o**4 - 1/3*o**3 + 2*o**2 + 3/5*o**5 + 0 - 9/20*o**6. Let c(d) be the first derivative of b(d). Factor c(h).
-2*(9*h - 2)**2
Let c(j) be the third derivative of -j**5/30 + j**4/2 - 9*j**2. Factor c(w).
-2*w*(w - 6)
Factor 1 - 16*n**2 - 8*n**3 - 3 - 3*n**4 + n**4 - 8*n + 4*n**2.
-2*(n + 1)**4
Let z(u) = u**5 - u**3 + 1. Let m(v) = -6*v**5 + 3*v**4 + 18*v**3 - 15*v**2 - 12*v + 9. Let b(t) = m(t) + 3*z(t). Determine l so that b(l) = 0.
-2, -1, 1, 2
Let r(t) be the third derivative of t**8/1008 + t**7/315 - t**5/90 - t**4/72 + 20*t**2. Factor r(q).
q*(q - 1)*(q + 1)**3/3
Let v(b) be the second derivative of -b**6/6 - 7*b**5/4 - 20*b**4/3 - 10*b**3 - 27*b. Determine o, given that v(o) = 0.
-3, -2, 0
Let s(n) be the first derivative of n**4/10 - 2*n**3/15 - 4*n**2/5 + 8*n/5 + 5. Find l, given that s(l) = 0.
-2, 1, 2
Factor -1/10*f**2 + 1/10*f + 0 + 1/10*f**4 - 1/10*f**3.
f*(f - 1)**2*(f + 1)/10
Let r(b) be the second derivative of 4/5*b**3 - 13/30*b**4 - 1/75*b**6 + 0 - 4/5*b**2 + 2*b + 3/25*b**5. Determine m so that r(m) = 0.
1, 2
Suppose 1/3*z**3 - 8/3*z - 7/3*z**2 + 0 = 0. What is z?
-1, 0, 8
Let o(s) be the first derivative of s**8/4200 - s**6/300 - s**5/150 + s**3/3 - 3. Let w(u) be the third derivative of o(u). Find x such that w(x) = 0.
-1, 0, 2
Suppose m**3 + 3/8*m**2 + 7/8*m**4 + 0 + 0*m + 1/4*m**5 = 0. Calculate m.
-3/2, -1, 0
Factor 2 + 3*x**2 - 4 + x**3 - x - 6*x**2 + 5*x**2.
(x - 1)*(x + 1)*(x + 2)
Let 23*s - s**2 - 3*s**2 - 8 - 35*s = 0. What is s?
-2, -1
Let j(r) be the second derivative of -1/80*r**5 - 1/48*r**4 + 0*r**2 + 0 - 4*r + 1/12*r**3. Factor j(x).
-x*(x - 1)*(x + 2)/4
Let n(x) = 2*x**5 - 2*x**4 - 7*x**2 + 7. Let i(c) = 2*c**5 - 2*c**4 - 6*c**2 + 6. Let g(d) = 7*i(d) - 6*n(d). Solve g(p) = 0.
0, 1
Let x(c) be the second derivative of 1/4*c**4 + 0*c**2 + 1/2*c**3 + 0 + 8*c. Solve x(k) = 0 for k.
-1, 0
Factor -16*s**4 + 49*s**3 - 32*s**2 + 8*s + 6*s**4 - 15*s**3.
-2*s*(s - 2)*(s - 1)*(5*s - 2)
Suppose -4 - 1/4*l**2 - 2*l = 0. What is l?
-4
Suppose -2*p + 16 = -0*p. Let x be (2 + -4)*(-22)/p. Factor x*g**2 + 8*g**3 + 0 + g + 7/2*g**4.
g*(g + 1)**2*(7*g + 2)/2
Let d(y) be the first derivative of 3*y**4/10 + 7*y**3/30 + y**2/20 + 10. Let d(l) = 0. What is l?
-1/3, -1/4, 0
Suppose 0 + z**2 - 1/5*z = 0. Calculate z.
0, 1/5
Factor 4/7*p**2 + 4/7*p + 0.
4*p*(p + 1)/7
Let w = -45 + 47. Let m(v) be the first derivative of 0*v - v**w + 1/2*v**4 - 3 + 0*v**3. Find l, given that m(l) = 0.
-1, 0, 1
Factor 12*w + 9*w**2 + 9*w**2 - 14*w**2.
4*w*(w + 3)
Suppose 17*v**2 - 9 - 93*v**2 - 73*v - 47*v - 12*v**3 - 23 = 0. What is v?
-4, -2, -1/3
Let q(k) be the third derivative of -k**5/60 + k**4/6 - 2*k**3/3 - 3*k**2. Determine o so that q(o) = 0.
2
Let a(g) = g**2 + g - 1. Let c(m) = -2*m**3 - 3*m**2 - 3*m + 3. Let x(f) = 3*a(f) + c(f). Determine z, given that x(z) = 0.
