*q - 2 + 2*q**2 - 16*q - q**2 + k*q = 0. Calculate q.
-1, 2
Let b(t) = 40*t**3 - 55*t**2 + 65*t. Let g(p) = -5*p**3 + 7*p**2 - 8*p. Let i(f) = 3*b(f) + 25*g(f). Factor i(m).
-5*m*(m - 1)**2
Let t(x) = -x**3 - 5*x**2 + 3*x - 6. Let w be t(-6). Suppose w = 4*s - 3*m, -5*s + 0*s = -m - 4. Let 3*r - 6*r**3 - r - 4*r**2 + s*r**3 = 0. What is r?
-1, 0, 1/3
Let k(n) = -4*n**2 + 59*n - 193. Let v(a) = 4*a**2 - 58*a + 194. Let t(s) = -2*k(s) - 3*v(s). Suppose t(l) = 0. Calculate l.
7
Let s(j) be the third derivative of j**7/3780 - j**6/360 + j**5/90 + j**4/6 + j**2. Let x(a) be the second derivative of s(a). Factor x(c).
2*(c - 2)*(c - 1)/3
Let n(l) be the first derivative of -1/4*l**2 - 1/4*l**3 + 1 + 0*l + 1/8*l**4. Factor n(d).
d*(d - 2)*(2*d + 1)/4
Suppose 11*k = 14*k - 6. Factor -2/3 - 1/3*x**k - x.
-(x + 1)*(x + 2)/3
Factor -8/3 - 16/3*a**3 + 0*a**4 + 4*a + 8/3*a**2 + 4/3*a**5.
4*(a - 1)**3*(a + 1)*(a + 2)/3
Let u = -803 - -806. Factor -24/5 + 147/5*t**u - 378/5*t**2 + 36*t.
3*(t - 2)*(7*t - 2)**2/5
Let n(b) be the second derivative of -b**7/399 + b**5/95 - b**3/57 + 22*b. Factor n(m).
-2*m*(m - 1)**2*(m + 1)**2/19
Let r be -1 + 1/(((-16)/12)/(-4)). Factor 0 - 2/3*f**r + 0*f.
-2*f**2/3
Let h(q) be the second derivative of q**8/84 - q**7/70 - q**6/24 + q**5/20 + q**4/24 + 9*q**2/2 - 4*q. Let x(u) be the first derivative of h(u). Factor x(z).
z*(z - 1)**2*(z + 1)*(4*z + 1)
Let h(f) be the first derivative of -2/9*f**3 - 1/6*f**4 + 0*f + 0*f**2 + 2. Factor h(i).
-2*i**2*(i + 1)/3
Let i(h) be the first derivative of 0*h**3 + 1/2*h**4 - 4*h - 3 - 3*h**2. Factor i(n).
2*(n - 2)*(n + 1)**2
Let g(n) = -n + 116. Let w be g(0). Let k = w + -338/3. Factor 4*c**2 + 1/3 + c**4 - k*c**3 - 2*c.
(c - 1)**3*(3*c - 1)/3
Let u(j) = 3*j**4 + 3*j**3 - j**2 - 3*j. Let k(y) = -13*y**4 - 13*y**3 + 4*y**2 + 13*y. Let f(h) = -2*k(h) - 9*u(h). Factor f(m).
-m*(m - 1)*(m + 1)**2
Let n(z) be the first derivative of z**8/4200 - z**6/450 + z**4/60 + z**3/3 + 4. Let j(s) be the third derivative of n(s). Factor j(w).
2*(w - 1)**2*(w + 1)**2/5
Let v(f) = f + 3. Let s be v(-3). Let x be 0*2/6*3. Factor -1/3*d**3 + 1/3*d + s + x*d**2.
-d*(d - 1)*(d + 1)/3
Let c be ((-8)/(-3))/2*17. Let o = 76/3 - c. Solve -7*m**3 - 4*m - 50/3*m**2 + o = 0.
-2, -2/3, 2/7
Let v(n) be the first derivative of -4*n**3/3 + 10*n**2 - 20. Let v(m) = 0. What is m?
0, 5
Let c(o) be the first derivative of 0*o**4 + 0*o**3 + 1 + 2/15*o**5 - 1/3*o**6 + 0*o + 0*o**2. Solve c(u) = 0 for u.
0, 1/3
Let s**3 + 1/3*s**4 + 1/3*s + s**2 + 0 = 0. Calculate s.
-1, 0
Suppose -2*y = 2*b - 14, -3*y - 2*b - 3 = -20. Factor -h**3 + 3*h**y + 16*h**5 - 18*h**5.
-2*h**3*(h - 1)*(h + 1)
Suppose -3*p + 12 = 2*z, 3*p - 5*z = -0*z + 12. Factor 1/7*n**2 + 3/7*n**p + 3/7*n**3 + 0 + 0*n + 1/7*n**5.
n**2*(n + 1)**3/7
Let w = -95/39 + 36/13. Let -w*s**2 + 1/3*s + 2/3 = 0. Calculate s.
