5 - 6/5*k + 3/5*k**2 = 0.
1
Let n(z) be the second derivative of -z**4/6 + z**3/3 - 19*z. Solve n(i) = 0 for i.
0, 1
Factor 1/3*q**4 - 1/3*q**2 + 0 + 0*q + 0*q**3.
q**2*(q - 1)*(q + 1)/3
Let x = -2 + 5. Determine r, given that x*r**2 - 6*r + 5*r - 3 + r = 0.
-1, 1
Factor -21/8*y - 3/8*y**2 - 15/4.
-3*(y + 2)*(y + 5)/8
Let s be (10 - 1)/((-3)/2). Let h(o) = -o**3 - 5*o**2 + 5*o - 3. Let d be h(s). Suppose -2*k**5 - k**4 - k**4 - k + 4*k**2 + 4*k**d - 2 - k = 0. Calculate k.
-1, 1
Factor 0 + 0*m**2 + 1/8*m**5 - 1/4*m**4 + 0*m**3 + 0*m.
m**4*(m - 2)/8
Let g be (3*(-5)/(-105))/15. Let w(j) be the third derivative of 0*j**4 - 1/15*j**6 + 0 + 0*j - 4*j**2 - 2/15*j**5 - g*j**7 + 0*j**3. Factor w(t).
-2*t**2*(t + 2)**2
Let n(u) = -u + 9. Let g be n(9). Let o(t) be the first derivative of 1 + 1/3*t**3 + g*t + 0*t**2. Let o(a) = 0. Calculate a.
0
Let o(p) = p**3 + 5*p**2 - 5*p - 1. Let q(s) = -s**2 + s. Let l(d) = -5*o(d) - 20*q(d). Find k, given that l(k) = 0.
-1, 1
Let c(f) be the second derivative of -f**7/7560 - f**6/2160 + f**4/3 + 4*f. Let i(b) be the third derivative of c(b). Factor i(a).
-a*(a + 1)/3
Suppose -2*s = -5*j + 5, s - 5*j = 6*s - 40. Suppose 0 = -h - 3*o - 1, 2*o + 16 - 4 = s*h. Solve -v + h*v - 3*v + 2*v**2 = 0 for v.
0, 1
Let i = 16 + -12. Suppose 3*l = i*l. Solve 3/2*s**2 + l - 3*s = 0.
0, 2
Let s(h) = -h**3 + 13*h**2 + 10*h + 56. Let a be s(14). Factor 0*f + 1/2*f**2 + 1/2*f**3 + a.
f**2*(f + 1)/2
Let q(o) = -o**2 + 4*o + 2. Let x be q(4). Suppose x*p - 6 = -0*p. Factor 4 - l - l**2 - p*l + 2*l**2.
(l - 2)**2
Find k, given that 1/6*k**4 + 0 + 0*k**2 + 0*k + 1/3*k**3 = 0.
-2, 0
Let g be 1*(-2 + (-74)/(-36)). Let n(d) be the first derivative of -2/45*d**5 + 0*d - 2 + 1/9*d**2 + 2/27*d**3 - g*d**4. Factor n(x).
-2*x*(x - 1)*(x + 1)**2/9
Let s(y) be the third derivative of -y**9/4032 + y**8/1680 + y**7/840 + 5*y**3/6 - 3*y**2. Let c(z) be the first derivative of s(z). Factor c(x).
-x**3*(x - 2)*(3*x + 2)/4
Let r(b) be the second derivative of -1/20*b**5 + 1/4*b**4 + 0 + 1/2*b**2 - 4*b - 1/2*b**3. Determine m so that r(m) = 0.
1
Let x(j) be the third derivative of -j**8/336 + 2*j**7/105 - j**6/30 - j**5/30 + 5*j**4/24 - j**3/3 - 45*j**2. Suppose x(z) = 0. Calculate z.
-1, 1, 2
Let c be (-3)/3*7/((-231)/6). Factor -2/11*u - c*u**2 + 0.
-2*u*(u + 1)/11
Let x(n) = 7*n**3 + 52*n**2 + 192*n + 4. Let p(f) = 48*f**3 + 363*f**2 + 1344*f + 27. Let v(d) = 4*p(d) - 27*x(d). Let v(k) = 0. Calculate k.
-8, 0
Let q(k) be the first derivative of -k**3 + 12*k + 11. Suppose q(r) = 0. Calculate r.
-2, 2
Factor 0*x + 0*x**2 + 8/5*x**3 + 8/5*x**4 + 2/5*x**5 + 0.
2*x**3*(x + 2)**2/5
Let r(w) be the second derivative of -2*w**7/21 - 2*w**6/15 + w**5/5 + w**4/3 + 5*w. Determine a so that r(a) = 0.
