 5*d. Let k(y) = 4*n(y) + 3*v(y). Find b, given that k(b) = 0.
0
Let d(c) = -4*c**3 + 13*c**2 + 33*c + 11. Let t(w) = 2*w**3 - 7*w**2 - 17*w - 5. Let z(h) = 6*d(h) + 10*t(h). Factor z(r).
-4*(r - 4)*(r + 1)**2
Let s(i) be the third derivative of -i**8/6720 - i**7/1680 + i**5/30 + 2*i**2. Let o(j) be the third derivative of s(j). Factor o(y).
-3*y*(y + 1)
Suppose 70*f - 30*f = 0. Factor f - 2/5*n - 1/5*n**2.
-n*(n + 2)/5
Suppose 0 = 11*a - 6*a. Suppose a - 8/5*c**3 - 2/5*c - 2*c**2 = 0. What is c?
-1, -1/4, 0
Let b = -156 + 475/3. Let n = b + -2. Find s such that s**2 + s**3 + n*s + 0 + 1/3*s**4 = 0.
-1, 0
Let h(j) = -j**2 + 6*j - 1. Let s be h(5). Suppose -2*u = -5*m + s, 5*m - 4*u = u - 5. Factor 2 - 4*f**m - 4*f - 4 + 2*f**2.
-2*(f + 1)**2
Let l(z) be the first derivative of 3/8*z**4 + 4 + 0*z - 1/2*z**3 - 3/2*z**2. Find y such that l(y) = 0.
-1, 0, 2
Let y(z) be the third derivative of z**6/180 - z**5/90 - z**4/36 + z**3/9 - 20*z**2. Find n, given that y(n) = 0.
-1, 1
Let n be (10/(-14))/5 + 30/14. Let q(x) be the first derivative of -x**4 + 2/5*x**5 + 0*x + 2/3*x**3 - 2 + 0*x**n. Solve q(u) = 0 for u.
0, 1
Suppose 8 = -4*p, -2*p = -5*w + 3*p + 40. Determine g, given that -8*g - 7*g**2 - w*g**2 + 1 + 22*g**3 - 2 + 32*g**4 - 32*g**5 = 0.
-1/2, -1/4, 1
Let s be 98/45 - (-36)/(-90). What is c in 16/9*c + 2/9 - 32/9*c**4 - s*c**3 + 10/3*c**2 = 0?
-1, -1/4, 1
Suppose -4 = -k + 1. Suppose 13 + 7 = k*a. Determine o so that -2*o**a + 3*o - 2*o**5 - 2*o**4 - o + 4*o**2 = 0.
-1, 0, 1
Let u(t) be the first derivative of t**4/12 - 3. Solve u(f) = 0.
0
Let x = 62 + -62. Find y, given that 0*y**2 - 1/3*y**5 + 0*y**3 + 0*y**4 + 0*y + x = 0.
0
Let u(m) = -m**4 + m**3 + m**2. Let q(v) = -5*v**4 + 15*v**3 + 17*v**2 + 4*v. Let j(l) = 2*q(l) - 14*u(l). Factor j(y).
4*y*(y + 1)**2*(y + 2)
Suppose 0 = r + 2*c + 1, 0 = 8*r - 3*r - c - 6. Let x(n) be the first derivative of 1/6*n**3 + n**2 - r + 2*n. What is s in x(s) = 0?
-2
Let w = 112 - 109. Factor -9/5*m**4 - 6/5*m**5 + 3/5*m**2 + 0*m**w + 0 + 0*m.
-3*m**2*(m + 1)**2*(2*m - 1)/5
Let d(u) = u**2 - u + 3. Let l be d(0). Suppose -8*m = 3*x - 4*m - 6, -2*x + 3*m + 4 = 0. Factor -s**x + 3*s**2 + s**l + s + 0*s**2.
s*(s + 1)**2
Let t(i) be the first derivative of -i**7/231 + 2*i**6/165 - i**4/33 + i**3/33 + i + 2. Let a(l) be the first derivative of t(l). Factor a(p).
-2*p*(p - 1)**3*(p + 1)/11
Let v(c) be the third derivative of c**7/350 + c**6/200 - c**5/100 - c**4/40 - 6*c**2. Find z, given that v(z) = 0.
-1, 0, 1
Let y = 10 - 13. Let w be (-7)/y - (-3 + 5). Let 0*a + 1/3*a**3 - 1/3*a**5 + 0 + w*a**4 - 1/3*a**2 = 0. Calculate a.
-1, 0, 1
Let c(j) be the first derivative of -1/32*j**4 - 2 + 1/12*j**3 + j**2 + 1/480*j**6 + 0*j**5 + 0*j. Let b(m) be the second derivative of c(m). Factor b(q).
