/4*f**4 - 3/2*f**3 + 1/10*f**6 + f + 0 - 11/20*f**j. Factor w(x).
(x - 1)**3*(3*x - 2)
Let t(u) = -u**3 - 5*u**2. Let o be t(-5). Factor 2*g**3 + o*g**2 - 5*g**4 + 0*g**2 - g**4.
-2*g**3*(3*g - 1)
Suppose 4*h = -5*r + 19, 0*r + 2*r = 2*h + 4. Factor 2 - 3*p**r + 8*p + 5 + p - 1.
-3*(p - 2)*(p + 1)**2
What is x in 1/2*x + 1/2*x**2 - 1/2 - 1/2*x**3 = 0?
-1, 1
Let h(s) = -3*s**3 - 6*s**2. Let v(d) = -9*d**3 - 17*d**2 + d + 1. Let b be ((-12)/(-10))/(9/60). Let z(o) = b*h(o) - 3*v(o). Factor z(l).
3*(l - 1)*(l + 1)**2
Find f, given that -89/4*f**3 + 25*f**5 + 15/4*f**2 + 9/4*f + 0 + 5/4*f**4 = 0.
-1, -1/4, 0, 3/5
Suppose 3*v = 4*j - 27, 2*v - 7 = -1. Suppose c - j = -2*c. What is n in -4*n**3 - 6*n - 3*n**3 - 3*n**c - 12*n**2 - 3*n**4 - 1 = 0?
-1, -1/3
Let a(k) be the second derivative of -1/2*k**2 + 1/2*k**3 - 5/24*k**6 + 0 - 3/8*k**5 + 11/48*k**4 + 4*k. Factor a(w).
-(w + 1)**2*(5*w - 2)**2/4
Let j(h) be the second derivative of h**7/84 - h**6/12 + 9*h**5/40 - 7*h**4/24 + h**3/6 + 23*h. Suppose j(v) = 0. What is v?
0, 1, 2
Let i(o) = o**2 - 2*o - 11. Let l be i(5). Let x(v) be the first derivative of -3 - 1/2*v**4 + v**2 + l*v - 2*v**3 + 2/5*v**5. Factor x(n).
2*(n - 2)*(n - 1)*(n + 1)**2
Let -4*u**5 - 3*u**3 + 7*u**3 + 7*u**3 - 3*u**3 - 4*u = 0. What is u?
-1, 0, 1
Let i = 184/15 - 48/5. Determine o so that -32/3*o - 6*o**3 + i + 14*o**2 = 0.
2/3, 1
Let d be (8/10)/((-105)/(-25) + -4). Factor -4/5*o - 18/5*o**3 - 14/5*o**2 - 2/5*o**5 - 2*o**d + 0.
-2*o*(o + 1)**3*(o + 2)/5
Let d(w) be the third derivative of -w**7/21 - w**6/20 + 7*w**5/30 + w**4/4 - 2*w**3/3 - 6*w**2. What is o in d(o) = 0?
-1, 2/5, 1
Let p(f) be the second derivative of -f**6/45 + f**5/30 + 5*f. Factor p(b).
-2*b**3*(b - 1)/3
Let i = 52 - 49. Let p(j) be the first derivative of 0*j**2 - 1/24*j**4 + 0*j + 0*j**3 - i. Factor p(w).
-w**3/6
Let w be (4/5)/((-1)/(-5)). Let 3*g**5 + 11 - 3*g**2 - 11 - 3*g**3 + 3*g**w = 0. What is g?
-1, 0, 1
Suppose -186*d - 8 = -188*d. Solve 0 + 0*b + 0*b**3 - 2/7*b**d + 2/7*b**2 = 0 for b.
-1, 0, 1
Let m(t) = 2*t**3 - 6*t**2 + 3*t + 4. Let r(j) = j**3 - 5*j**2 + 2*j + 4. Let x(f) = -2*m(f) + 3*r(f). Determine p so that x(p) = 0.
-2, 1
Factor -22/9*g**4 - 4/9*g + 0 - 2*g**2 - 10/3*g**3 - 2/3*g**5.
-2*g*(g + 1)**3*(3*g + 2)/9
Factor -45*t + 29*t + 0*t**4 + 10*t**3 + 4*t**4 + 2*t**3.
4*t*(t - 1)*(t + 2)**2
Factor 2*a**4 + 2*a - 3*a**4 - a**3 + 8*a**2 - a**3 - 7*a**2.
-a*(a - 1)*(a + 1)*(a + 2)
Let t(f) = -f**4 - f**3 + 2*f**2 - f. Let u(q) = 18*q**3 + 76*q**2 + 110*q + 64. Let a(y) = 4*t(y) - 2*u(y). Solve a(w) = 0 for w.
