*w**5/5 - 11*w**4 + 12*w**3 + 8*w**2 - 16*w + 12. Factor s(c).
4*(c - 1)**3*(c + 2)*(3*c + 2)
Let p(t) be the second derivative of t**7/21 - t**5/5 + t**3/3 + 7*t. Factor p(q).
2*q*(q - 1)**2*(q + 1)**2
Let r = -17 + 53/3. Let u(g) be the first derivative of -7/9*g**3 - 1/3*g**2 - r*g**4 - 1/5*g**5 + 0*g + 3. Suppose u(i) = 0. What is i?
-1, -2/3, 0
Let f(j) be the third derivative of 0*j + 5/156*j**4 - 1/39*j**3 - 7/390*j**5 + 0 + 6*j**2 + 1/260*j**6. Factor f(k).
2*(k - 1)**2*(3*k - 1)/13
Factor 9*g**2 - g + 9*g - 2*g - 3*g - 12*g**3.
-3*g*(g - 1)*(4*g + 1)
Solve n**2 - 1 + 2*n**3 - 1/2*n**5 - 3/2*n + 0*n**4 = 0.
-1, 1, 2
Let x be 2/8 - (-7)/4. Suppose 4*r = x*r + 4. Let -2/5 - 4/5*w - 2/5*w**r = 0. What is w?
-1
Let m(n) be the third derivative of 8/735*n**7 + 0*n**3 - 3*n**2 + 0 + 0*n + 0*n**5 + 1/392*n**8 - 1/84*n**4 + 1/70*n**6. Find b such that m(b) = 0.
-1, 0, 1/3
Find b, given that -5*b - 6*b**3 + 10*b - b**2 - 3 + 5*b**3 = 0.
-3, 1
Let n(a) be the first derivative of 3*a**4/28 + 3*a**3/7 + 9*a**2/14 + 3*a/7 - 6. Find p, given that n(p) = 0.
-1
Let 64*n**4 - 12/5*n**2 - 4/5*n + 0 + 96/5*n**3 = 0. What is n?
-1/4, 0, 1/5
Factor 0*m**2 + 0 + 2/9*m**5 - 4/9*m**3 + 2/9*m + 0*m**4.
2*m*(m - 1)**2*(m + 1)**2/9
Let l(f) be the second derivative of 7*f**4/12 + 61*f**3/6 - 9*f**2 - 3*f - 14. Factor l(z).
(z + 9)*(7*z - 2)
Factor -2/5 + 4/5*t - 2/5*t**2.
-2*(t - 1)**2/5
Suppose 4*r - 24 = -2*w, -5*w - 2*r + 28 = -0*r. Determine u, given that 2/3*u**w + 0 + 2/3*u - 2/3*u**2 - 2/3*u**3 = 0.
-1, 0, 1
Let t(o) be the third derivative of o**8/84 - o**7/30 - 3*o**6/40 + 13*o**5/60 + 5*o**4/24 - o**3 + 19*o**2. Find g such that t(g) = 0.
-1, 3/4, 1, 2
Let o(m) be the third derivative of -m**5/20 - 3*m**4/4 - 9*m**3/2 - 2*m**2. Factor o(n).
-3*(n + 3)**2
Let x(y) be the second derivative of 0 - 28/45*y**6 + y + 0*y**2 + 14/9*y**4 - 4/9*y**3 - 3/2*y**5 + 7/9*y**7. Find m, given that x(m) = 0.
-1, 0, 2/7, 1
Let i = 12 - 9. Let h(c) be the third derivative of -1/6*c**4 + c**2 + 1/3*c**i + 0*c + 1/30*c**5 + 0. What is w in h(w) = 0?
1
Let n be ((-2)/(-3))/(2/6). Suppose -8*l + l = -14. Factor -z**n - 2*z**5 + 11*z**4 + 4*z**2 - l*z**4 + 5*z**5 + 9*z**3.
3*z**2*(z + 1)**3
Let l be (-27)/(-2) + (-36)/24. Suppose -4*s = -s - l. Factor 3/5*w + 0 - 6/5*w**3 + 0*w**s + 0*w**2 + 3/5*w**5.
3*w*(w - 1)**2*(w + 1)**2/5
Find w such that -28/5*w + 26/5*w**4 - 29/5*w**3 + 16/5 + 7/5*w**5 - 92/5*w**2 = 0.
-4, -1, 2/7, 2
Let q be ((-1)/((-42)/(-8)))/((-8)/12). Let n = -1641/7 + 235. Factor q*o**2 + 0 - n*o.
2*o*(o - 2)/7
Let u(x) be the second derivative of 0 + 64/63*x**7 + 4/9*x**4 - 22/15*x**5 - 1/3*x**2 + 5/9*x**3 - 3*x - 32/45*x**6. Find y such that u(y) = 0.