-1, 2
Let w(x) be the first derivative of -x**6/3 + 3*x**4/2 + 4*x**3/3 - 9. Factor w(j).
-2*j**2*(j - 2)*(j + 1)**2
Let s(y) be the third derivative of -y**5/100 + y**4/20 - y**3/10 + 5*y**2. Find k such that s(k) = 0.
1
Let o(v) be the first derivative of 0*v + 5 + 3/10*v**5 - 1/2*v**3 + 3/8*v**2 + 0*v**4 - 1/8*v**6. Factor o(i).
-3*i*(i - 1)**3*(i + 1)/4
Let z(a) be the first derivative of -a**4/6 - 2*a**3/3 - 2*a**2/3 - 2. Suppose z(s) = 0. Calculate s.
-2, -1, 0
Let t(g) be the first derivative of g**8/1680 + g**7/336 + g**6/720 - g**5/48 - g**4/16 - 2*g**3/3 - 5. Let d(f) be the third derivative of t(f). Factor d(b).
(b - 1)*(b + 1)**2*(2*b + 3)/2
Let s(a) be the first derivative of -27*a**4/10 + 2*a**3 + 32*a**2/15 + 8*a/15 - 5. Determine k so that s(k) = 0.
-2/9, 1
Factor 9 - 4 + 1 + 4*x - 2*x**2.
-2*(x - 3)*(x + 1)
Let r be ((-2)/6)/(-7 + (-10)/(-5)). Let l(h) be the first derivative of -r*h**3 + 1/10*h**4 + 2 + 0*h - 1/25*h**5 + 0*h**2. Let l(u) = 0. What is u?
0, 1
Let g(t) be the second derivative of -t**6/6 - 3*t**5/4 - 5*t**4/12 + 5*t**3/2 + 5*t**2 + t. Find x, given that g(x) = 0.
-2, -1, 1
Let x(m) be the first derivative of m**7/63 - 2*m**6/45 + m**5/30 - 3*m + 2. Let p(w) be the first derivative of x(w). Solve p(n) = 0 for n.
0, 1
Let w(l) = -2*l**4 + 6*l**3 + 2*l**2 - 4*l + 2. Let f(r) = 10*r**4 - 31*r**3 - 11*r**2 + 20*r - 10. Let g(t) = 2*f(t) + 11*w(t). Factor g(h).
-2*(h - 1)**3*(h + 1)
Let q(x) be the third derivative of x**5/180 - 7*x**4/36 + 49*x**3/18 - x**2 + 7*x. Let q(j) = 0. What is j?
7
Let a(u) be the first derivative of 0*u + 1 + 4/15*u**5 + 0*u**4 - 4/9*u**3 - 1/3*u**2 + 1/9*u**6. Factor a(r).
2*r*(r - 1)*(r + 1)**3/3
Let c(d) be the first derivative of d**6/2 - 9*d**4/4 - 2*d**3 - 33. Find l, given that c(l) = 0.
-1, 0, 2
Suppose -4*n - 5*n + 4*n - 40*n**2 - 35*n**3 = 0. What is n?
-1, -1/7, 0
Let m = 60516 - 10590348/175. Let c = m + 14/25. Factor 2/7*g**2 + 0 - c*g.
2*g*(g - 1)/7
Let j be (-2)/(-3) - (-7)/3. Let x(o) = o**3 - 2*o**2 - 3*o + 1. Let k be x(j). Factor y**2 + 8*y + 11*y**2 + 8*y**3 + 3 + 2*y**4 - k.
2*(y + 1)**4
Let t(j) = j**5 + 2*j**3 - 3*j + 3. Let p be (18/12)/((-1)/2). Let v(o) = 6*o**5 + 10*o**3 - 16*o + 16. Let h(w) = p*v(w) + 16*t(w). Let h(i) = 0. What is i?
-1, 0, 1
Let g(h) = -h**2 - 4*h + 7. Let t be g(-5). Suppose -2 + t + 6*o**3 - 3*o**5 - 3*o = 0. What is o?
-1, 0, 1
Let i(v) be the first derivative of v**6/3 - 34*v**5/25 + 21*v**4/10 - 22*v**3/15 + 2*v**2/5 - 15. Solve i(j) = 0 for j.
0, 2/5, 1
Suppose -84 = -3*y + 69. Suppose -2*t + 30 = -t - 4*q, -3*t + y = q. Let z(u) = u - 1. Let x(m) = -m**2 + 12*m - 11. Let f(o) = t*z(o) - 2*x(o). Factor f(b).
