 -6. Factor -3*h**w + 4*h**2 - 2*h**5 + 2*h + 7*h**4 - 8*h**2.
-2*h*(h - 1)**3*(h + 1)
Let o be (-3 - 2) + 4 + -5. Let d(n) = -n**3 - 5*n**2 + 6*n + 4. Let m be d(o). Suppose 5/2*r**2 - r + 0 + 1/2*r**5 - 1/2*r**m - 3/2*r**3 = 0. What is r?
-2, 0, 1
Factor -4/3*m**3 + 2/3*m**5 + 2/3*m - 4/3*m**2 + 2/3 + 2/3*m**4.
2*(m - 1)**2*(m + 1)**3/3
Let q(h) be the third derivative of 1/60*h**6 + 0*h**3 + 0 - 1/12*h**4 + 3*h**2 + 2/105*h**7 - 1/15*h**5 + 0*h. Solve q(u) = 0 for u.
-1, -1/2, 0, 1
Factor 1/3*i + 1/3*i**3 + 0 + 2/3*i**2.
i*(i + 1)**2/3
Suppose -1 + 7 = 4*m + 3*r, 0 = 5*r + 10. Factor -a**2 - a**2 + 0*a**2 - a + 6 - m*a.
-2*(a - 1)*(a + 3)
Let l(v) be the third derivative of -v**6/40 + v**5/5 + 22*v**2. Factor l(b).
-3*b**2*(b - 4)
Let b(v) be the second derivative of 2*v**7/63 - 14*v**6/45 + 19*v**5/15 - 25*v**4/9 + 32*v**3/9 - 8*v**2/3 - 34*v. Factor b(n).
4*(n - 2)**2*(n - 1)**3/3
Let q(b) be the first derivative of -b**7/3780 + b**6/1620 + 2*b**3/3 + 2. Let d(w) be the third derivative of q(w). Suppose d(r) = 0. What is r?
0, 1
Let z(v) be the second derivative of 3/2*v**2 + 1/12*v**4 - 2/3*v**3 - 5*v + 0. Factor z(y).
(y - 3)*(y - 1)
Let g(u) = -6*u**2 - 3*u + 11. Let h(y) = y**2 - y - 1. Let c(o) = g(o) + 5*h(o). Let s be c(-8). Let 0*q**2 - s*q**3 + 4*q**2 - q**2 + 9*q**3 = 0. Calculate q.
-1, 0
Let w(l) be the first derivative of -l**6/6 + l**5/5 + 7*l**4/4 - l**3/3 - 3*l**2 + 46. Suppose w(q) = 0. Calculate q.
-2, -1, 0, 1, 3
Let x(k) be the third derivative of -k**5/20 + 3*k**4/8 + 2*k**3 - 2*k**2. Factor x(j).
-3*(j - 4)*(j + 1)
Suppose y - 2*q - 17 - 3 = 0, y + 5*q = -1. Solve -12*s**2 - 2*s**2 - 4 + 17*s**4 - y*s**5 + s**2 - 20*s - 18*s**3 + 52*s**3 = 0.
-1, -1/2, -2/7, 1, 2
Let f(b) be the second derivative of b**6/6 - 5*b**5/4 + 15*b**4/4 - 35*b**3/6 + 5*b**2 - 14*b. Let f(g) = 0. What is g?
1, 2
What is c in -3 - 6*c - 3/4*c**3 - 15/4*c**2 = 0?
-2, -1
Factor 12*f**3 + 6*f**2 + 2*f**2 - 8*f**3 + 4*f.
4*f*(f + 1)**2
Solve -1/3*p**2 + 1 + 2/3*p = 0 for p.
-1, 3
Suppose 0 = 6*b - 2*b. Suppose -5*m + b*m = 0. Solve -2*d**2 + 2*d + m*d**2 + d - 5*d = 0.
-1, 0
Let v(r) = -r**2 - 10*r - 23. Let w(q) = -1. Let l(c) = 2*v(c) + 4*w(c). What is z in l(z) = 0?
-5
Let g(j) be the first derivative of -2*j**5/25 + 3*j**4/10 - 4*j**3/15 + 2. What is d in g(d) = 0?
0, 1, 2
Let z(x) be the second derivative of 3*x**7/14 + x**6/10 - 27*x**5/20 + 3*x**4/4 + x**3 - 28*x. Let z(h) = 0. Calculate h.
-2, -1/3, 0, 1
Let m = 321 - 318. Determine d, given that -5/9*d**m - 4/3*d**2 - 2/9 - d = 0.
-1, -2/5
Let q(f) be the second derivative of -f**4/3 + 2*f**3/3 + 4*f**2 - 2*f. What is d in q(d) = 0?
-1, 2
Let w(s) be the third derivative of -s**9/15120 - s**8/2240 - s**7/840 - s**6/720 + s**4/12 - 2*s**2. Let v(t) be the second derivative of w(t). Factor v(l).
