r(b) be the third derivative of b**7/1680 - b**6/360 + b**5/240 - b**3/6 - 2*b**2. Let u(d) be the first derivative of r(d). Solve u(p) = 0 for p.
0, 1
Find b such that 0*b - 1/3*b**2 + 0 = 0.
0
What is u in -3/8*u**2 + 1/8*u**3 - 1/8 + 3/8*u = 0?
1
Factor -7*c - 16 - 3*c**2 - c**2 + 9*c + 18*c.
-4*(c - 4)*(c - 1)
Let m(u) = -2*u**2 - 2*u - 8. Let a(n) = n - 1. Let j(t) = -4*a(t) + m(t). Factor j(c).
-2*(c + 1)*(c + 2)
Let y = 7/22 - -9/110. Factor -y*x**3 - 2/5*x**4 + 0 + 2/5*x**5 + 2/5*x**2 + 0*x.
2*x**2*(x - 1)**2*(x + 1)/5
Factor -6/7*z**3 + 0 + 0*z + 6/7*z**2.
-6*z**2*(z - 1)/7
Let -4/7*v**3 + 0 - 16/7*v + 16/7*v**2 = 0. What is v?
0, 2
Suppose -6*y = -3*y - 9. Find b, given that -3*b**2 - y + 3 - 9*b - 6 = 0.
-2, -1
Let m(a) = -a**3 - 23*a**2 - 42*a + 2. Let n be m(-21). Let r(o) be the third derivative of 1/30*o**5 - n*o**2 + 0 + 1/3*o**3 + 0*o + 1/6*o**4. Factor r(u).
2*(u + 1)**2
Let t(x) = x + 13. Let o be t(-11). Let w(b) be the first derivative of -4/3*b**3 + 4/5*b**5 - 1/2*b**4 + 0*b + b**o - 2. What is q in w(q) = 0?
-1, 0, 1/2, 1
Let q = 1015/3 + -333. Let o(a) be the first derivative of 19/2*a**4 + q*a**3 + 4 + 0*a - 4*a**2 + 14/5*a**5. Determine c, given that o(c) = 0.
-2, -1, 0, 2/7
Let a(z) be the first derivative of -1/3*z**3 + 3/10*z**5 + 1/4*z**4 + 1/12*z**6 - 1/2*z - 3/4*z**2 - 2. Factor a(p).
(p - 1)*(p + 1)**4/2
Let n(z) be the second derivative of z**3/6 - z**2/2 + 2*z. Let o be n(5). Factor -8*j + 0*j**2 - 3*j**2 - j**3 - o - 2*j**2.
-(j + 1)*(j + 2)**2
Let a(h) = 3*h**3 - 10*h**2 - 21*h - 3. Let i(r) = 2*r**3 - 10*r**2 - 20*r - 4. Let z(n) = -4*a(n) + 5*i(n). Solve z(w) = 0.
-2, -1
Let c(z) be the first derivative of -3*z**5/10 + 3*z**4/2 + 5*z**3/2 + 30. What is r in c(r) = 0?
-1, 0, 5
Let f(z) = 5*z**3 - 3*z**2 - 2*z. Let s(i) = i**2 + i - i**2 + i**2 - 2*i**3. Let c(u) = 3*f(u) + 7*s(u). Solve c(t) = 0 for t.
0, 1
Factor 0 + 2*f**4 + f**2 + 5/2*f**3 + 0*f + 1/2*f**5.
f**2*(f + 1)**2*(f + 2)/2
Factor 8 - 3*r - 2*r**2 + 4 + 0*r + r.
-2*(r - 2)*(r + 3)
Suppose 0*t + 8 = 4*t. Suppose t*k = -3*k + 10. Factor -k*x**4 + 4*x**5 + 0*x**3 + 4*x**5 - x**3.
x**3*(2*x - 1)*(4*x + 1)
Let r(g) = -g**2 - 11*g - 4. Let o be r(-7). Suppose 5*l - l = 4*u + 4, u - o = -4*l. Factor -v**2 - v**l + 0*v**5 + 4*v**4 + v**3 - 3*v**4.
-v**2*(v - 1)**2*(v + 1)
Let q(k) = -k**3. Let a(p) = -18*p**4 - 11*p**3 + 10*p**2 - 2*p. Let j = -4 - -9. Let m(d) = j*q(d) - a(d). Factor m(l).
2*l*(l + 1)*(3*l - 1)**2
Let l(p) = p**2 + 5*p. Let o = 9 + -3. Let d = 27 + -10. Let s(x) = -3*x**2 - 14*x. Let k(n) = d*l(n) + o*s(n). Factor k(q).
-q*(q - 1)
Let q(l) be the second derivative of l**5/5 + l**4/3 - 2*l**3/3 - 2*l**2 + 12*l. Factor q(s).
