*5/80 - z**4/8 + z**3/8 + 3*z**2/4 + 45*z. Find j, given that k(j) = 0.
-2, -1, 1
Suppose 5*m - 3*m = 24. Factor -2*c**2 + 3*c**2 - 32*c - 5*c**2 - 12 + m*c**3 - 4.
4*(c - 2)*(c + 1)*(3*c + 2)
Let z(n) = -20*n**3 - 20*n**2 - 8*n - 8. Let h(r) = r**3 + r**2. Let g(t) = -44*h(t) - 2*z(t). Solve g(x) = 0.
-2, -1, 2
Let j(y) be the second derivative of y**7/294 - y**5/35 + y**4/42 + y**3/14 - y**2/7 + 3*y. Determine i so that j(i) = 0.
-2, -1, 1
Factor 27/2 + 3/2*g**2 - 9*g.
3*(g - 3)**2/2
Let p(t) be the first derivative of 1 - 2/3*t**3 - t + 0*t**2 - 1/6*t**4. Let c(h) be the first derivative of p(h). Let c(y) = 0. Calculate y.
-2, 0
Let v(k) be the second derivative of k**7/14 - 3*k**6/10 + 3*k**5/10 - 8*k. Factor v(h).
3*h**3*(h - 2)*(h - 1)
Let j(n) = n**3 - 3*n**2. Let y(s) = 2*s**3 - 2*s**2. Let z(l) = 2*j(l) - 3*y(l). Determine m so that z(m) = 0.
0
Factor 7*a**2 + 2*a**2 + 4*a - 5*a**3 - 4*a**2 + 6*a.
-5*a*(a - 2)*(a + 1)
Suppose 8/5*l**4 + 28/5*l**5 - 8/5*l**2 - 28/5*l**3 + 0 + 0*l = 0. What is l?
-1, -2/7, 0, 1
Let b(j) = 6*j + 1. Let l be b(-4). Let q = l + 23. Find u such that 0*u**2 + 0 - 2/9*u**5 - 2/9*u**4 + q*u + 4/9*u**3 = 0.
-2, 0, 1
Let z(p) be the second derivative of p**6/180 + p**5/45 - p**4/9 - 8*p**3/9 - 3*p**2/2 + 2*p. Let d(y) be the first derivative of z(y). Factor d(r).
2*(r - 2)*(r + 2)**2/3
Suppose -5 = 3*f - 5*y, -4*f - 3*y - 2 = -5. Factor 2/5*x**3 + 0*x**2 - 2/5*x + f.
2*x*(x - 1)*(x + 1)/5
Let k(i) = -i + 7. Let o be k(5). Let 2/5*m**3 + 0*m**o - 2/5*m + 0 = 0. What is m?
-1, 0, 1
Suppose 3*z + 0*p + 4*p - 20 = 0, z + 3*p - 15 = 0. Let g(w) be the first derivative of 4 + 0*w + z*w**2 - 1/6*w**3 - 1/8*w**4. Suppose g(d) = 0. What is d?
-1, 0
Let w be (33/154)/((-57)/(-24) - 2). Let -2/7 + w*r**3 + 0*r + 6/7*r**2 = 0. Calculate r.
-1, 1/2
Let j(m) = -5 - 2*m**2 + 2*m**2 + m**2. Let z(l) = -1. Suppose -d - 20 = -3*d - 2*c, -c = -5. Let w(q) = d*z(q) - j(q). Suppose w(y) = 0. What is y?
0
Suppose 2*y + q - 3 = 0, y + 3*y - 2*q + 6 = 0. Factor 2/9*i**3 - 2/9*i**4 - 2/9*i + y + 2/9*i**2.
-2*i*(i - 1)**2*(i + 1)/9
Let u(y) be the second derivative of 64*y**6/45 + 8*y**5/15 - 2*y**4 + 11*y**3/9 - y**2/3 + 9*y. Factor u(o).
2*(o + 1)*(4*o - 1)**3/3
Let y(l) be the first derivative of l**7/420 + l**6/90 + l**5/60 - l**3/3 + 6. Let o(z) be the third derivative of y(z). Factor o(h).
2*h*(h + 1)**2
Suppose -30 = 6*q - q. Let z be (q - -6) + 2/8. Factor 0 - y**4 - z*y + y**2 + 1/4*y**3.
-y*(y - 1)*(y + 1)*(4*y - 1)/4
Let s = -57 - -61. Let q(y) be the second derivative of -2*y - 1/18*y**s - 1/60*y**5 - 1/18*y**3 + 0 + 0*y**2. Find u such that q(u) = 0.
-1, 0
Let s = 30/19 + 111/38. Let u(m) be the second derivative of 0 + 1/12*m**4 + m**3 - m + s*m**2. Factor u(i).