0
Let i = -76/7 + 1375/126. Let d = i + 4/9. What is r in 1/2*r**3 - 3/2*r**2 - d + 3/2*r = 0?
1
Solve 0 - 4/9*x**5 + 4/3*x**4 - 4/9*x**3 + 8/9*x - 4/3*x**2 = 0 for x.
-1, 0, 1, 2
Let f(l) = -l**2 - 9*l - 5. Let v be f(-8). Factor -2*x**4 + 2*x**2 + v*x**3 - 15*x - x**3 + 5*x + 8*x.
-2*x*(x - 1)**2*(x + 1)
Suppose -2/3*z**3 - 2/3*z + 4/3*z**2 + 0 = 0. What is z?
0, 1
Suppose 4*u - 2*m - 12 = 0, -3*m = 3*u - 0*m - 18. Let o = u + 1. Factor 1/3*k**3 + 1/3*k**4 + 0 - 1/3*k**o + 0*k - 1/3*k**2.
-k**2*(k - 1)**2*(k + 1)/3
Let s(m) be the second derivative of -m**6/27 - m**5/45 + 5*m**4/18 - 4*m**3/27 - 4*m**2/9 + m. Solve s(p) = 0 for p.
-2, -2/5, 1
Let z be ((-6)/(-8))/(2/8). Let r be (-1)/(-3)*(3 + (-5 - -3)). Find o, given that -1/3*o**4 - o**2 + 0 + o**z + r*o = 0.
0, 1
Let r(s) = 3*s**4 - 5*s**3 - 14*s**2 - 6*s. Let j(p) = p**4 - 2*p**3 - 5*p**2 - 2*p. Let v(b) = -11*j(b) + 4*r(b). Factor v(l).
l*(l - 1)*(l + 1)*(l + 2)
Factor -2/3*y + 4/3 + 2/3*y**3 - 4/3*y**2.
2*(y - 2)*(y - 1)*(y + 1)/3
Let l(v) be the third derivative of -v**6/540 - v**5/270 - 24*v**2. Suppose l(y) = 0. What is y?
-1, 0
Let t(o) be the first derivative of -o**3 + 1/4*o**4 - o - 3 + 3/2*o**2. Let t(r) = 0. Calculate r.
1
Let b(o) be the second derivative of 0 + 1/3*o**2 - 1/15*o**6 + 1/3*o**3 - 1/15*o**5 + 1/9*o**4 + 2*o - 1/63*o**7. Find n such that b(n) = 0.
-1, 1
Factor 30*r**4 + 80*r**2 - 6*r + 4*r - 5*r**5 - 70*r**3 + 94 - 84 - 43*r.
-5*(r - 2)*(r - 1)**4
Let g(q) be the second derivative of q**7/168 + q**6/40 + q**5/80 - q**4/16 - q**3/12 + 3*q. Let g(l) = 0. Calculate l.
-2, -1, 0, 1
Let a(p) = p**3 + 3*p**2 - 5*p - 6. Let h be a(-4). Let l = h - -2. Factor 7*d + 12*d**2 + l*d - 4*d.
3*d*(4*d + 1)
Suppose 4*a**2 + 408 - 16*a - 408 = 0. Calculate a.
0, 4
Let h(l) be the third derivative of l**7/1050 - l**6/200 - l**5/60 + l**4/40 + 2*l**3/15 - 15*l**2. Factor h(z).
(z - 4)*(z - 1)*(z + 1)**2/5
Factor 102 + 546 + 54*t**2 - 3*t**3 - 324*t + 0*t**3.
-3*(t - 6)**3
Let s = -1 - -1. Let q be -13 - -12 - (s - 1). Determine p so that 0*p + 3/4*p**3 - 3/2*p**4 + 3/4*p**5 + 0*p**2 + q = 0.
0, 1
Let i(v) be the first derivative of -v**8/560 + v**6/120 + 2*v**3 - 6. Let x(z) be the third derivative of i(z). Factor x(j).
-3*j**2*(j - 1)*(j + 1)
Suppose 2*d = -2*y, -4*d + 6*d = -4. Factor 0 - 1/4*s + 1/4*s**y.
s*(s - 1)/4
Let u be (7/36)/((-58)/(-78)). Let i = u + -1/87. Factor -t**2 + 0 + i*t.
-t*(4*t - 1)/4
Solve 2/5*a**4 + 2/5 - 2/5*a + 4/5*a**3 - 2/5*a**5 - 4/5*a**2 = 0 for a.
-1, 1
Let k be (14/(-4))/(1/2). Let v = -5 - k. Factor 4*u**4 + 2*u**4 - 6*u**v - 3*u + 0*u**4 + 3*u**5.
3*u*(u - 1)*(u + 1)**3
Factor 0*o - 2/3*o**3 + 2/3*o**2 + 0.