4*(s - 1)*(s + 1)**2
Let h(l) = -3*l**3 + 8*l**2 - 8*l. Let o(b) = 2*b**3 - 5*b**2 + 5*b. Let q(f) = -5*h(f) - 7*o(f). Let z be q(4). Factor 2*m**2 - m**2 - z*m**2 + 4*m**2.
m**2
Suppose -29*u + 15 = -24*u. Let z(g) be the first derivative of 1/2*g**4 + g**2 + 4/3*g**u + 0*g + 1. Factor z(b).
2*b*(b + 1)**2
Suppose 2*p + 10 = b - 0*p, -2*b - 2*p + 2 = 0. Let q be 4/(-6) + b/6. Factor 2/3*j**2 + q - 2/3*j**3 + 0*j.
-2*j**2*(j - 1)/3
Let q be 4*(3 - (-13)/(-2)). Let c = 16 + q. Find o such that -2/3*o + 1/3 + 1/3*o**c = 0.
1
Let u(y) be the third derivative of -y**7/63 + 11*y**6/90 - 11*y**5/30 + 5*y**4/9 - 4*y**3/9 + 3*y**2. Solve u(o) = 0 for o.
2/5, 1, 2
Let j(x) be the second derivative of x**4/12 - x**3/6 + x**2/8 - 18*x. Factor j(v).
(2*v - 1)**2/4
Let t = 38 - 189/5. Factor -1/5*d**3 + 1/5*d - 1/5*d**4 + t*d**2 + 0.
-d*(d - 1)*(d + 1)**2/5
Factor 4/5*v**4 + 0*v**3 + 0 - 4/5*v**2 + 0*v.
4*v**2*(v - 1)*(v + 1)/5
Let v = 6 - 7. Let w be 26/8 - 0/v. Let -62*u**4 - 151/4*u**3 + w*u - u**2 - 28*u**5 + 1/2 = 0. Calculate u.
-1, -1/4, 2/7
Let r(g) be the third derivative of -g**5/60 - g**4/8 - g**3/3 + 22*g**2. Solve r(l) = 0.
-2, -1
Factor -29 + 3*h**2 - 32*h + 93 + h**2.
4*(h - 4)**2
Determine o, given that 4 + 7*o**2 - 12*o - 8*o**3 - 4*o + 13*o**2 = 0.
1/2, 1
Let m(t) be the second derivative of 0 + t + 1/80*t**5 - 1/24*t**3 + 0*t**2 - 1/48*t**4 + 1/120*t**6. Factor m(z).
z*(z - 1)*(z + 1)**2/4
Let h(y) be the third derivative of -y**8/112 + y**7/70 + 3*y**6/40 - y**5/4 + y**4/4 - 10*y**2. Suppose h(z) = 0. Calculate z.
-2, 0, 1
Let c(b) be the first derivative of -b**7/2940 - b**6/420 - b**5/210 + b**3/3 - 3. Let z(a) be the third derivative of c(a). Determine i so that z(i) = 0.
-2, -1, 0
Let j be (-32)/(-20)*(-2)/(-8). Suppose 4 = 3*l - 2. Solve 0*u - 4/5*u**3 - 2/5*u**4 + 0 - j*u**l = 0.
-1, 0
Factor 0 + 2/5*j - 16/15*j**2 + 4/5*j**3 + 0*j**4 - 2/15*j**5.
-2*j*(j - 1)**3*(j + 3)/15
Factor -7*z**4 + 6*z**3 + 11*z**4 - 3*z**4 + 9*z**2.
z**2*(z + 3)**2
Let o(t) = -2*t**2 - 3. Let h(n) = -14*n**2 - 22. Let v(f) = -6*h(f) + 44*o(f). Let v(p) = 0. Calculate p.
0
Let c(x) = -5*x**3 - 20*x**2 - 20*x. Let o(m) = -5*m**3 - 20*m**2 - 20*m. Let q(w) = 6*c(w) - 5*o(w). Solve q(l) = 0 for l.
-2, 0
Suppose -10 = -7*z + 9*z. Let c be z/15 + (-2)/(-3). Find q, given that 1/3*q**3 + 2/3*q**2 + 0*q - c*q**4 + 0 = 0.
-1, 0, 2
Factor -64*n**5 - 2 + 9 + 432*n**4 - 85*n - 876*n**3 - 29*n + 2 + 505*n**2.
-(n - 3)**2*(4*n - 1)**3
Suppose -5*p + 33 - 33 - p**2 = 0. Calculate p.
-5, 0
Let t(b) = 4*b**5 - 6*b**3 + 2*b**2 + 4*b. Let n(z) = -9*z**5 + 13*z**3 - 5*z**2 - 9*z. Let p(w) = -2*n(w) - 5*t(w). Let p(l) = 0. What is l?
-1, 0, 1
Let b be ((-3)/(-54)*-16)/((-4)/6). Factor b - 2*g**3 - 4*g + 1/3*g**4 + 13/3*g**2.