(i + 3)**2
Let b be 0 + 0 - (-27)/(-1). Let n be 6/b - 47/(-9). Factor 4*a**n + 8*a**2 - 4*a**3 - 16*a**4 - 6 + 4 + 10*a**4.
2*(a - 1)**3*(a + 1)*(2*a + 1)
Let s = -31 - -33. Factor 1/4*h**s + 0 + 0*h.
h**2/4
Let b(f) be the third derivative of f**6/120 - f**5/12 + 7*f**4/24 - f**3/2 - 12*f**2. Suppose b(l) = 0. Calculate l.
1, 3
Let j be (-8)/(-28) + (-19)/(-7). Factor -10*l**3 + 24*l**j - 2 + 6*l**3 - 18*l**4 - 28*l**2 + 4*l**5 + 12*l + 12*l**3.
2*(l - 1)**4*(2*l - 1)
Suppose -3 + 8 = t. Suppose 1 - 5 = -2*y. Solve -2*z**5 - 5*z**t + 8*z**3 - 15*z**4 + 2*z**y - z**5 + 13*z**4 = 0.
-1, -1/4, 0, 1
Let s be (4/8)/((-1)/2). Let j be s/(-12)*-2*-2. Solve 2/3*f**3 + 0 + 0*f + 1/3*f**2 + j*f**4 = 0 for f.
-1, 0
Let d(b) = -4*b**4 - 25*b**3 - 5*b**2 + 19*b + 15. Let n(j) = -7*j**4 - 50*j**3 - 10*j**2 + 37*j + 30. Let s(t) = -13*d(t) + 6*n(t). Factor s(o).
5*(o - 1)*(o + 1)**2*(2*o + 3)
Let k(y) = 3*y - 32. Let g be k(12). Factor 1/3*l**2 - 1/3*l**g + 1/3*l**3 - 1/3*l + 0.
-l*(l - 1)**2*(l + 1)/3
Let j(a) = -a + 7. Suppose -20 = -r + 4*p - 6, 3*p = r - 12. Let d be j(r). Let f**2 + 2*f**3 + 5*f**2 + 3*f**4 - 10*f**3 - d + 0*f**3 = 0. What is f?
-1/3, 1
Let x be (70/84)/(5/9). Let d(l) be the first derivative of l**3 + 1/4*l**4 + x*l**2 + l + 1. Factor d(b).
(b + 1)**3
Factor 0 + 0 - 33*z**2 - z + 34*z**2.
z*(z - 1)
Let d be (-91)/135 + 4/6. Let c = 263/945 - d. Find k, given that 16/7*k**3 + 0 + c*k + 2*k**2 - 32/7*k**4 = 0.
-1/4, 0, 1
Let o be -1 + (-2 - 23/(-7)). Let d be (2/8)/(7/8). Factor 0 + o*i - d*i**2.
-2*i*(i - 1)/7
Suppose -w + x + 3 = -8, -3*x = 12. Suppose -3*y + w = 1. Factor -g**2 + 2*g**2 + 13*g**y + 9*g - 6 + g**2.
3*(g + 1)*(5*g - 2)
Let b(x) be the second derivative of -3*x**5/140 + x**4/28 - 8*x. Determine w, given that b(w) = 0.
0, 1
Let a(u) be the third derivative of -u**6/360 + 2*u**5/45 - 7*u**4/72 + 32*u**2. Find n, given that a(n) = 0.
0, 1, 7
Let s(f) be the first derivative of f**6/1980 - f**5/660 - f**4/66 + f**3/3 + 2. Let g(z) be the third derivative of s(z). Find o, given that g(o) = 0.
-1, 2
Suppose -4*h + 15*n + 28 = 11*n, -h + 3*n + 17 = 0. Factor -1/2*d**3 - d**4 + 0 + 0*d - 1/2*d**5 + 0*d**h.
-d**3*(d + 1)**2/2
Factor -3/2*u**4 - 63/2*u**2 - 27*u - 12*u**3 + 0.
-3*u*(u + 2)*(u + 3)**2/2
What is x in -15/4 - 3*x + 3/4*x**2 = 0?
-1, 5
Factor 5/2*o**2 + o - 1/4*o**3 - 2 - o**4 - 1/4*o**5.
-(o - 1)**2*(o + 2)**3/4
Let b(a) be the third derivative of 7/180*a**6 + 0*a - 19/90*a**5 + 4/9*a**3 + 2/9*a**4 - 3*a**2 + 0. Solve b(k) = 0 for k.
-2/7, 1, 2
Let p(g) = -g + 4. Let w be p(6). Let u be (-20)/30 - w*1. Factor u + 2/3*k**2 + 2*k.
2*(k + 1)*(k + 2)/3
Determine p, given that -9/2*p**2 + 39/4*p**3 + 0*p + 0 - 4*p**5 - 2*p**4 = 0.
-2, 0, 3/4
Suppose -4*p + 3*d = 1, -4*p + 0*d - 2*d = -14. Factor -12 + n + 12 - n**p.
