9*h - 9. Let z(j) = 1. Let t(q) = -2*q - 4. Let o(c) = -t(c) - 2*z(c). Let r(u) = 9*o(u) + 2*v(u). Factor r(n).
-2*n**2*(n - 1)
Let h(x) be the second derivative of 1/2*x**2 + 5/48*x**4 + 0 - x + 1/3*x**3 + 1/80*x**5. Let h(l) = 0. Calculate l.
-2, -1
Suppose 0 = 3*g + 7 - 4. Let w be (g/(-2))/((-12)/(-8)). Solve 4*o**3 - 8/3*o**2 + 0*o + w*o**5 + 0 - 2*o**4 = 0 for o.
0, 2
Let s(b) = -3265*b**2 + 398*b - 14. Let p(y) = -3264*y**2 + 399*y - 15. Let z(d) = 2*p(d) - 3*s(d). Suppose z(g) = 0. Calculate g.
2/33
What is o in 1/3*o**3 + 2/3*o**2 + 1/3*o + 0 = 0?
-1, 0
Let x(j) = 4*j - 9. Let b be x(3). Let v(c) be the first derivative of 7/2*c**4 + 0*c - 10/3*c**3 - b - 2*c**2. Factor v(n).
2*n*(n - 1)*(7*n + 2)
Suppose -71*n - 1974*n**2 - 25*n - 576 + 1970*n**2 = 0. Calculate n.
-12
Let y(l) be the third derivative of -8*l**6/15 - 8*l**5/3 + 23*l**4/6 - 2*l**3 - 9*l**2. Factor y(b).
-4*(b + 3)*(4*b - 1)**2
Let l(z) = z**3 - 21*z**2 - 15*z - 3. Let r(w) = -w**3 + 10 - 2*w**2 + 33*w**2 + 23*w - 5. Let m(f) = -7*l(f) - 5*r(f). Factor m(k).
-2*(k + 1)**2*(k + 2)
Let w(c) be the first derivative of -3/2*c**4 + 2 - 3*c - 5*c**3 - 6*c**2. Factor w(g).
-3*(g + 1)**2*(2*g + 1)
Suppose 7*n = 12 + 2. Let c(j) be the first derivative of 1/10*j**5 - 1/8*j**n - 1 + 1/3*j**3 - 5/16*j**4 + 0*j. Determine a so that c(a) = 0.
0, 1/2, 1
Let r(o) be the first derivative of o**3/3 + 2*o**2 - 11. Factor r(n).
n*(n + 4)
Let v be 5 - (-3)/(2 + 1). Let w(n) be the second derivative of -2/15*n**v + 0 + 0*n**4 + 0*n**2 - 2*n + 0*n**3 + 5/21*n**7 + 0*n**5. Let w(i) = 0. What is i?
0, 2/5
Factor 2/3 + 2/3*z - 2/3*z**2 - 2/3*z**3.
-2*(z - 1)*(z + 1)**2/3
Suppose -k = -3*h - 6*k - 4, 3*k + 6 = 0. Suppose 2*s = 2*y + 6 + 2, -h*y = -3*s + 10. Factor -n**s + 2*n**3 - n**2 + 8 - 4*n**2.
2*(n - 2)**2*(n + 1)
Factor -5*y**2 - 2 + 3 + 4.
-5*(y - 1)*(y + 1)
Find o, given that o**3 + 0 + 0*o**2 + 0*o + 1/3*o**4 = 0.
-3, 0
Let y be 2*3/1*-1. Let t be 2/y + -1 - -2. Factor t + 2/3*b**2 - 4/3*b.
2*(b - 1)**2/3
Determine a, given that 64/9*a - 128/9 - 2/9*a**4 + 8/3*a**2 - 8/9*a**3 = 0.
-4, 2
Let a(v) be the first derivative of -12*v**4 + 24*v**3 + 45*v**2/2 + 6*v - 19. Find x, given that a(x) = 0.
-1/4, 2
Let x(u) = 3*u**2 + 12*u - 27. Let g(p) = p**2 + 5*p - 11. Let q(o) = -12*g(o) + 5*x(o). Factor q(z).
3*(z - 1)*(z + 1)
Let i be (-12)/(-2)*(-9)/(-18). Suppose 2*p + 2 = -2*h - 0*h, 0 = -i*h - 15. Solve -1/2 + r**3 - r + 2*r**2 - 3/2*r**p = 0 for r.
-1, -1/3, 1
Factor -8/3*m**3 - 10/3*m**2 - 4/3*m - 2/3*m**4 + 0.
-2*m*(m + 1)**2*(m + 2)/3
Let h(w) be the first derivative of 2/5*w**5 + 4 - 1/9*w**6 - 1/2*w**4 + 2/9*w**3 + 0*w**2 + 0*w. Find m, given that h(m) = 0.