(g - 2)**2*(g - 1)**2/3
Suppose -2*k - k = -15. Suppose 5*q + 4 = -3*j, k*j = -4*q - q. Factor j*s**2 + 0 - 1 - 4*s**4 + 3*s**4.
-(s - 1)**2*(s + 1)**2
Let a(o) = -o - 1. Let w(l) = -5*l**4 + 25*l**3 - 45*l**2 + 37*l - 8. Let q(t) = 2*a(t) + w(t). Factor q(z).
-5*(z - 2)*(z - 1)**3
Find p, given that 4*p**4 + 7*p**3 + 0*p**4 + 3*p - 14*p**2 + 0*p**3 = 0.
-3, 0, 1/4, 1
Let y be 4 - 6*2/4. Let t = 3 - y. Factor -2/3*q**t - 8/3 - 8/3*q.
-2*(q + 2)**2/3
Let j(c) be the second derivative of -c**5/5 + c**4/3 + 2*c**3/3 - 2*c**2 - 6*c. Factor j(m).
-4*(m - 1)**2*(m + 1)
Determine c so that 15*c - 3 - 15/4*c**2 - 15*c**3 + 27/4*c**4 = 0.
-1, 2/9, 1, 2
Let a be 10 - 2/(-4)*-2. Let w = -4 + a. Factor 6*l**w - 2*l**3 - l - 5*l**5 + 2*l.
l*(l - 1)**2*(l + 1)**2
Suppose -3*b - 12 = -6*b. Let c = 22 - 19. Solve 1/2*o**c + 0*o + 1/4*o**2 + 1/4*o**b + 0 = 0.
-1, 0
Let a(w) = 11*w - 2. Let l(s) = -5*s + 1. Let i(k) = 4*a(k) + 9*l(k). Let o(q) = q**2 + q - 1. Let u(d) = 3*i(d) + 6*o(d). Factor u(t).
3*(t + 1)*(2*t - 1)
Let u(v) be the second derivative of -v**4/16 - v**3/4 + 9*v**2/8 - 16*v. Factor u(i).
-3*(i - 1)*(i + 3)/4
Let v(k) be the third derivative of k**8/1848 - k**7/385 + k**6/220 - k**5/330 - k**2. Find j, given that v(j) = 0.
0, 1
Let a(h) = h**3 - 5*h**2 - 8*h. Let g(m) = -15*m + 5*m**3 - 3*m**3 - m**2 - 8*m**2. Let w(q) = -11*a(q) + 6*g(q). What is j in w(j) = 0?
-2, 0, 1
Suppose 2*c = -3*f + 4*f + 7, -7 = -c - 3*f. Let m(b) be the third derivative of 2*b**2 + 0*b + 0*b**3 + 1/210*b**5 + 0 + 0*b**c. Factor m(s).
2*s**2/7
Let d(f) = 3*f**2. Let o be d(1). Factor -10*m**5 - 21*m + 4 - 13*m + 44*m**4 + 64*m**2 + 8*m - 76*m**o.
-2*(m - 1)**4*(5*m - 2)
Let b be 2/(-12) + (-122)/(-12). Let w be ((-4)/b)/(6/(-5)). Factor -1/3*t**2 - 2/3*t + w*t**3 + 0.
t*(t - 2)*(t + 1)/3
Suppose 2*f = -3*n + 18, -2*n + 23 = 2*f + 3*f. What is p in 3*p**f - p + 4 - 2*p**3 - 2*p**2 - 2 = 0?
-1, 1, 2
Let k(b) be the third derivative of 1/40*b**5 - 1/24*b**4 + 0*b**3 + 0*b + 0 - 4*b**2 - 1/240*b**6. Factor k(h).
-h*(h - 2)*(h - 1)/2
Let z(k) = -2*k - 4. Let d be z(-4). Factor 4*c**3 - 2*c + 0*c - 2*c**3 - 1 + 0*c**3 + d*c**2 - 3*c**4.
-(c - 1)**2*(c + 1)*(3*c + 1)
Let x(w) be the second derivative of -w**4/6 - w**3/3 - 2*w. Find c such that x(c) = 0.
-1, 0
Let x(y) = y**2 + y + 1. Let i(d) = -8*d**2 - 16*d - 4. Let o(z) = i(z) + 4*x(z). Suppose o(u) = 0. Calculate u.
-3, 0
Let a(j) = -17*j**3 + 7*j**2 - 29*j - 5. Let g(r) = -6*r**3 + 2*r**2 - 10*r - 2. Let d(h) = 4*a(h) - 11*g(h). Factor d(l).
-2*(l - 1)**3
Let y(m) be the third derivative of m**5/120 + 5*m**4/48 + 12*m**2. Factor y(v).
v*(v + 5)/2
Let c = -37 - -149/4. Let k be (-4)/10*15/(-12). Solve -1/4 - k*l - c*l**2 = 0 for l.
-1
Suppose 27*y**4 + 21*y**5 - 80*y**3 - 12*y**4 + 12*y**2 + 32*y**3 