-2*o**2*(o - 1)/3
Let w(o) = -2*o**4 - 5*o**3 + 2*o**2 + o. Let r(k) = -4*k**4 - 11*k**3 + 3*k**2 + k + 1. Let q(p) = 2*r(p) - 5*w(p). Solve q(y) = 0.
-2, -1, 1/2, 1
Factor -4*r**3 - 1/2*r - 8*r**4 + 0 + 7/2*r**2.
-r*(r + 1)*(4*r - 1)**2/2
Let f(p) be the second derivative of 2*p**7/147 + 3*p**6/70 - p**5/14 - 5*p**4/12 - 4*p**3/7 - 2*p**2/7 - 3*p. Let f(g) = 0. What is g?
-2, -1, -1/4, 2
Let u(y) = -y**3 - 3*y**2 + 3. Let s be u(-3). Suppose -s*w + 4 = -w. Suppose -2/3*j - 2/9 - 2/9*j**3 - 2/3*j**w = 0. What is j?
-1
Solve -4/3*u**3 + 2/3*u**4 + 4/3*u - 2/3 + 0*u**2 = 0.
-1, 1
Let b(j) be the first derivative of -j**4/4 + 5*j**3/3 + 56. Let b(v) = 0. What is v?
0, 5
Factor -v + 0 - 1/3*v**2.
-v*(v + 3)/3
Let u(w) be the first derivative of -w**6/540 - w**5/108 - w**4/54 + 2*w**3/3 + 4. Let l(k) be the third derivative of u(k). Determine c so that l(c) = 0.
-1, -2/3
Let z(b) = 33*b**2 + 393*b - 2127. Let g(l) = 5*l**2 + 56*l - 304. Let y(m) = -27*g(m) + 4*z(m). Factor y(s).
-3*(s - 10)**2
Let u(i) be the second derivative of 1/105*i**6 - 4*i - 1/21*i**4 + 0 + 0*i**5 + 1/7*i**2 + 0*i**3. Solve u(j) = 0 for j.
-1, 1
Let u(a) = -10*a**3 - 4*a**2 + 36*a + 44. Let n(f) = -2*f**3 - f**2 + 7*f + 9. Let v(g) = 14*n(g) - 3*u(g). Suppose v(z) = 0. Calculate z.
-1, 3
Let w(k) = k**5 - k**3 + 1. Let j(s) = 20*s**5 - 10*s**4 - 30*s**3 + 25. Let p(h) = -j(h) + 25*w(h). Find x such that p(x) = 0.
-1, 0
Let p be (0/(-3))/(44 + -48). Factor p*s + 1/3*s**2 - 4/3.
(s - 2)*(s + 2)/3
Let i(b) be the second derivative of -b**6/90 + b**5/15 - b**4/12 + 32*b. Factor i(f).
-f**2*(f - 3)*(f - 1)/3
Let s(i) be the first derivative of 2 + 3*i**3 - 6*i**2 - 12*i - 6*i**3 + 2*i**3. Factor s(t).
-3*(t + 2)**2
Let s(h) be the second derivative of -h**7/70 + h**6/40 + h**5/20 - h**4/8 - 4*h**2 + 7*h. Let w(t) be the first derivative of s(t). Factor w(j).
-3*j*(j - 1)**2*(j + 1)
Let 0 - 1/4*p**3 + p + 0*p**2 = 0. Calculate p.
-2, 0, 2
Let q(j) be the second derivative of -3/80*j**5 - 1/16*j**4 + 1/40*j**6 + 9*j + 0*j**2 + 1/56*j**7 + 0 + 0*j**3. Let q(a) = 0. Calculate a.
-1, 0, 1
Let j(f) = -4*f**3 + 12*f**2 - 16. Let c(m) = 2*m**3 - 6*m**2 + 8. Let d(z) = -10*c(z) - 6*j(z). Factor d(v).
4*(v - 2)**2*(v + 1)
Let w be (-2)/((-2)/3 + 0). Let l(x) = 3 - x**w - 4 + 2. Let k(p) = -p**4 - 4*p**3 + 3*p**2 - 5*p + 7. Let i(j) = k(j) - 5*l(j). What is q in i(q) = 0?
-2, 1
Let d(w) be the third derivative of 0*w + 1/30*w**5 - w**2 - 1/60*w**6 + 0*w**3 + 0 + 0*w**4. Factor d(j).
-2*j**2*(j - 1)
Let x(t) be the second derivative of -t**5/60 - t**4/24 + 2*t**3/9 - t**2/4 + 11*t. Factor x(k).
-(k - 1)*(k + 3)*(2*k - 1)/6
Suppose 2*k = -0*k + 10. Factor -4*t**2 + t**4 - t + t**3 + k*t**2 - 2*t**4.
-t*(t - 1)**2*(t + 1)
Let 