i - 64.
-4*(i - 4)**2
Let g(y) = -9*y**4 + 72*y**3 + 165*y**2 + 141*y + 57. Let b(j) = 2*j**4 - 18*j**3 - 41*j**2 - 35*j - 14. Let w(v) = 21*b(v) + 5*g(v). Factor w(n).
-3*(n + 1)**3*(n + 3)
Let y(m) = m**2 + 6*m + 5. Let x be y(-5). Let t = -11 - -15. Suppose x*h**4 + h**t + 5*h**3 - 4*h**3 = 0. What is h?
-1, 0
Let w = -2/13 - -122/117. Factor 4/3*a**3 - 26/9*a**2 + 8/3*a - 2/9*a**4 - w.
-2*(a - 2)**2*(a - 1)**2/9
Let f be 2/(-10) + 143/65. Let b(y) be the second derivative of -y + 0 - 1/3*y**f - 1/6*y**4 - 1/3*y**3 - 1/30*y**5. Solve b(m) = 0.
-1
Let x(h) be the first derivative of -3*h**3/2 - 3*h**2 - 3*h/2 - 25. Factor x(k).
-3*(k + 1)*(3*k + 1)/2
Let d = -390/7 + 56. Factor -d + 2/7*j**2 + 0*j.
2*(j - 1)*(j + 1)/7
Let n = 15631/7440 + -65/31. Let b(y) be the third derivative of y**2 + 1/12*y**3 + 1/48*y**4 - 1/120*y**5 + 0*y - n*y**6 + 0. Find f, given that b(f) = 0.
-1, 1
Factor 7*j**3 - 10*j - 5*j + 21*j - 23*j**2 + 0*j.
j*(j - 3)*(7*j - 2)
Let k be (-354)/(-295)*5/3. Solve -3/4*z + 0 - 1/4*z**k = 0 for z.
-3, 0
Let v(k) = k**5 - k**4 - k**2 - 1. Let p(m) = 20*m**5 - 10*m**4 + 8*m**3 - 22*m**2 - 10*m - 22. Let y(u) = -2*p(u) + 36*v(u). Suppose y(t) = 0. Calculate t.
-2, -1, 1
Suppose -4*u = -6*u + 20. Suppose u = 2*j + 3*j. Factor -2/5*k**3 + 2/5*k - 2/5 + 2/5*k**j.
-2*(k - 1)**2*(k + 1)/5
Let c(a) = a**2 - 9*a + 11. Let p be c(8). Let -4/5*t**2 - 18/5*t**5 + 18/5*t**p + 4/5*t**4 + 0 + 0*t = 0. Calculate t.
-1, 0, 2/9, 1
Factor 0 - 1/4*r - 1/8*r**3 - 3/8*r**2.
-r*(r + 1)*(r + 2)/8
Let h(j) be the first derivative of -3*j**5/40 - j**4/12 + j**3/4 + j**2/2 + 8*j - 2. Let n(z) be the first derivative of h(z). Determine m so that n(m) = 0.
-1, -2/3, 1
Factor -32/3*a + 10/3 + 19/2*a**2 - 3/2*a**3.
-(a - 5)*(3*a - 2)**2/6
Factor -4*s + 26*s**2 - 24*s**2 + s - s.
2*s*(s - 2)
Let z(h) be the second derivative of h**7/840 - h**5/40 + h**4/4 + 5*h. Let y(i) be the third derivative of z(i). Factor y(x).
3*(x - 1)*(x + 1)
Let d be (0 - (-12)/8) + -1. Let w(f) be the first derivative of -3*f**2 - 2 + 8/3*f**3 - 9/5*f**5 + f + d*f**4 + 2/3*f**6. Factor w(b).
(b - 1)**3*(b + 1)*(4*b - 1)
Factor -5/2*t**4 + 5*t**2 + 0 + 0*t - 5/2*t**3.
-5*t**2*(t - 1)*(t + 2)/2
Let x(q) = 3*q + 16. Let h be x(-8). Let n = -5 - h. Let -1/4*j**5 + 3/4*j**n + 0 + j**2 - 1/2*j**4 - j = 0. Calculate j.
-2, 0, 1
Let h = 5/22 - 19/132. Let s(p) be the second derivative of 0 + 4*p + 0*p**2 - h*p**4 + 1/6*p**3. Factor s(x).
-x*(x - 1)
Let v(a) = a**3 - 6*a**2 - 7*a + 1. Suppose 2*r - 39 = -5*w, -5*w + 0*r = -r - 33. Let p be v(w). Factor 3/2*b - p + 3/2*b**3 + 4*b**2.
(b + 1)*(b + 2)*(3*b - 1)/2
Let r(a) be the third derivative of a**6/10 - 7*a**5/15 + 8*a**3/3 - 16*a**2. Solve r(h) = 0 for h.