-4, -2
Let p be 34/5 + (-12)/(-15). Let b(a) be the first derivative of -6*a**2 - 8/5*a + 2 + 147/25*a**5 - p*a**3 + 7/4*a**4. Suppose b(u) = 0. Calculate u.
-2/3, -2/7, 1
Let o = -39/10 - -27/5. Let a(p) = -3*p**2 - 42*p. Let r be a(-14). Factor 0 - 3/2*v**3 + r*v**2 + o*v.
-3*v*(v - 1)*(v + 1)/2
Let d(f) = -8*f**2 - 4*f + 8. Let q(i) = 32*i**2 + 17*i - 33. Suppose 3*h - 36 = -h. Let c(s) = h*d(s) + 2*q(s). Solve c(x) = 0 for x.
-1, 3/4
Let u = 83 + -81. Factor 0 + 1/3*q**3 + 1/3*q**u + 0*q.
q**2*(q + 1)/3
Let y(o) be the second derivative of 3*o**5/100 + o**4/10 + o**3/10 + 8*o. Factor y(n).
3*n*(n + 1)**2/5
Let p(x) be the first derivative of -x**6/18 - 2*x**5/15 + x**4/4 + 4*x**3/9 - 2*x**2/3 + 6. Factor p(z).
-z*(z - 1)**2*(z + 2)**2/3
Suppose 2*v - 8 = 4*s - 2*s, v - 2*s - 6 = 0. Factor 0 - 1/4*l**v - 1/4*l.
-l*(l + 1)/4
Let n(o) be the third derivative of -o**6/1440 + o**4/96 + o**3/3 - 2*o**2. Let y(w) be the first derivative of n(w). Let y(a) = 0. Calculate a.
-1, 1
Let x(y) be the third derivative of 0*y**3 + 2*y**2 + 0*y + 1/40*y**6 + 1/10*y**5 + 0 + 1/8*y**4. Factor x(l).
3*l*(l + 1)**2
Let g = 19 - 15. Suppose 2*y = g, -2*h - y = -6*h + 6. Factor 1/2*c**3 + c**h - 1/2*c**4 + 0*c + 0.
-c**2*(c - 2)*(c + 1)/2
Determine x so that 0*x**2 - 6*x - x**2 - 11 + 0*x**2 + 2 = 0.
-3
Let m(h) be the first derivative of -1/2*h - 1/2*h**2 - 1/6*h**3 - 3. Factor m(d).
-(d + 1)**2/2
Let a be (-1 - (-5)/3) + 0/99. Solve a*t**2 + 7/3*t**3 + 0*t + 0 + 5/3*t**4 = 0.
-1, -2/5, 0
Suppose 2*i - 7*i - 5 = 0. Let a(x) = 3*x**2 - 7*x + 5. Let r(u) be the first derivative of u**3/3 - u**2/2 + u - 1. Let n(j) = i*a(j) + r(j). Factor n(p).
-2*(p - 2)*(p - 1)
Let s(c) be the third derivative of 0 - 1/18*c**4 + 1/90*c**5 - 3*c**2 + 0*c + 1/9*c**3. Factor s(k).
2*(k - 1)**2/3
Let j(h) be the second derivative of h**4/18 - 2*h**3/9 + 13*h. Find c such that j(c) = 0.
0, 2
Let i(n) be the second derivative of 2*n**7/21 + 4*n**6/15 - 3*n**5/5 - 4*n**4/3 + 8*n**3/3 + 3*n. Factor i(d).
4*d*(d - 1)**2*(d + 2)**2
Let c = -331/4 + 83. Factor 0 - 1/4*a**2 + c*a.
-a*(a - 1)/4
Let r(t) = t**4 + t**3 - t**2 - 1. Let x(b) = 18*b**4 - 2*b**3 - 18*b**2 + 8*b - 6. Let h(v) = 6*r(v) - x(v). Let h(z) = 0. What is z?
-1, 0, 2/3, 1
Let i be 4/8 + 3/6. Let c be 33/18 - i/2. Factor -2/3*y**4 - 2/3 + c*y**2 + 0*y + 0*y**3.
-2*(y - 1)**2*(y + 1)**2/3
Let h(s) be the third derivative of -1/1050*s**7 + 0 - 1/150*s**6 + 3*s**2 + 0*s - 1/50*s**5 - 1/30*s**3 - 1/30*s**4. Factor h(o).
-(o + 1)**4/5
Let w(p) be the third derivative of p**2 + 1/18*p**3 + 1/180*p**5 - 1/36*p**4 + 0*p + 0. Factor w(b).
(b - 1)**2/3
Let b(o) be the first derivative of -o**7/70 - o**6/120 + 3*o**5/20 - o**4/8 - o**3/3 - o**2 + 3. Let a(u) be the second derivative of b(u). Solve a(k) = 0.