0, 1
Let j(w) = w**2 - 3*w - 5. Let d be j(5). Factor -8*r**d + 0*r**2 + 6*r**5 + 0*r**2 + 4*r**4 - 2*r**3.
-2*r**3*(r - 1)**2
Let w(g) = -6*g - 92. Let i be w(-16). Suppose -i*x**2 - 3*x - 1/2 + 3*x**3 + 9/2*x**4 = 0. What is x?
-1, -1/3, 1
Suppose 89*z**2 - 87*z**2 + 2*z + 6*z - 10 = 0. What is z?
-5, 1
Suppose -3 = -2*y + 7. Factor -7*x**2 - 2*x + 0*x + y*x**2.
-2*x*(x + 1)
Let x(k) be the second derivative of -k**4/3 - 22*k**3/3 - 30*k. Factor x(o).
-4*o*(o + 11)
Factor 8*n**3 - 4*n**5 - 1323 + 1323 - 4*n.
-4*n*(n - 1)**2*(n + 1)**2
Let s(k) be the second derivative of -k**7/16380 + k**5/780 + k**4/6 - 5*k. Let m(r) be the third derivative of s(r). Find o, given that m(o) = 0.
-1, 1
Let g(n) be the third derivative of -n**8/112 + n**6/40 - 34*n**2. Factor g(o).
-3*o**3*(o - 1)*(o + 1)
Let l(t) be the first derivative of -t**5/5 + t**4/12 - 4*t + 3. Let q(y) be the first derivative of l(y). Factor q(c).
-c**2*(4*c - 1)
Suppose 5*i + 4*t + 10 = 0, 0 = -5*i - t - t. Solve -2/5*w**i + 0 - 2/5*w**4 - 4/5*w**3 + 0*w = 0.
-1, 0
Let n(j) be the third derivative of j**7/630 - j**6/60 + 13*j**5/180 - j**4/6 + 2*j**3/9 - 32*j**2. Find v such that n(v) = 0.
1, 2
Let i(m) be the third derivative of m**7/105 + 2*m**6/15 + 8*m**5/15 + 2*m**2. What is b in i(b) = 0?
-4, 0
Let w(k) be the first derivative of -17*k**5 + 5*k**4/2 + 85*k**3/3 - 5*k**2 - 48. Suppose w(t) = 0. What is t?
-1, 0, 2/17, 1
Let i(u) be the first derivative of u**6/9 + 16*u**5/45 + u**4/18 - 16*u**3/27 - 4*u**2/9 - 2. Determine n, given that i(n) = 0.
-2, -1, -2/3, 0, 1
Let 0 - 3/8*j**3 + 3/4*j - 3/8*j**2 = 0. What is j?
-2, 0, 1
Let r = -15 - -12. Let q(o) = -o**2. Let h(n) = -7*n**2 - 6*n + 9. Let p(a) = r*h(a) + 24*q(a). Factor p(g).
-3*(g - 3)**2
Factor 27/2 - 9*m + 3/2*m**2.
3*(m - 3)**2/2
Let x(g) = -g - 3. Let t be x(-6). Factor -w**5 - 1 - w**2 + w**t + w**4 + 1.
-w**2*(w - 1)**2*(w + 1)
Factor -6*q**2 - 2 + 56/3*q.
-2*(q - 3)*(9*q - 1)/3
Solve 47*c - 24*c + 4*c**2 + 4*c**3 - 23*c = 0 for c.
-1, 0
Let a(l) = -2*l**3 - 2*l**2 + 4*l - 4. Let i(d) = -2*d**3 - d**2 + 3*d - 3. Let t(q) = 3*a(q) - 4*i(q). Factor t(z).
2*z**2*(z - 1)
Let z(c) = -10*c - 6*c**2 - 2 + 18*c**2 + 8*c + 7*c. Let d(s) = -18*s**2 - 8*s + 3. Let u(n) = -5*d(n) - 7*z(n). Factor u(b).
(b + 1)*(6*b - 1)
Let a(z) be the second derivative of -3/4*z**2 + 11*z + 0 + 17/20*z**6 - 69/40*z**5 - 1/8*z**3 + 3/2*z**4 - 9/56*z**7. Determine n so that a(n) = 0.
-2/9, 1
Let t(o) be the third derivative of -o**8/60480 + o**7/7560 - o**6/2160 - o**5/30 - o**2. Let k(a) be the third derivative of t(a). Suppose k(h) = 0. What is h?
1
Let f(x) = -x**2 + 9*x - 12. Let l be f(8). Let s(z) = -3*z**2 - 7*z. Let t(a) = 3*a**2 + 6*a. Let p(k) = l*t(k) - 3*s(k). Factor p(w).
-3*w*(w + 1)
Let l(v) be the first derivative of v**5/5 - 3*v**4/4 + v**3 - v**2/2 + 5. Factor l(d).
d*(d - 1)**3
Let -43*y - 1 + 16*y + 19 - 24*y + 15*y**2 = 0. What is y?