(q - 1)**2*(q + 2)/4
Suppose -10*g**5 - 4*g**2 + 14*g**5 + g**4 + 2*g**4 - 4*g**3 + g**4 = 0. What is g?
-1, 0, 1
Let p = 3481/30 + -116. Let c(r) be the second derivative of -r + 0*r**2 + 0 - p*r**4 + 0*r**3. Factor c(x).
-2*x**2/5
Suppose 0 = 3*u + 5*m + 40, 3*m + 20 = 2*u + 53. Let x = u - -17. Factor -1/4*k - 1/4*k**x + 0.
-k*(k + 1)/4
Factor -2/5*v**4 - 2/5*v**3 + 2/5*v**2 + 0 + 2/5*v.
-2*v*(v - 1)*(v + 1)**2/5
Let a = 1364/5 + -272. Factor -a*g + 2/5*g**2 + 2/5.
2*(g - 1)**2/5
Suppose -2*w + 34 = -6. Let o be 20/6*4/w. Factor -1/3*u + o*u**2 - 1/3*u**3 + 0.
-u*(u - 1)**2/3
Let s(l) be the third derivative of l**8/2240 - l**7/840 - l**6/240 + l**5/40 - l**4/6 + l**2. Let v(q) be the second derivative of s(q). Factor v(r).
3*(r - 1)**2*(r + 1)
Let k(u) be the second derivative of u**7/21 + 19*u**6/105 + 3*u**5/14 + u**4/42 - 2*u**3/21 + 5*u. Determine f so that k(f) = 0.
-1, 0, 2/7
Let l(d) be the third derivative of d**9/12096 + d**8/3360 + d**7/3360 - d**3/2 + 3*d**2. Let z(j) be the first derivative of l(j). Let z(u) = 0. What is u?
-1, 0
Let w be (-68)/(-144) + (-26)/117. Factor w*f**2 + 0*f + 0.
f**2/4
Let l = -84 - -260/3. Factor 8/3*y**3 + 2/3*y**4 + 0*y + 0 + l*y**2.
2*y**2*(y + 2)**2/3
Let i(k) be the third derivative of 0*k**3 + 0 + 0*k**4 - 1/280*k**7 + 1/80*k**6 + 0*k - 1/80*k**5 + 3*k**2. Factor i(n).
-3*n**2*(n - 1)**2/4
Let q(w) be the first derivative of 5*w**4/16 + 5*w**3/4 + 5*w**2/4 - 11. Factor q(x).
5*x*(x + 1)*(x + 2)/4
Let k(d) = -d**3 - 7*d**2 - 8*d + 1. Let h be k(-6). Suppose -5*f = 3 - h. Let 2*r**4 + 12*r**2 + 2 + 6*r - r**3 + 9*r**3 + f*r = 0. What is r?
-1
Let p(s) be the third derivative of -4*s**7/105 + s**6/10 + 2*s**5/15 - 10*s**2. Suppose p(z) = 0. What is z?
-1/2, 0, 2
Let i(y) = y**4 - y**3 + y**2 + y + 1. Let j(t) = -35*t**4 - 25*t**2 - 15. Let b(s) = 25*i(s) + j(s). Let b(n) = 0. What is n?
-2, -1, -1/2, 1
Suppose -5*p - 547 + 562 = 0. Factor 8/9 - 16/9*o - 2/9*o**p + 10/9*o**2.
-2*(o - 2)**2*(o - 1)/9
Let j be (-2)/((-3)/(-9) - 1). Suppose 0 = -2*s + f + 11, 0 = s + j*f + 4 + 1. Factor 1 - 2 + 5*u - 5*u - s*u + 5*u**2.
(u - 1)*(5*u + 1)
Let u(t) be the first derivative of 1/6*t**4 + t + 2 - 2*t**2 - 1/3*t**3. Let f(o) be the first derivative of u(o). Factor f(a).
2*(a - 2)*(a + 1)
Let i be (8/6)/(-11 + 13). Solve i - 2*n + 4/3*n**2 = 0.
1/2, 1
Suppose 22 = 5*b - 3*f, -5*f + 2 - 24 = -b. Factor 1/3*t + 1/6 + 1/6*t**b.
(t + 1)**2/6
Let h(b) be the third derivative of -b**11/332640 - b**10/151200 + b**5/30 - b**2. Let o(y) be the third derivative of h(y). Factor o(m).
-m**4*(m + 1)
Factor 2*l - 2 - 1/2*l**2.
-(l - 2)**2/2
Determine r, given that 18*r + 290*r**2 + 16*r - 252*r**2 - 4 = 0.