-2, -1/3, 1
Let w(f) be the third derivative of f**9/75600 + f**8/33600 - f**7/6300 - f**4/8 - f**2. Let i(h) be the second derivative of w(h). Solve i(m) = 0.
-2, 0, 1
Let q = 1062863/180 + -5905. Let n = 1/60 - q. Determine h so that n - 4/9*h + 2/9*h**2 = 0.
1
Let q(y) be the first derivative of -y**5/15 - y**4/2 - 4*y**3/3 - 5*y**2/2 - 9. Let x(h) be the second derivative of q(h). Suppose x(c) = 0. Calculate c.
-2, -1
Let o(n) be the second derivative of n**4/96 + n**3/48 + 5*n. Suppose o(g) = 0. What is g?
-1, 0
Let c(q) be the second derivative of -q**6/720 + q**5/60 - q**4/12 - q**3/6 + 5*q. Let o(t) be the second derivative of c(t). Let o(p) = 0. What is p?
2
Let f(c) = c - 1. Let b(w) = 4*w**2 - 15*w + 3. Let j(x) = -b(x) - 3*f(x). Factor j(l).
-4*l*(l - 3)
Let c(s) = -18*s**4 - 21*s**3 - 45*s**2 - 9*s + 6. Let q(k) = -k**4 + k**3 - k**2 + k + 1. Let a(r) = c(r) - 9*q(r). Factor a(f).
-3*(f + 1)**3*(3*f + 1)
Let j(s) be the third derivative of 2*s**7/735 + s**6/210 - s**5/105 - s**4/42 - 20*s**2. Determine u, given that j(u) = 0.
-1, 0, 1
Let g(o) be the second derivative of 3*o**5/20 - o**4/4 + 2*o**3/3 - 3*o. Let z(q) = -5*q**3 + 5*q**2 - 7*q. Let a(k) = 7*g(k) + 4*z(k). Factor a(p).
p**2*(p - 1)
Determine a, given that -4/11*a**2 + 0*a + 14/11*a**3 + 0 = 0.
0, 2/7
Factor 3/4*i**2 + 27/4 - 9/2*i.
3*(i - 3)**2/4
Let y(t) = -t**3 - 3*t**2 + 3*t - 1. Let m be y(-4). Let h = 5 - m. Find k such that 0 + 0*k - 1/4*k**h = 0.
0
Let k(h) be the second derivative of -h**6/5 - h**5/5 - 5*h. Solve k(t) = 0.
-2/3, 0
Let c(v) be the second derivative of v**6/20 + v**5/40 - v**4/3 + v**3/3 + 10*v. Factor c(x).
x*(x - 1)*(x + 2)*(3*x - 2)/2
Let y(u) be the second derivative of -1/42*u**4 + 0*u**2 - 2/21*u**3 - 2*u + 0. Factor y(f).
-2*f*(f + 2)/7
Let a(m) be the second derivative of -5*m**7/42 + m**6/3 - m**5/4 - 12*m. Factor a(o).
-5*o**3*(o - 1)**2
Let o(i) = i**3 - 7*i**2 - 9*i + 12. Let c be o(8). Suppose -5*k - 3*h = -3, -4*k + 3*h = c - 1. Determine b so that -2 + 4*b**2 + 4*b**2 - 6*b + k = 0.
-1/4, 1
Let h(p) be the third derivative of p**6/360 - p**5/20 + 3*p**4/8 - 2*p**3/3 - p**2. Let c(r) be the first derivative of h(r). Determine m so that c(m) = 0.
3
Let s be (-49)/(-196) - (1 + -1). Find q, given that 0*q**2 - 1/4*q - s*q**5 + 1/2*q**3 + 0*q**4 + 0 = 0.
-1, 0, 1
Let n(r) be the third derivative of r**7/1470 + r**6/420 - r**4/84 - r**3/42 - 10*r**2. Factor n(m).
(m - 1)*(m + 1)**3/7
Let w(q) be the third derivative of -q**8/2352 - q**7/1470 + q**6/280 + q**5/84 + q**4/84 + 5*q**2. Factor w(a).
-a*(a - 2)*(a + 1)**3/7
Let x(h) be the third derivative of 1/8*h**4 + 0*h - 1/40*h**6 - 2*h**2 - 1/2*h**3 + 0 + 1/20*h**5. Solve x(u) = 0 for u.
-1, 1
Let x be (-1120)/(-240) - (4 - 0/2). Suppose -2/3 - x*u**2 - 4/3*u = 0. What is u?
-1
Suppose 20 = 5*b, -b + 14 = 5*d - 5. Let z = -3/4 - -5/4. Factor -1/2 - 1/2*v**d 