-1/2, 1/4, 1
Let o(x) be the first derivative of x**5/70 - x**4/14 + x**3/7 - x**2/7 + x - 3. Let l(w) be the first derivative of o(w). Determine q, given that l(q) = 0.
1
Let v = -194 - 100. Let y be (-133)/v - (-2)/(-12). Let 0 + 6/7*k**3 + 2/7*k**2 + y*k**5 + 0*k + 6/7*k**4 = 0. What is k?
-1, 0
Let c(p) be the third derivative of -p**6/120 - p**5/60 + 5*p**4/24 - p**3/2 - 4*p**2. Solve c(v) = 0 for v.
-3, 1
Let v(q) = -4912*q**4 - 9252*q**3 - 3808*q**2 + 516*q - 28. Let b(a) = -a**4 - a**3 - a**2 - a - 1. Let s(t) = -12*b(t) + v(t). Factor s(u).
-4*(u + 1)**2*(35*u - 2)**2
Let j(m) be the first derivative of -m**8/2016 + m**7/1260 - m**2 - 4. Let k(z) be the second derivative of j(z). Determine r so that k(r) = 0.
0, 1
Let h(v) = 88*v + 354. Let k be h(-4). Let w = 1/25 + 23/50. Factor -2*c + 1/2*c**4 + 3*c**k - 2*c**3 + w.
(c - 1)**4/2
Suppose p = -3*u, 3*p = -2*p + 5*u + 40. Let c = p + -6. What is q in -3/4*q**3 + c + 1/2*q + 1/4*q**2 = 0?
-2/3, 0, 1
Suppose 0 = -3*c - 2*c + 40. Factor 3*b + 2*b**2 - 8 - 19*b + c*b**2.
2*(b - 2)*(5*b + 2)
Let o(v) be the second derivative of 0*v**5 + 4/3*v**3 - 1/2*v**4 - 3/2*v**2 + 2*v + 0 + 1/30*v**6. Factor o(q).
(q - 1)**3*(q + 3)
Suppose 3*x - 22 = -4. Let y(p) = 6*p**3 - 2*p**2 - 5*p - 4. Let g(i) = -7*i**3 + 3*i**2 + 6*i + 4. Let d(l) = x*y(l) + 5*g(l). Factor d(k).
(k - 1)*(k + 2)**2
Let p(a) = a**3 - a**2 - a - 1. Let l(f) = 7*f**3 - 7*f**2 - 9*f - 9. Let h(d) = 2*l(d) - 18*p(d). Factor h(m).
-4*m**2*(m - 1)
Solve -2 + 3/2*w**2 + 1/2*w**4 + 2*w**3 - 2*w = 0 for w.
-2, -1, 1
Let l = -4 + 6. Let s be 2*(-4)/((-8)/4). Factor 6*y + 5*y**l + 3*y**2 - s + 2*y**2.
2*(y + 1)*(5*y - 2)
Let c(v) be the third derivative of v**8/420 + v**7/70 + v**6/30 + v**5/30 + 7*v**3/6 + 4*v**2. Let n(j) be the first derivative of c(j). Factor n(w).
4*w*(w + 1)**3
Let n(z) = -z**2 - 7*z. Let w(l) = -2*l**2 - 6*l. Let m(r) = -3*n(r) + 2*w(r). Let m(f) = 0. Calculate f.
0, 9
Let p(f) be the first derivative of -f**6/60 + f**5/20 - f**4/16 + 5*f**3/3 + 4. Let c(g) be the third derivative of p(g). Solve c(l) = 0.
1/2
Let o(l) be the first derivative of 4 + 0*l**3 + 0*l + 0*l**2 - 2/5*l**5 + 1/6*l**4. Let o(p) = 0. Calculate p.
0, 1/3
Let u(m) = m**3 + 3*m**2 + 3*m + 5. Let l be u(-2). Factor 8 - 24*a + 3*a**5 + 0*a**5 - 6*a**5 + 15*a**l + 4 + 3*a**2 - 3*a**4.
-3*(a - 1)**3*(a + 2)**2
Let k(h) = 2*h**3 + 4*h**2 - 4*h - 3. Let w(u) = -u**3 - 4*u**2 + 4*u + 2. Let i(z) = 2*k(z) + 3*w(z). What is s in i(s) = 0?
0, 2
Suppose 0*u = 3*u - 6. Let b(c) be the first derivative of 0*c**3 + 0*c - 1/2*c**u - 1 + 1/4*c**4. Solve b(y) = 0 for y.
-1, 0, 1
Let a(f) be the second derivative of -f**8/560 + f**7/280 + f**6/40 - f**5/40 - f**4/4 + f**3/6 - 7*f. Let h(p) be the second derivative of a(p). Factor h(g).
-3*(g - 2)*(g - 1)*(g + 1)**2
Let b = 56 - 54. Factor 2/7*s - 4/7 + 6/7*s**b.