-l*(l + 1)**3
Let o(u) = 5*u**2 + 13*u. Let x(r) = -16*r**2 - 40*r. Let c(p) = -10*o(p) - 3*x(p). Factor c(h).
-2*h*(h + 5)
Suppose 0*i - 8/3*i**3 - 2/3*i**4 + 0 - 8/3*i**2 = 0. Calculate i.
-2, 0
Factor -9*a**3 + 3*a**2 + 7*a**2 + 14*a**3.
5*a**2*(a + 2)
Let n(s) be the third derivative of 7*s**8/96 + 17*s**7/60 + 67*s**6/240 - 23*s**5/120 - s**4/3 + s**3/3 + 5*s**2. Factor n(o).
(o + 1)**3*(7*o - 2)**2/2
Let q(v) be the first derivative of 1/6*v**3 + 1/16*v**4 - 2 + 1/8*v**2 + 0*v. Let q(o) = 0. What is o?
-1, 0
Suppose -3/2*d**4 + 0*d + 0 + 9/2*d**3 + 0*d**2 = 0. Calculate d.
0, 3
Suppose -5*p = 7 - 17. Factor 5*f**5 + 3*f**p - 18*f**3 - 8*f**5 - 9*f**5 + 27*f**4.
-3*f**2*(f - 1)**2*(4*f - 1)
Let y(d) be the second derivative of -3*d - 1/20*d**5 - 1/4*d**2 + 1/6*d**3 + 0 + 0*d**4 + 1/60*d**6. What is f in y(f) = 0?
-1, 1
Factor -1/5*w**3 + 0 + 2/5*w**4 + 0*w - 2/5*w**2 + 1/5*w**5.
w**2*(w - 1)*(w + 1)*(w + 2)/5
Let b = -11/5 + 4. What is y in 6/5*y - b - 1/5*y**2 = 0?
3
Suppose 3*t + 5 = 4*t. Suppose 0 = -4*q + 3*p + 17, -t*q = -4*q + p + 1. Determine s so that 0 - 2/3*s + 1/3*s**q = 0.
0, 2
Factor -4/7*u**2 - 16/7 + 16/7*u.
-4*(u - 2)**2/7
Let n(x) be the first derivative of x**5/5 - x**3 - x**2 + 1. Factor n(r).
r*(r - 2)*(r + 1)**2
Let b(s) be the third derivative of -5*s**8/1512 - s**7/105 + s**6/270 + s**5/27 + s**4/36 - s**3/27 + s**2. Suppose b(z) = 0. Calculate z.
-1, 1/5, 1
Let n = 3036 + -9361/3. Let w = n + 85. Factor 0 + 2/3*s**3 + 0*s**2 + 0*s + w*s**4.
2*s**3*(s + 1)/3
Let v(k) = k**2 - k. Let a(r) = -8*r**2 - 11*r - 17. Let f(l) = 4*l**2 + 6*l + 8. Let g(j) = 2*a(j) + 5*f(j). Let c(x) = g(x) - v(x). Factor c(t).
3*(t + 1)*(t + 2)
Let t(v) = v**3 + 5*v**2 + 3*v + 7. Let d be t(-5). Let g = d - -10. Factor -i - 3*i**g + 0*i**4 - 2*i**3 - i**3 - i**4.
-i*(i + 1)**3
Let h(l) be the first derivative of -5*l**3/3 + 5*l**2 - 5*l + 1. Factor h(y).
-5*(y - 1)**2
Let u(v) be the third derivative of v**6/220 + v**5/110 - 5*v**4/44 + 3*v**3/11 + 12*v**2. Suppose u(a) = 0. What is a?
-3, 1
Let r(v) be the third derivative of -v**5/180 - 5*v**4/36 + 6*v**2 - 2*v. Factor r(h).
-h*(h + 10)/3
Factor -3/2 + 0*d**3 + 3*d**2 - 3/2*d**4 + 0*d.
-3*(d - 1)**2*(d + 1)**2/2
Let y(g) be the first derivative of 3 + 0*g + 0*g**3 - 1/30*g**4 - 1/150*g**5 - g**2. Let h(l) be the second derivative of y(l). Factor h(f).
-2*f*(f + 2)/5
Factor -4/3*n**2 + 4/3*n**3 + 2/3*n**4 - 2/3*n + 2/3 - 2/3*n**5.
-2*(n - 1)**3*(n + 1)**2/3
Let m = 13 - 12. Suppose m + 7 = 2*y, -c = y - 6. Factor 2/9*t**3 + 2/9*t**c - 2/9*t - 2/9.
2*(t - 1)*(t + 1)**2/9
Solve -26*n**3 + 41*n - 29*n**3 - 31*n - 20*n**4 - 25*n**2 = 0.