-1, 2/19
Let t(u) be the third derivative of -u**9/30240 + u**8/4480 - u**7/1680 + u**6/1440 + u**4/8 - 3*u**2. Let h(c) be the second derivative of t(c). Factor h(y).
-y*(y - 1)**3/2
Let k(b) = -3*b**5 - 15*b**4 - 39*b**3 - 45*b**2 - 24*b - 3. Let z(p) = -p**4 - p**3 - p**2 - p - 1. Let t(d) = k(d) + 3*z(d). Find a such that t(a) = 0.
-2, -1
Let c(d) be the third derivative of 1/240*d**5 - 1/840*d**7 + 0*d + 0 - 1/480*d**6 - 6*d**2 + 0*d**4 + 0*d**3 + 1/1344*d**8. Factor c(v).
v**2*(v - 1)**2*(v + 1)/4
Let j(v) be the second derivative of v**2 - 1/42*v**7 - 3/2*v**3 + 4/3*v**4 + 0 + 1/5*v**6 + 2*v - 7/10*v**5. Factor j(i).
-(i - 2)*(i - 1)**4
Let u be ((-3)/2*1)/(9/(-12)). Factor 0*y + 3/2*y**3 + 3*y**u + 0.
3*y**2*(y + 2)/2
Let q be ((-3)/12)/(-1)*-27. Let d = 7 + q. Factor 0*p + 0 + 1/4*p**2 + 1/2*p**3 + d*p**4.
p**2*(p + 1)**2/4
Let g be 1/((-2)/(-6)) + 0. Suppose -21 = -3*c + g*w, 0 = c + w - 0 + 1. Suppose -d**3 + d**c - d**2 - d**3 = 0. Calculate d.
-1, 0
Factor 0*u - 1/4*u**3 + 3/4*u**2 + 0.
-u**2*(u - 3)/4
Let n(p) be the third derivative of p**5/60 + p**4/24 + 60*p**2. Factor n(c).
c*(c + 1)
Determine i so that -6/7*i + 0 - 3/7*i**2 + 3/7*i**3 = 0.
-1, 0, 2
Suppose -2*q + 12 = 4*p - p, -4*q + 3*p + 6 = 0. Factor -4/7 - 18/7*k - 20/7*k**2 - 6/7*k**q.
-2*(k + 1)*(k + 2)*(3*k + 1)/7
Let n(m) be the third derivative of m**2 + 0*m + 0*m**5 - 1/4*m**4 + 0 + 1/70*m**7 - 1/2*m**3 + 1/20*m**6. Factor n(j).
3*(j - 1)*(j + 1)**3
Let q(h) be the first derivative of h**6/24 + 7*h**5/20 + h**4 + 2*h**3/3 - 2*h**2 - 4*h - 5. Let q(r) = 0. What is r?
-2, 1
Suppose -2/9 + 4/9*j**2 + 0*j - 2/9*j**4 + 0*j**3 = 0. Calculate j.
-1, 1
Let q(n) be the second derivative of 0*n**2 - n + 0*n**3 + 1/18*n**4 + 0 + 1/63*n**7 - 1/30*n**5 - 1/45*n**6. Factor q(w).
2*w**2*(w - 1)**2*(w + 1)/3
Let x(k) = 12*k**4 - 8*k**3 - 12*k**2 + 8*k + 7. Let f(u) = 6*u**4 - 4*u**3 - 6*u**2 + 4*u + 4. Let t(i) = -7*f(i) + 4*x(i). Factor t(a).
2*a*(a - 1)*(a + 1)*(3*a - 2)
Let n(l) be the third derivative of l**5/60 + l**4/4 + 3*l**3/2 - 10*l**2. Factor n(i).
(i + 3)**2
Factor 0*p**2 + 0*p + 0 + 0*p**4 + 0*p**3 + 2/7*p**5.
2*p**5/7
Let 1 + 2 - 35*k + 12 + 25*k**2 - 5*k**3 = 0. Calculate k.
1, 3
Let z(w) be the first derivative of -w**5/75 - w**4/30 + w**2 + 1. Let f(c) be the second derivative of z(c). Let f(h) = 0. Calculate h.
-1, 0
Let x(w) be the first derivative of w**3/7 + 9*w**2/14 - 12*w/7 + 31. Find b, given that x(b) = 0.
-4, 1
Let p(y) be the second derivative of -5*y**7/147 - 13*y**6/105 - 9*y**5/70 + y**4/42 + 2*y**3/21 + 5*y. Solve p(l) = 0.
-1, 0, 2/5
Let h(u) be the second derivative of -u**8/2240 + u**6/240 + u**4/6 - 3*u. Let k(a) be the third derivative of h(a). Let k(g) = 0. Calculate g.
-1, 0, 1
Let d be (1/1)/((-3)