-2/3, 1, 2
Suppose 5*a = -p + 10, -2*a + 0*a - 9 = 3*p. Determine t, given that 0 - 4/9*t**2 + 0*t - 2/9*t**a = 0.
-2, 0
Let q be 2/((-6)/9) - 1. Let m be (0*(-1)/q)/(-2). Determine l, given that -2/3*l**2 + 0*l + m = 0.
0
Determine q so that -3/2*q**3 + 15/2*q**2 + 9/2 - 21/2*q = 0.
1, 3
Let t(p) be the second derivative of p**7/840 - p**5/80 - p**4/48 - p**2 - 4*p. Let f(d) be the first derivative of t(d). Determine u, given that f(u) = 0.
-1, 0, 2
Let j(n) be the second derivative of 2*n**7/21 - 16*n**6/45 + 7*n**5/15 - 2*n**4/9 - 16*n. Find m such that j(m) = 0.
0, 2/3, 1
Let r(s) be the third derivative of 1/168*s**8 - 1/3*s**3 - 1/15*s**5 - 3*s**2 + 1/35*s**7 - 1/4*s**4 + 1/30*s**6 + 0*s + 0. Suppose r(m) = 0. Calculate m.
-1, 1
Let k(w) be the first derivative of -2*w**5/45 + w**4/18 + 2*w**3/3 + 11*w**2/9 + 8*w/9 - 11. Factor k(m).
-2*(m - 4)*(m + 1)**3/9
Let o(g) be the third derivative of g**2 + 0*g**5 + 0*g - 1/21*g**3 + 1/840*g**6 + 0 - 1/56*g**4. Factor o(z).
(z - 2)*(z + 1)**2/7
Solve -5*o**4 - 2*o**3 - o**5 - 5*o**3 + 9 - 5 + o**2 + 12*o - 4*o = 0.
-2, -1, 1
Factor -3/7*f**2 + 15/7*f - 12/7.
-3*(f - 4)*(f - 1)/7
Let a(b) be the third derivative of b**7/210 + b**6/30 + b**5/12 + b**4/12 - 14*b**2. Factor a(d).
d*(d + 1)**2*(d + 2)
Let x(d) = 3*d**2 - 4*d. Let f be x(3). Let -6*h**2 - 7*h**4 + 4*h**3 + h**4 - h - f*h**3 = 0. What is h?
-1, -1/2, -1/3, 0
Let n(m) = -m + 12. Let b be n(9). Find y, given that 2/5*y**b + 0*y**2 - 2/5*y + 0 = 0.
-1, 0, 1
Let r(i) be the second derivative of -i**4/30 - i**3/15 - 2*i. Suppose r(l) = 0. What is l?
-1, 0
Let q(o) = -5*o**2 - 8*o - 3. Let v(c) = c**2 + c. Let f(u) = -q(u) - 6*v(u). What is w in f(w) = 0?
-1, 3
Let a(b) be the first derivative of 2/15*b**3 + 3/5*b**2 + 4/5*b + 3. Factor a(x).
2*(x + 1)*(x + 2)/5
Let o(m) be the third derivative of m**8/20160 - m**7/7560 - m**4/8 + 2*m**2. Let b(z) be the second derivative of o(z). Factor b(y).
y**2*(y - 1)/3
Let z(d) = d**2 - 6*d - 1. Let f = 3 - 9. Let l(y) = -2*y**2 + 11*y + 2. Let s(v) = f*l(v) - 11*z(v). Factor s(q).
(q - 1)*(q + 1)
Let x(o) be the third derivative of o**5/390 + o**4/156 - 2*o**3/39 - 6*o**2. Find f such that x(f) = 0.
-2, 1
Suppose -2*z = 6, -2*z + 72 = 5*o - 6*z. Suppose 5*m - 3 = 2*v + o, -m = -3*v - 3. Factor -14*c**4 + c**3 + 0*c**5 - 2*c**m - 3*c**3 - 10*c**5.
-2*c**3*(c + 1)*(5*c + 2)
Let t(v) be the first derivative of -1/2*v**4 + 2/5*v**3 + 1 + 2/5*v**2 + 0*v. Factor t(o).
-2*o*(o - 1)*(5*o + 2)/5
Find l, given that -3*l + 1 - 1 + 0*l**2 + 3*l**2 = 0.
0, 1
Let r = 24 - 16. Let c be 7/28*r/6. Suppose 0*i + 1/3 - c*i**2 = 0. What is i?
-1, 1
Factor 0*r - 1/7*r**4 + 0*r**2 + 0 - 1/7*r**3.
-r**3*(r + 1)/7
Let r(v) = 4*v**5 + 6*v**3 - v**2 + 3*v - 3. Let n(s) = 23*s**5 - s**4 + 35*s**3 - 6*s**2 + 17*s - 17. Let a(l) = 6*n(l) - 34*r(l). Factor a(p).
2*p**2*(p - 1)**3
Factor -5/6*v**2 - 1/6*v + 0.