2*(b - 2)*(b - 1)
Let d(i) be the third derivative of i**8/112 - i**7/70 - i**6/40 + i**5/20 + 4*i**2. What is a in d(a) = 0?
-1, 0, 1
Let d(b) = -b**4 - 2*b - b**3 + 3*b - 3 + 4. Let r(o) = -o**5 + 5*o**4 + 8*o**3 + 2*o**2 - 7*o - 7. Let u(j) = 6*d(j) + r(j). Suppose u(c) = 0. What is c?
-1, 1
Let m be 0 + (-3)/(-2) - (-22)/44. Let y(z) be the second derivative of -m*z + 0*z**3 + 1/3*z**2 - 1/18*z**4 + 0. Factor y(i).
-2*(i - 1)*(i + 1)/3
What is u in -3 - 4*u**2 - 7*u**3 - 7*u + 11*u**3 + 1 = 0?
-1/2, 2
Let a = -4 + 6. Suppose 5*l - 14 = a*c, -2 = 3*c + 4. Find b such that -2/7*b + 0 + 2/7*b**5 - 4/7*b**4 + 4/7*b**l + 0*b**3 = 0.
-1, 0, 1
Let w(m) = m**4 + m**2 - m + 1. Let c(h) = 9*h**4 - 6*h**3 + 9*h**2 - 6*h + 6. Let o(v) = -c(v) + 6*w(v). What is r in o(r) = 0?
0, 1
Factor 5/2*s**4 - 20*s**3 + 100*s + 15*s**2 + 125/2.
5*(s - 5)**2*(s + 1)**2/2
Let o(n) = -n + 1. Let s(g) = -g**2 - 2*g + 3. Let p(q) = 4*o(q) - s(q). Let i be p(2). Factor 1/2*h**2 + i - 3/2*h.
(h - 2)*(h - 1)/2
Let k(j) be the third derivative of -j**8/26880 - j**7/2880 - j**6/1440 + j**5/60 + 3*j**2. Let c(o) be the third derivative of k(o). Factor c(h).
-(h + 2)*(3*h + 1)/4
Determine o, given that 31 - 34 - 17 - 45*o - 25*o**2 = 0.
-1, -4/5
Suppose 5*t = 4*i + 71, t + 4*t - 47 = -2*i. Suppose 0 = t*u - 16*u. Determine p so that u*p + 0*p**4 - 1/4*p**5 + 0 + 1/4*p**3 + 0*p**2 = 0.
-1, 0, 1
Let 1/5*v**2 + 1/5*v + 0 = 0. What is v?
-1, 0
Factor 16*n**3 + 2*n**2 - 8*n**3 - 10*n + 4*n + 2*n**2 - 4 - 2*n**5.
-2*(n - 2)*(n - 1)*(n + 1)**3
Let g(w) = 4*w + 28. Let i be g(-7). Suppose 0 + i*z + 1/2*z**2 - 1/2*z**3 = 0. What is z?
0, 1
Let l(s) be the first derivative of -1 - 1/15*s**3 + 2*s + 1/10*s**2 + 1/60*s**4. Let j(v) be the first derivative of l(v). Factor j(h).
(h - 1)**2/5
Let v be 5/(-4)*(-1 + 25). Let o be ((-12)/v)/(6/10). Factor o*w**3 + 4/3*w**2 + 2/3*w + 0.
2*w*(w + 1)**2/3
Suppose 3*p - 4 = 2*p. Suppose 0 = 5*y + 4*x + p, 2*x + 4 = 5*y + 2. What is q in 3*q**3 + y + 5/4*q**2 - 1/2*q = 0?
-2/3, 0, 1/4
Suppose 2 = 3*d - 4. Solve 2*x**d + 3*x + 0*x**2 + 18*x**3 + 3*x**3 + 9*x**4 + 13*x**2 = 0.
-1, -1/3, 0
Let n = -8 + 15. Let r(x) = -x**3 + 7*x**2 + 3. Let a be r(n). Factor 1/2*u**a - 1/2*u - 3/2*u**2 + 0 + 3/2*u**4.
u*(u - 1)*(u + 1)*(3*u + 1)/2
Let r = 15 + -11. Suppose r*w - 9 = s, 2 = w + 4*s + 4. Factor -1/2*o**3 - 1/2*o**4 + 0*o + 1/2*o**5 + 0 + 1/2*o**w.
o**2*(o - 1)**2*(o + 1)/2
Suppose -5*w = -4*r - 63, 0*w - 4*r = -3*w + 41. Suppose -7*t**2 + 8*t + 3 + 5*t**2 - w = 0. Calculate t.
2
Let h(r) be the second derivative of r**6/30 + 3*r**5/20 + r**4/12 - r**3/2 - r**2 + 5*r. Factor h(l).
(l - 1)*(l + 1)**2*(l + 2)
Let k = 1/68 - -31/204. Let b(z) be the secon