-2, -1, 0, 1/4
Suppose z = -4*a + 14, 4*z - 4 = -4*a + a. Suppose -4*k - 25 = -5*h - k, a*k = -h + 5. Suppose g**4 + h*g**4 + 2*g**5 - 4*g**4 = 0. What is g?
-1, 0
Let x(k) = -k**5 - k**4 + 5*k**3 + 3*k. Let z(w) = -w**2 - w. Let c(m) = -x(m) - 3*z(m). Find l such that c(l) = 0.
-3, 0, 1
Let h(x) be the first derivative of x**4/32 + 13*x**3/24 + 3*x**2 + 9*x/2 - 59. Suppose h(m) = 0. Calculate m.
-6, -1
Let i(x) = -2*x**2 - 7*x + 3. Let v(o) = -18*o**2 - 62*o + 26. Let k(s) = -52*i(s) + 6*v(s). Solve k(b) = 0 for b.
-2, 0
Solve a**4 + 2*a**5 - a**3 + 5*a**4 + 5*a**3 = 0.
-2, -1, 0
Let t(z) = -z**2 + 8*z + 13. Let j be t(9). Let f(p) be the second derivative of -5/9*p**3 - 2/3*p**2 - 1/30*p**5 + p + 0 - 2/9*p**j. Solve f(b) = 0.
-2, -1
Factor -3*t**2 + 3/2*t**3 - 3/2*t + 3.
3*(t - 2)*(t - 1)*(t + 1)/2
Let p(z) be the third derivative of z**5/480 + z**4/64 + z**3/24 - 9*z**2. Determine n so that p(n) = 0.
-2, -1
Suppose 2*l - 5*w - 35 = 0, 2*l - 26 = w + w. Let d = -8 + l. Factor -2/5*z**5 + 4/5*z**4 + 0*z**d + 0*z + 0 - 2/5*z**3.
-2*z**3*(z - 1)**2/5
Let p = 1 - -9. Let -5*q + q**5 - 10*q**3 + 1 + 5*q**4 - 5*q**5 + p*q**2 + 3*q**5 = 0. Calculate q.
1
Let m(k) be the second derivative of -k**4/4 - k**3/2 - 9*k. Factor m(j).
-3*j*(j + 1)
Let g(t) be the first derivative of 1/4*t**3 + 4 - 1/16*t**4 + 1/4*t - 3/8*t**2. Factor g(p).
-(p - 1)**3/4
Let z(b) = -2*b + 2. Let a be z(1). Let s(i) be the second derivative of 2/27*i**4 - 1/9*i**2 - 2*i + a - 1/9*i**3. Factor s(d).
2*(d - 1)*(4*d + 1)/9
Let m(o) be the first derivative of o**6/1440 - o**5/160 + o**4/48 - 2*o**3/3 + 4. Let z(p) be the third derivative of m(p). Suppose z(c) = 0. Calculate c.
1, 2
Let f(n) be the second derivative of -n**6/6 - n**5/4 + 5*n**4/12 + 5*n**3/6 - 24*n. Factor f(s).
-5*s*(s - 1)*(s + 1)**2
Let i = 4 - 3. Suppose -3*j - 5*c + 19 = 0, 5*j + i = 2*j + 5*c. Let -2/7 + 2/7*a**2 - 2/7*a**j + 2/7*a = 0. Calculate a.
-1, 1
Let p = 1/322 + 317/1610. Suppose p*t**3 - 1/5*t + 0 + 0*t**2 = 0. Calculate t.
-1, 0, 1
Let y(r) be the first derivative of -105*r**6/2 - 186*r**5 - 505*r**4/2 - 500*r**3/3 - 115*r**2/2 - 10*r + 22. Determine j so that y(j) = 0.
-1, -1/3, -2/7
Let n(k) be the second derivative of -1/15*k**6 + 1/20*k**5 + 0 - 7/24*k**3 + 1/56*k**7 + 1/8*k**4 + 1/4*k**2 - 7*k. Factor n(c).
(c - 1)**3*(c + 1)*(3*c - 2)/4
Let z(h) = -h - 6. Let a be z(-12). Let x be (-1)/a*2*-129. Factor -x*t + 1 + 9*t**2 + 2 + 52*t + 3*t**3.
3*(t + 1)**3
Let n(c) = -2*c**3 - 23*c**2 - 16*c - 8. Let r(m) = -m**3 - 11*m**2 - 8*m - 4. Let s(p) = 6*n(p) - 13*r(p). Suppose s(w) = 0. What is w?
-2, -1
Let o = -17 + 21. Let f(z) be the first derivative of 2 + 0*z - 5/8*z**o - 3/10*z**5 + 0*z**2 - 1/3*z**3. Suppose f(h) = 0. What is h?
-1, -2/3, 0
Let r be (-5)/5*0/3.