/4*c**4 + 0*c + 0 - 1/4*c**l.
-c**2*(c - 1)**2*(c + 1)/4
Factor -18*w**2 + 14*w**2 + 20 - 10*w**3 - 5*w**4 + 19*w**2 + 40*w.
-5*(w - 2)*(w + 1)**2*(w + 2)
Let w(v) be the first derivative of v**3/30 - 3*v**2/20 + v/5 - 19. Factor w(j).
(j - 2)*(j - 1)/10
Let k(f) = f**3 + 5*f**2 + 3. Let j = -10 + 5. Let m be k(j). Solve 5*q**4 + 4 + 0*q**2 - 4*q**4 - 2*q**2 + 6*q**m - 3*q**4 - 6*q = 0.
-1, 1, 2
Suppose -25 = 2*h - 11. Let w(r) = -19*r**3 + 5*r**2 - 7. Let j(c) = -9*c**3 + 2*c**2 - 3. Let y(f) = h*j(f) + 3*w(f). Find s, given that y(s) = 0.
-1/6, 0
Factor 9/8 - 3/2*j + 3/8*j**2.
3*(j - 3)*(j - 1)/8
Let b be (2 - -1) + 4 + -3. Factor -3 + 3*l**b + 27*l**2 - 15*l**3 + 5 + 4 - 21*l.
3*(l - 2)*(l - 1)**3
Let n(d) = 3*d**3 - d**2 - 11*d + 3. Let j(k) = -k**3 + k**2 + 5*k - 1. Let x(r) = 10*j(r) + 4*n(r). Suppose x(c) = 0. Calculate c.
-1
Suppose 0 = 5*q + 25, 0*q = -3*d + 2*q + 16. Suppose 24/7*c**4 - 18/7*c + 10/7*c**5 - 20/7*c**d + 8/7*c**3 - 4/7 = 0. What is c?
-1, -2/5, 1
Let k(g) be the third derivative of -g**5/20 - 2*g**3/3 + 7*g**2. Let l(o) = -1. Let f(h) = -k(h) + 4*l(h). Factor f(s).
3*s**2
Let q be 50/36 + (-16)/(-144). Factor -9*w**3 - 12*w + q*w**4 + 0 + 18*w**2.
3*w*(w - 2)**3/2
Let t(v) be the third derivative of v**7/70 - v**6/20 + v**5/20 + 4*v**2. Suppose t(i) = 0. Calculate i.
0, 1
Factor -9*q**3 - 2*q**5 - q**3 - 4*q**2 - 37*q**4 + 29*q**4.
-2*q**2*(q + 1)**2*(q + 2)
Let j(l) = 6*l**3 - l**2 + 2*l - 1. Let i be j(1). Let p be i/(-9)*(-3)/4. Solve -p - 1/2*w**2 + w = 0 for w.
1
Let m(r) be the first derivative of 3*r**5/5 + 6*r**4 + 23*r**3 + 99*r**2/2 + 51*r - 2. Let q(b) = -b**2 + b + 1. Let k(w) = m(w) - 3*q(w). Factor k(v).
3*(v + 2)**4
Suppose -8*a + 3*a + 19 = 2*i, 0 = -a - 2*i + 7. Suppose -2*u = -5 - a. What is x in 2*x**2 + 4 + 6*x + u + 0*x**2 - 4 = 0?
-2, -1
Let h be -1*4/(-8) - (-1 - -1). Solve h*c**3 - 1/2*c**4 + 0*c + 0*c**2 + 0 = 0.
0, 1
Suppose 0 = 4*w + 20, -3*w = n + w + 17. Let c(t) = -4*t**2 - 5. Let y(u) = 2*u**2 + 3. Let x(k) = n*c(k) + 5*y(k). Let x(b) = 0. What is b?
0
Let f(l) be the first derivative of -1/4*l**2 + 1 + 1/3*l**3 + 0*l - 1/8*l**4. Factor f(v).
-v*(v - 1)**2/2
Suppose -3*r + 4*r = 0. Suppose 3*i + 0*i - o = 12, -3*o = r. Factor 5/4*l**3 + 0 - l + 3/4*l**i - l**2.
l*(l - 1)*(l + 2)*(3*l + 2)/4
Let b = 39665 - 2181512/55. Let r = b + -1/385. Determine x, given that 218/7*x**2 + 36*x**3 + 14*x**4 + 72/7*x + r = 0.
-1, -2/7
Let i(p) = -80*p**5 + 135*p**4 + 80*p**3 - 135*p**2. Let f(x) = -3*x**5 + 5*x**4 + 3*x**3 - 5*x**2. Let s(m) = -55*f(m) + 2*i(m). Factor s(z).
5*z**2*(z - 1)**2*(z + 1)
Let h = -3 + 5. Suppose 0 = -q - h*q + 6. Find l, given that 3*l + 2*l - 2*l**3 + 2*l**2 - q - 3*l = 0.
-1, 1
Determine u so that 0*u + 50/9*u**4 + 8/9*u**2 + 0 - 40/9*u**3 = 0.
0, 2/5
Let d be (-264)/(-144) - (-1)/(-2). Let u(z) be the second derivative of -z**2 - d*z**3 - 1/2*z**4 + 2*z + 0. Determine n so that u(n) = 0.