-1, 0, 1
Let a(x) = x**3 + 5*x**2 - 5*x + 8. Let m be 2 + -5 - 6/2. Let c be a(m). Factor 1/2*r**c - 1/4*r + 0.
r*(2*r - 1)/4
Let i = 18679543/81283356 + -2/205261. Let z = i - -2/99. Factor z*w**2 + 1/2*w + 1/4.
(w + 1)**2/4
Let k(p) = -2*p**3 + 10*p**2 - 8. Let j(s) = 4*s**3 - 19*s**2 + 16. Suppose -4*i + 11 = d, 4*i + 3*d + 2 = 3. Let y(z) = i*j(z) + 7*k(z). Factor y(a).
2*(a - 2)**2*(a + 1)
Let q(i) be the first derivative of i**6/24 + i**5/10 + i**4/16 + 22. Factor q(z).
z**3*(z + 1)**2/4
Solve 22*k - 36 + 4*k**3 - 40*k**2 + 38*k + 12*k**2 = 0.
1, 3
Let u = -15/22 - -161/220. Let p(a) be the second derivative of -1/6*a**4 - 3*a + 1/8*a**5 + 0 - 1/3*a**3 + 0*a**2 + u*a**6. Let p(b) = 0. What is b?
-2, -2/3, 0, 1
Let k(y) be the first derivative of 5*y**3/9 - 4*y**2/3 - 4*y/3 - 5. Solve k(o) = 0.
-2/5, 2
Let p be 1/(2/8) + -1. Solve p + 0 - r - r**2 - 1 = 0 for r.
-2, 1
Let q(t) = 2*t**3 - 2*t**2 + t + 2. Let y(g) = -3*g**2 - 3 + 3*g**2 - 3*g**3 + 0 - 2*g + 3*g**2. Let b(a) = -5*q(a) - 3*y(a). Factor b(n).
-(n - 1)**2*(n + 1)
Let s(m) be the second derivative of 1/6*m**2 + 1/36*m**4 - 1/9*m**3 + 0 - 3*m. Let s(g) = 0. What is g?
1
Let b = -1265/7 + 181. Factor -4/7*x**2 + 0 - 2/7*x**3 - b*x.
-2*x*(x + 1)**2/7
Suppose 0*f - f = h - 8, -4*h - f = -29. Factor m**3 - 5*m**2 - 3*m**3 + h*m**2.
-2*m**2*(m - 1)
Suppose 23 + 25 = -4*l. Let r be 33/12 + 9/l. Factor 2*u**2 - 2*u**2 - 3*u**r + 3*u**3 - 3*u + 3.
3*(u - 1)**2*(u + 1)
Let -9/5*c**2 + 3/5*c**3 + 9/5*c - 3/5 = 0. What is c?
1
Let o be -3 + 3 + 825/(-20). Let v = 42 + o. Factor -v*y - 1/4*y**2 - 1/2.
-(y + 1)*(y + 2)/4
Suppose -3*b = -v + 19, 2*v - b = 3*v + 1. Let -1/2*u - 1/2*u**5 - u**2 + u**3 + 1/2*u**v + 1/2 = 0. Calculate u.
-1, 1
Factor 0 + 0*r**2 - 1/2*r**4 + 0*r - 7/3*r**5 + 1/3*r**3.
-r**3*(2*r + 1)*(7*r - 2)/6
Let x(f) = -2*f**5 + 4*f**4 + 5*f**3 - 4*f**2 - 3*f. Let q(m) = -10*m**5 + 20*m**4 + 26*m**3 - 20*m**2 - 16*m. Let n(r) = 3*q(r) - 16*x(r). Factor n(l).
2*l**2*(l - 2)*(l - 1)*(l + 1)
Suppose 0 = w - 2 - 4. Let s be ((-2)/w)/(2/(-12)). Suppose q**s - 4*q**2 - q + 2*q**2 + 0*q = 0. Calculate q.
-1, 0
Determine p so that p**2 + 0*p**3 + 0 - 1/2*p**5 + 1/2*p - p**4 = 0.
-1, 0, 1
Let m(g) be the first derivative of 9/2*g - 3/2*g**2 - 1/2*g**3 + 2. Factor m(r).
-3*(r - 1)*(r + 3)/2
Let a be 30/9 - (-2)/(-6). Let i be 0*((-6)/2 - -2). Solve -4/3*p**4 + 2/3*p**a + i*p + 0 + 0*p**2 = 0 for p.
0, 1/2
Let h(q) be the second derivative of -q**8/42 - 2*q**7/105 + 7*q**6/240 - q**5/120 - q**2 - 4*q. Let d(b) be the first derivative of h(b). Factor d(f).
-f**2*(f + 1)*(4*f - 1)**2/2
Suppose 2*q + q + m - 11 = 0, -3*q + 17 = 4*m. Factor 5*t**4 + 4*t**3 - 4*t**3 + q*t**2 - 8*t**4.