-v*(5*v + 1)/6
Suppose -2*g - 10 = -g. Let n = g - -10. What is u in n*u - 2/5*u**2 - 2/5*u**3 + 0 = 0?
-1, 0
Let n(c) = 4*c**2. Let w(h) = 11*h**2 - 7*h + 2. Let x(m) = 20*n(m) - 4*w(m). Factor x(d).
4*(d + 1)*(9*d - 2)
Suppose -7*u = -10*u + 5*d - 13, -5*d = 3*u - 37. Factor 0*c**3 + 0*c + 0 - 1/2*c**2 + 1/2*c**u.
c**2*(c - 1)*(c + 1)/2
Let x(z) = -6*z**2 - z - 2. Let r(t) = -t**2 - t - 1. Let d(a) = 3*r(a) - x(a). Let d(g) = 0. Calculate g.
-1/3, 1
Let k(v) be the second derivative of 1/15*v**4 - 1/10*v**5 + 0*v**3 - 2*v + 4/75*v**6 + 0 - 1/105*v**7 + 0*v**2. Factor k(d).
-2*d**2*(d - 2)*(d - 1)**2/5
Let h(n) be the first derivative of n**5/20 + n**4/8 - n**3 + 5*n**2/2 - 1. Let a(b) be the second derivative of h(b). Factor a(r).
3*(r - 1)*(r + 2)
Factor -5/6*r + 0 - 1/6*r**3 + r**2.
-r*(r - 5)*(r - 1)/6
Suppose -n = 5*g + 22, -4*n - 8 = 2*g + 2*g. Factor -2/3*s + 0 + 8/9*s**n - 22/9*s**2.
2*s*(s - 3)*(4*s + 1)/9
Factor -l**3 - 5*l**4 + 9*l**4 + 5*l**3.
4*l**3*(l + 1)
Let p(u) be the second derivative of 1/10*u**3 - 1/5*u**2 + 1/150*u**6 + 0 - 3/100*u**5 - u + 1/60*u**4. Factor p(j).
(j - 2)*(j - 1)**2*(j + 1)/5
Let u = -4/7 - -50/63. Determine n, given that -u*n**2 + 0*n + 0 + 0*n**3 + 2/9*n**4 = 0.
-1, 0, 1
Factor 0 + 3*a**2 + 3/2*a**3 + 0*a - 3/2*a**4.
-3*a**2*(a - 2)*(a + 1)/2
Let -170/9*l - 8*l**3 + 64/3*l**2 + 50/9 = 0. What is l?
5/6, 1
Factor -22*i**4 - 89*i**3 + 13*i**3 + 16*i - 32*i**2 - 6*i**4.
-4*i*(i + 1)*(i + 2)*(7*i - 2)
Let p(s) be the second derivative of s**5/80 - s**4/48 - s**3/24 + s**2/8 + 5*s. Determine v so that p(v) = 0.
-1, 1
Factor -1/4*u**3 + 1/4*u**5 + 0 + 0*u + 1/2*u**2 - 1/2*u**4.
u**2*(u - 2)*(u - 1)*(u + 1)/4
Suppose 0 = -0*i - 4*i. Suppose 2*p = p + 3*x - 5, -3*p - 2*x + 18 = i. Factor -30*k**4 - p*k**3 + 2*k**5 + 2*k + 30*k**4.
2*k*(k - 1)**2*(k + 1)**2
Let h(r) = r - 1. Let t(j) = -10*j**2 - 6*j + 10. Let s(u) = -10*h(u) - t(u). Factor s(b).
2*b*(5*b - 2)
Let g = 1 - -3. Let u = g - 2. Determine a so that 2*a**u + 20*a**3 - 6*a**2 - 2*a**4 - 26*a**3 = 0.
-2, -1, 0
Suppose -4*d + 7 + 1 = 0. Factor -1/3*h - 1/3*h**d + 1/3 + 1/3*h**3.
(h - 1)**2*(h + 1)/3
Let s be 10/4 + (-5)/(-10). Let f be (-5)/s*(-2)/5. Factor 4/3*i + f*i**2 + 0.
2*i*(i + 2)/3
Let z = -174/5 - -36. Find j such that 0 - 6/5*j**4 + z*j**2 - 8/5*j**5 + 2*j**3 - 2/5*j = 0.
-1, 0, 1/4, 1
Let s be (3/(-6))/(6/(-396)). Let o = s - 30. Factor -3/4*l**o - 3/4*l**4 - 1/4*l**2 + 0 - 1/4*l**5 + 0*l.
-l**2*(l + 1)**3/4
Let v(w) = -w**3 + 12*w**2 - 12*w + 13. Let l be v(11). Suppose l*p + 10 = 7*p. Factor -1/3*y**p + 1/3*y + 2/3.
-(y - 2)*(y + 1)/3
Let u(g) be the second der