-n*(n - 1)
Let r(i) be the second derivative of i**6/120 - i**5/80 - i**4/16 + i**3/24 + i**2/4 - 10*i. Factor r(s).
(s - 2)*(s - 1)*(s + 1)**2/4
Let i(n) = 7*n**2 - 7*n. Let k(w) = -3*w**2 - 3*w + 6. Let d(f) = -3*f**2 - 2*f + 5. Let m(y) = -6*d(y) + 5*k(y). Let a(g) = -6*i(g) + 15*m(g). Factor a(c).
3*c*(c - 1)
Let a(w) be the second derivative of 3*w**5/20 + 3*w**4/2 + 3*w**3/2 - 15*w**2 - 18*w. Factor a(h).
3*(h - 1)*(h + 2)*(h + 5)
Let m(y) be the second derivative of 5*y**7/42 - 11*y**6/3 + 145*y**5/4 - 190*y**4/3 - 2080*y**3/3 - 1280*y**2 - y + 14. Factor m(l).
5*(l - 8)**3*(l + 1)**2
Let b(p) = 2*p + 16. Let z(r) = r**3 - 7*r**2 + r - 14. Let u be z(7). Let t be b(u). Factor 2/5*a**5 + 6/5*a**3 + 0 + 2/5*a**t + 6/5*a**4 + 0*a.
2*a**2*(a + 1)**3/5
Suppose w + 12 = 4*w. Determine s so that 2*s**2 + 2*s**4 - 3*s**3 - s**w + 2*s**5 - 3*s**4 + s**3 = 0.
-1, 0, 1
Suppose 6 = 5*y - 14. Find j such that 6 + 12*j + 12*j**3 + 6*j**2 + 2*j**4 + j**y + 12*j**2 - 3 = 0.
-1
Let i(g) = 3*g**3 - g**2 + g + 1. Let r be 1*((-4)/(-2) - 4). Let u(l) = l**3 + l**2 - l + 1. Let x(w) = r*u(w) + i(w). Solve x(v) = 0 for v.
1
Let h(l) be the second derivative of l**4/3 + 10*l**3/3 + 8*l**2 - 21*l. Determine o so that h(o) = 0.
-4, -1
Let p be (0 - (2 - 2))/(-2). Let j be (-1)/6 - 169/(-78). Factor 1/2*d**4 - 1/2*d**j + 1/2*d - 1/2*d**3 + p.
d*(d - 1)**2*(d + 1)/2
Let x(l) = -l**2 + 9*l + 8. Let w(z) = z**2 - 4*z - 4. Let m(q) = -7*w(q) - 4*x(q). Suppose m(n) = 0. What is n?
-2, -2/3
Factor -3/4*o**3 - 3/2*o**2 + 0*o + 0.
-3*o**2*(o + 2)/4
Suppose -2*q = 3 - 9. Let f(y) be the second derivative of 0 + 1/21*y**4 - 1/70*y**5 - 1/21*y**q - y + 0*y**2. Suppose f(m) = 0. Calculate m.
0, 1
Let f be (4 + -1)*(-2)/(-2). Factor 6*b**f - 3*b**3 - 3*b**2 - 2*b**3 + 2*b + 0*b**3.
b*(b - 2)*(b - 1)
Determine x so that 11*x + 5*x**5 - 25*x**3 + 5*x**2 + 37*x - 8*x + 20 - 5*x**4 = 0.
-1, 2
Let o be 0*3/(-1 + 4). Let q be (1 - o)/1 - -2. Factor 4*i**3 + 4*i**q - 2*i**3 - 12*i**2 - i**4 + 8*i.
-i*(i - 2)**3
Let y = -4 + 6. Find z, given that -4*z**y + 2*z**5 - 2*z**3 + z**2 + 4*z**4 + z**2 - 2*z**4 = 0.
-1, 0, 1
Let g(m) be the second derivative of -m**4/30 + 2*m**3/5 - m**2 - 17*m. Factor g(a).
-2*(a - 5)*(a - 1)/5
Let f(h) be the first derivative of 2*h**3/27 + 22*h**2/9 + 242*h/9 + 34. Factor f(a).
2*(a + 11)**2/9
Factor -4*j**4 + 4*j**2 - j**3 - 8*j**3 - 4*j**3 + 8*j + 5*j**3.
-4*j*(j - 1)*(j + 1)*(j + 2)
Let s(d) be the second derivative of d**6/150 + d**5/10 + 2*d**4/15 - d**3/3 - 9*d**2/10 - 9*d. Suppose s(u) = 0. Calculate u.
-9, -1, 1
Factor -1/3*k**4 + 0 - 1/3*k**3 + 0*k**2 + 0*k.
-k**3*(k + 1)/3
Let p(i) be the second derivative of 1/15*i**6 + 0 + 3