2*(s + 1)*(3*s - 2)/7
Let j(b) be the first derivative of -1/21*b**6 + 1/14*b**4 + 0*b + 0*b**2 + 2/35*b**5 - 2/21*b**3 - 2. Determine h so that j(h) = 0.
-1, 0, 1
Let y(i) be the third derivative of i**7/280 - i**6/60 - i**3/6 + 6*i**2. Let r(d) be the first derivative of y(d). Let r(q) = 0. Calculate q.
0, 2
Factor k - k**5 - 2*k**2 + 2*k**4 + 576*k**3 - 576*k**3.
-k*(k - 1)**3*(k + 1)
Let f be 0/(8 - 10)*1. What is h in 72/7*h**2 - 60/7*h**3 + f - 50/7*h**4 - 16/7*h = 0?
-2, 0, 2/5
Let p be 2/(2/(-1 - -3)). Factor 0 + 0*h - 1/4*h**p + 1/4*h**3.
h**2*(h - 1)/4
Let t = 333/4 - 83. Factor t*g**4 - 1/4*g - 1/4*g**2 + 1/4*g**3 + 0.
g*(g - 1)*(g + 1)**2/4
Let n(c) be the second derivative of -c**9/75600 - c**8/16800 + c**6/1800 + c**5/600 + c**4/4 + 5*c. Let l(z) be the third derivative of n(z). Solve l(o) = 0.
-1, 1
Suppose 0 = -7*y + 4 + 10. Suppose 0 = -4*g + 3*i - 15, -y*i + 4 + 6 = 0. Factor g - 2/13*r + 2/13*r**2.
2*r*(r - 1)/13
Let q(u) = -2*u**3 + 4*u**2 + 5*u + 13. Let k(w) = 6*w**3 - 10*w**2 - 14*w - 38. Let y(o) = 5*k(o) + 14*q(o). Let y(j) = 0. Calculate j.
-2, 1
Let p be ((-2)/(-6))/((-3)/(-3)). Let r(q) be the first derivative of 2 + q - 1/2*q**2 - p*q**3 + 1/4*q**4. Solve r(v) = 0 for v.
-1, 1
Let b = -1 + 4. Factor -2 + b*u**2 - 3*u**2 - 4*u**2 + 6*u**2.
2*(u - 1)*(u + 1)
Let m(h) be the second derivative of -h**7/21 - 13*h**6/60 - 9*h**5/80 + 5*h**4/12 - h**3/6 - 20*h. What is w in m(w) = 0?
-2, 0, 1/4, 1/2
Let l(x) be the third derivative of x**7/42 + x**6/6 - x**5/4 - 35*x**4/12 - 20*x**3/3 + 5*x**2. Factor l(q).
5*(q - 2)*(q + 1)**2*(q + 4)
Let n = -431 + 3883/9. Let -2/9*p + 2/9*p**5 - 4/9*p**4 + 0 + 0*p**3 + n*p**2 = 0. Calculate p.
-1, 0, 1
Let f(t) = t**5 - 7*t**4 - t**3 - t**2 - 4*t - 4. Let b(q) = -q**5 + 6*q**4 + q**3 + 3*q + 3. Let v(j) = 4*b(j) + 3*f(j). What is z in v(z) = 0?
-1, 0, 1, 3
Let x(p) be the first derivative of 49*p**5/20 + 7*p**4/2 + 2*p**3 + p**2/2 - 2. Let a(z) be the second derivative of x(z). Factor a(j).
3*(7*j + 2)**2
Let s(t) be the second derivative of 5*t**7/168 - t**6/24 - 5*t**5/16 + 5*t**4/48 + 5*t**3/3 + 5*t**2/2 + 15*t. Factor s(d).
5*(d - 2)**2*(d + 1)**3/4
Factor 4/5*y**2 - 4 - 16/5*y.
4*(y - 5)*(y + 1)/5
Let n be (-15)/40 + 125/120. Factor n*h**2 + 1/3*h**3 + 0*h + 0.
h**2*(h + 2)/3
Let h(f) = 5*f**2 - 124*f + 720. Let b(t) = t. Let x(c) = 4*b(c) + h(c). Factor x(s).
5*(s - 12)**2
Let n be 4 + -2 + (1 - -1). Let d(z) = -6 - 5*z**2 + 2*z**3 - 1 + 0*z**3. Let w(f) = f**3 - 3*f**2 - 4. Let b(x) = n*d(x) - 7*w(x). Factor b(m).
m**2*(m + 1)
Suppose 15*d - 20*d + 30 = 0. Let z = d + -2. Factor 1/3*w - 1/3*w**5 - 2/3*w**z + 2/3*w**2 + 0 + 0*w**3.
-w*(w - 1)*(w + 1)**3/3