-3*t**2*(t - 1)*(t + 1)
Let o(m) = 132*m**4 + 63*m**3 - 42*m**2 - 27. Let a(q) = -19*q**4 - 9*q**3 + 6*q**2 + 4. Let c(n) = -27*a(n) - 4*o(n). Determine z so that c(z) = 0.
-1, 0, 2/5
Let k(h) be the third derivative of -h**6/300 + h**5/150 + h**4/30 + 19*h**2. Suppose k(t) = 0. Calculate t.
-1, 0, 2
Let w(i) be the second derivative of i**4/18 - 4*i**3/9 + i**2 + 4*i. Factor w(u).
2*(u - 3)*(u - 1)/3
Solve -2/5*b**2 + 8/5 + 0*b = 0.
-2, 2
Suppose -33 = -5*m + 4*w, 6*w - w = -3*m + 42. Factor -3*x - 2*x**3 - x**3 - 3*x + m*x**2.
-3*x*(x - 2)*(x - 1)
Let k(o) be the first derivative of -o**6/360 - o**5/120 + o**4/12 - 4*o**3/3 - 4. Let b(w) be the third derivative of k(w). Factor b(j).
-(j - 1)*(j + 2)
Let n(f) = 10*f**2 + 17*f + 11. Let p(d) = 3*d**2 + 6*d + 4. Let a(i) = -4*n(i) + 11*p(i). Determine o so that a(o) = 0.
-2/7, 0
Let n(g) be the first derivative of 1/3*g**3 + 1/2*g**2 + 0*g + 1. Solve n(r) = 0 for r.
-1, 0
Let d(b) be the third derivative of -b**6/60 + b**5/6 + b**4/12 - 5*b**3/3 + 2*b**2 + 16. Suppose d(v) = 0. What is v?
-1, 1, 5
Let b be (-1)/(-4)*(7 - -5). Suppose b*j + 4*u + 4 = 0, 2*j - 7*j = -2*u - 2. Factor j*x + 0 + 2/3*x**3 + 4/3*x**2 - 2/3*x**4.
-2*x**2*(x - 2)*(x + 1)/3
Let b(c) be the second derivative of 1/60*c**6 + 0*c**2 - 4*c - 1/24*c**4 + 0*c**3 + 0*c**5 + 0. Solve b(j) = 0 for j.
-1, 0, 1
Suppose 3*v + 18 + 7 = 5*s, -23 = s + 5*v. Suppose -9*k**2 + 3*k - 2 + 5*k**s + 3 + 0 = 0. What is k?
-1/4, 1
Let r = 19 + -19. Let y(v) be the second derivative of 1/50*v**5 + 0*v**3 - 1/15*v**4 + 0*v**2 + r - 2*v. Factor y(w).
2*w**2*(w - 2)/5
Let f(u) be the third derivative of 1/12*u**4 + 0*u - 1/60*u**6 + 0 + 1/3*u**3 - 1/30*u**5 + 9*u**2. Suppose f(k) = 0. What is k?
-1, 1
Let l(y) be the first derivative of -3*y**5/20 + 3*y**4/4 - y**3 - 10*y - 11. Let d(h) be the first derivative of l(h). Suppose d(k) = 0. Calculate k.
0, 1, 2
Suppose -2*z - 3*z + 21 = 2*m, 5*m = 5*z. Let q(x) be the first derivative of -2/3*x**2 + 2/9*x**3 + 2/3*x - m. Factor q(y).
2*(y - 1)**2/3
Let s be (-26)/(-156) + -1*(-1)/2. Factor 0*n + 0 - 1/3*n**3 - s*n**2.
-n**2*(n + 2)/3
Let d be -1 + 4 - (-2)/((-6)/9). Let q(b) be the second derivative of 0*b**2 + b + 0 + 1/6*b**4 + d*b**3. Factor q(n).
2*n**2
Suppose g - 3611 = -3*m, 3614 = g - 0*m + 2*m. Let o = g - 17998/5. Find q, given that -4/5 - 34/5*q - 94/5*q**4 - o*q**2 - 142/5*q**3 - 24/5*q**5 = 0.
-1, -2/3, -1/4
Suppose 0 = 16*r - 19*r + 6. Let 8/3 + 10/3*o**r + 8*o = 0. Calculate o.
-2, -2/5
Let y = -16 - -22. Let f be (y/25)/(15/100). Factor -f*o + 4/5 + o**3 - 7/5*o**2.
(o - 2)*(o + 1)*(5*o - 2)/5
Let f be (4 - 320/75) + (-4)/(-6). Let -f*c**2 + 4/5*c - 2/5 = 0. Calculate c.
1
Let j(c) be the second derivative of c**6/165 - c**4/33 + c**2/11 + 4*c. Factor j(k).
2*(k - 1)**2*(k