-1, -1/3
Let m = -6 + -7. Let u = m + 13. Suppose -4/5 + 2/5*x**3 + u*x**2 - 6/5*x = 0. Calculate x.
-1, 2
Let i(d) = -4*d**3 - 6*d**2 + 5*d + 7. Suppose 3*b = 16 + 47. Let p(w) = w**3 + w**2 - w - 1. Let t(k) = b*p(k) + 3*i(k). Factor t(c).
3*c*(c + 1)*(3*c - 2)
Factor 8/7 + 36/7*r + 4/7*r**5 + 8*r**3 + 24/7*r**4 + 64/7*r**2.
4*(r + 1)**4*(r + 2)/7
Let u(g) = g**3 - 7*g**2 + 6*g + 2. Let w be u(6). Let k(j) be the second derivative of 0*j**2 + 1/30*j**5 + 1/9*j**3 + 0 + 1/9*j**4 - w*j. Factor k(h).
2*h*(h + 1)**2/3
Let m(y) be the second derivative of y**7/231 - 2*y**6/165 - y**5/55 + 4*y**4/33 - 7*y**3/33 + 2*y**2/11 - 4*y. Factor m(r).
2*(r - 1)**4*(r + 2)/11
Let w(o) be the third derivative of -o**8/5040 + o**7/1260 - o**5/15 + 4*o**2. Let t(i) be the third derivative of w(i). Factor t(c).
-4*c*(c - 1)
Let s(j) be the first derivative of 3*j**5/20 + 3*j**4/8 + j**3/4 + 15. Determine p, given that s(p) = 0.
-1, 0
Let m(o) be the second derivative of 0 - 1/12*o**4 + 2*o + 0*o**2 + 1/6*o**3. Factor m(w).
-w*(w - 1)
Let o = 9/7 + -20/21. Let b = -4 + 7. What is s in -o*s**4 + 0*s + 0 + 1/3*s**b + 0*s**2 = 0?
0, 1
Let f = -3 - -6. Suppose -21 = -4*n - z, n + f*z = -10 + 29. Solve w - 2*w**3 + n*w**3 - 3*w**3 = 0.
-1, 0, 1
Determine u so that -1/2*u + u**2 + 1/2*u**3 - 1 = 0.
-2, -1, 1
Let 0 + 1/3*a**2 - 4/3*a = 0. Calculate a.
0, 4
Let q(c) = c**2 + 4*c + 4. Let n be q(-4). Let r(m) be the second derivative of 0*m**3 - 1/48*m**n + 0*m**2 + m + 0. Factor r(p).
-p**2/4
Let m(o) be the third derivative of -o**9/241920 - o**8/80640 + o**7/20160 + o**6/2880 + o**5/20 + o**2. Let h(z) be the third derivative of m(z). Factor h(s).
-(s - 1)*(s + 1)**2/4
Suppose 9*y**2 - 3*y**2 + 8*y**3 + 3*y**4 - 20*y**3 - 12*y + 3 + 12*y**2 = 0. Calculate y.
1
Let h be 2*3/((-15)/(-10)). Let g(x) be the second derivative of -1/5*x**5 - 1/5*x**6 + 1/3*x**h + x + 0 - 1/21*x**7 + x**2 + x**3. What is k in g(k) = 0?
-1, 1
Let q be ((-1)/3)/((2 - -11)/(-78)). Suppose 4/7*j**3 - 6/7*j + 2/7*j**5 + 6/7*j**4 - 4/7*j**q - 2/7 = 0. What is j?
-1, 1
Let r(w) be the first derivative of -2*w**7/105 + w**6/20 - w**4/12 - 3*w**2 - 6. Let g(j) be the second derivative of r(j). Determine f so that g(f) = 0.
-1/2, 0, 1
Let m(y) be the first derivative of 2*y**3/63 - 2*y**2/21 - 2*y/7 + 2. Factor m(f).
2*(f - 3)*(f + 1)/21
Let i be (-1 + 2)/((-8)/(-16)). Let d be (i/(-5))/(3/(-9)). What is f in 4/5 + d*f**2 + 2*f = 0?
-1, -2/3
Let c(d) be the first derivative of 1/60*d**5 + 0*d**3 + 2 - d**2 + 0*d - 1/24*d**4. Let m(a) be the second derivative of c(a). Suppose m(g) = 0. Calculate g.
0, 1
Let w = -103 + 107. Let t(m) be the third derivative of 1/6*m**3 - 1/8*m**w - 1/120*m**6 + 1/20*m**5 + 0 + m**2 + 0*m. Factor t(f).
-(f - 1)**3
Let y be ((-16)/6)/8 - 14/(-15). Suppose 0 - y*b**3 + 2/5*b + 1/5*b**2 = 0. Calculate b.
-2/3, 0, 1
Let m(o) be the third derivative of 7*o**5/360 + o**4/16 + o**3/18 - 2*o**2. Factor m(r).
(r + 1)*(7*r + 2)/6
Let l(q) = -9*q**3 + 21*q**2 + 90*q - 60. Let b(r) = -r**3 + 2*r**2 + 9*r - 6. Suppose 5*f + 7 = -3. Let p(o) = f*l(o) + 21*b(o). Solve p(d) = 0 for d.
-2, 1
Let l(w) be the second derivative of -w**7/6300 +