2/5, 3
Determine x so that x**2 + 4/5*x**4 - 2/5*x + 11/5*x**3 + 0 = 0.
-2, -1, 0, 1/4
Let m(r) be the first derivative of -r**4/2 - 44*r**3/15 - 28*r**2/5 - 16*r/5 - 14. Factor m(c).
-2*(c + 2)**2*(5*c + 2)/5
Solve -16/5 - 4/5*f**2 + 4*f = 0 for f.
1, 4
Factor 12*b**3 + 0*b**5 - b**5 - 3*b**5 - 4*b**4 + 20*b**2 + 8*b.
-4*b*(b - 2)*(b + 1)**3
Let p(r) be the first derivative of -1/2*r**4 + 0*r - 2/3*r**3 + 1 - 2/15*r**5 - 1/3*r**2. Factor p(x).
-2*x*(x + 1)**3/3
Let q be -1 - (0 + -1 + -3). Suppose -z - h = z - 7, -z - q*h + 1 = 0. Solve -21/4*y**3 - 6*y**2 + 49/4*y**z - y + 0 = 0.
-2/7, 0, 1
Suppose -c = -5*c. Let c + m**2 - 8*m + 9*m + 0 = 0. Calculate m.
-1, 0
Let x(v) = 1 + 4*v**2 + 5*v - v - 5*v + 4. Let k(r) = -2*r**2 - 2. Let f(q) = -5*k(q) - 2*x(q). Suppose f(m) = 0. Calculate m.
-1, 0
Let m be (6/4)/((-1)/(-2)). Let k(f) be the second derivative of -21/10*f**6 - 109/40*f**5 - 1/3*f**m - 3/2*f**4 - 7/12*f**7 - f + 0*f**2 + 0. Factor k(w).
-w*(w + 1)**2*(7*w + 2)**2/2
Let v(o) be the first derivative of 1/2*o**6 + 0*o - 3/4*o**4 + 0*o**2 - 8 + 3/5*o**5 - o**3. Factor v(i).
3*i**2*(i - 1)*(i + 1)**2
Let l(s) = 6*s**2 + 2*s - 8. Let g(c) = 13*c**2 + 5*c - 15. Let y(u) = -4*g(u) + 9*l(u). Factor y(p).
2*(p - 3)*(p + 2)
Let y(d) be the third derivative of d**7/1995 + d**6/570 - d**4/114 - d**3/57 - 11*d**2. What is l in y(l) = 0?
-1, 1
Let v(d) = 4*d - 4. Let q(a) = a**2 - 2*a**2 + 0*a**2 + a. Let s(p) = -2*q(p) + v(p). Suppose s(z) = 0. What is z?
-2, 1
Determine p, given that 10*p**2 + 20*p**2 - 24 - 26 + 45*p - 25*p**2 = 0.
-10, 1
Suppose 0 = 4*t - 6*t. Factor -3*y**2 + 4*y - 2*y + t*y + 5*y**2.
2*y*(y + 1)
Let 4/5*w + 4/5 - 1/5*w**4 - 3/5*w**2 - 4/5*w**3 = 0. Calculate w.
-2, -1, 1
Suppose 5*d = 2*x + 14, -2*d + 7 + 1 = -2*x. What is k in 0*k + 1/4*k**3 - 1/4*k**5 + 1/4*k**d - 1/4*k**4 + 0 = 0?
-1, 0, 1
Let g(o) be the third derivative of -1/40*o**5 + 1/40*o**7 - 1/48*o**6 + 1/24*o**3 - 3/448*o**8 + 1/32*o**4 + 4*o**2 + 0*o + 0. Factor g(w).
-(w - 1)**3*(3*w + 1)**2/4
Let o be (-1248)/33 - 10/55. Let b = o + 153/4. Determine z so that -1/4 + 1/4*z + 1/4*z**2 - b*z**3 = 0.
-1, 1
Let g(w) be the second derivative of w**5/140 - w**4/28 + w**3/14 - w**2 - w. Let y(s) be the first derivative of g(s). Suppose y(h) = 0. What is h?
1
Let z(n) = -2*n**3 + 4*n**2 - 3*n. Let s(l) = l**3 - 4*l**2 + 2*l. Let f(v) = 3*s(v) + 2*z(v). Find r, given that f(r) = 0.
-4, 0
Let u(y) = 2*y**2 - y + 1. Let s be u(1). Let 3*j**s - 3 + 3*j + 3 + 3*j**2 = 0. Calculate j.
-1/2, 0
Let w(l) = l**3 + l**2 + l + 1. Let a(i) = -4*i**3 - 3*i**2 - 3*i - 4. Suppose j = 3*j + 8. Let x(f) = j*a(f) - 14*w(f)