4*q, 4*q = -b. Factor -4*z**2 - z**4 + 0*z + 2*z + 4*z**3 - z**2 + q*z**4.
-z*(z - 2)*(z - 1)**2
Let s(w) be the second derivative of w**4 - 16*w**3/3 - 6*w**2 + 16*w. Factor s(h).
4*(h - 3)*(3*h + 1)
Solve -1/2 - 1/2*u**2 - u = 0.
-1
Let c(z) be the second derivative of -5*z + 2*z**3 - 6/7*z**7 - 14/5*z**6 - 2*z**5 + 2*z**4 + 0 - 2*z**2. Find s such that c(s) = 0.
-1, 1/3
Let m(u) be the first derivative of u**4/8 - 3*u**3/2 + 27*u**2/4 - 27*u/2 - 1. Suppose m(t) = 0. Calculate t.
3
Let q(g) be the third derivative of g**7/42 + g**6/40 - g**5/30 + g**2. Let q(h) = 0. What is h?
-1, 0, 2/5
Let h(z) be the second derivative of z**4/6 - 8*z**3/3 + 16*z**2 + 13*z. Factor h(o).
2*(o - 4)**2
Let n(x) = -x**2 - x + 2. Let v(l) be the third derivative of -l**5/30 - l**4/12 + l**3/2 - 3*l**2. Let y(u) = 3*n(u) - 2*v(u). What is o in y(o) = 0?
-1, 0
Let n(x) = -4*x**4 + 8*x**2 - 3*x - 1. Let g(a) = 4*a**4 - 8*a**2 + 4*a. Let z(q) = -3*g(q) - 4*n(q). Find p, given that z(p) = 0.
-1, 1
Let w(m) be the third derivative of -1/840*m**8 + 0*m**5 + 0*m**4 + 2*m**2 + 0*m**3 + 2/525*m**7 - 1/300*m**6 + 0*m + 0. Find l, given that w(l) = 0.
0, 1
Let f be -3 - (56/(-10) - (-3)/5). Factor 0*t**f + 0 + 1/5*t**3 - 1/5*t.
t*(t - 1)*(t + 1)/5
Let a(z) = z**2 - 4*z - 4. Let q be a(5). Let x = 1 + q. Factor 2*m**2 + 3 + 3 - x - 6*m.
2*(m - 2)*(m - 1)
Let i(t) = -t**5 + t**3 + t - 1. Suppose -3 = 3*f - 4*f. Let p(j) = -j**5 + j**3 + 3*j - 3. Let x(l) = f*i(l) - p(l). Solve x(s) = 0 for s.
-1, 0, 1
Suppose -2*l - 5*k = -9, 0*l - 1 = 2*l - 5*k. Let o = l + 0. Solve o*j**2 - 2*j**2 - 2 + 2*j**2 = 0 for j.
-1, 1
Let a(x) be the third derivative of x**9/1680 + x**8/560 - x**7/840 - x**6/120 + x**4/24 - 4*x**2. Let n(y) be the second derivative of a(y). Factor n(b).
3*b*(b + 1)**2*(3*b - 2)
Determine o, given that 33*o**3 + 19*o + 13*o**2 + 9*o**4 + 6 + 8*o + 32*o**2 = 0.
-1, -2/3
Let w(r) be the second derivative of 0*r**2 + 1/60*r**6 + 0 - 2*r - 1/40*r**5 + 0*r**3 + 0*r**4. Find m such that w(m) = 0.
0, 1
Find x, given that -1/3 + 2/3*x - 1/3*x**2 = 0.
1
Let r(n) be the first derivative of n**6/18 - 4*n**5/15 + 5*n**4/12 - 2*n**3/9 - 4. Let r(s) = 0. Calculate s.
0, 1, 2
Suppose -5*h + w = 17, 2*h - 3 + 5 = 2*w. Let l be h/7*(-14)/4. Find u such that 2/9*u**l - 2/9*u**3 + 0*u + 0 = 0.
0, 1
Let d(s) be the first derivative of -7/3*s**6 + 2*s**2 + 5/2*s**4 + 18/5*s**5 + 0*s + 2 - 6*s**3. Determine r so that d(r) = 0.
-1, 0, 2/7, 1
Factor -3/7 - 10/7*z - 3/7*z**2.
-(z + 3)*(3*z + 1)/7
Suppose 6*v - 7*v + 5 = 0. Let g(s) be the second derivative of -1/12*s**4 - 1/9*s**3 + 0*s**2 - s - 1/60*s**v + 0. Determine k, given that g(k) = 0.
-2, -1, 0
Let q(c) be the first derivative of -c**5/5 + c**4/2 - c**2 + c - 23. Factor q(d).
-(d - 1)**3*(d + 1)
Solve 13*r - 10*r - 4*r**3 - 7*r**3 + 3*r**5 + 5*r**3 = 0 for r.
-1, 0, 1
Let c = -19 + 44. Factor -21*h + c*h**2 - 3*h - 10*h**2 - 12.
3*(h - 2)*(5*h + 2)
Solve -6*n**3 + 2*n**5 + 138*n**2 - 68*n**2 - 66*n**2 = 0.
-2, 0, 1
Let h be (1 - (-10)/(-12))/(39/104). Factor 0 - h*o**2 + 2/9*o**3 + 2/9*o.
2*o*(o - 1)**2/9
Factor 2/11*s**3 - 6/11*s**2 + 4/11*s + 0.
2*s*(s - 2)*(s - 1)/11
Let l(w) = 3*w**5 - w**4 - 4*w**3 + w + 3. Let b(c) = -4*c**5 + 2*c**4 + 5*c**3 - c**2 - c - 4. Let x = 8 + -6. Let g(h) = x*b(h) + 3*l(h). Factor g(o).
(o - 1)**2*(o + 1)**3
Let x(k) be the second derivative of 0*k**2 + 7/75*k**6 + 0 + 1/15*k**4 + 9/50*k**5 + 0*k**3 + 3*k. Factor x(r).
2*r**2*(r + 1)*(7*r + 2)/5
Let c = -490/3 + 164. Let l be 0 - (-2 + 1 - 1). Factor 0 - c*p**3 + 2/3*p + 0*p**l.
-2*p*(p - 1)*(p + 1)/3
Let t = 1102/9 + -6968/45. Let y = -32 - t. Solve -2/5*b + 4/5*b**3 - y*b**5 + 0*b**2 + 0*b**4 + 0 = 0.
-1, 0, 1
Let k(s) be the third derivative of s**7/1050 - s**6/300 + s**5/300 + 7*s**2. Find h, given that k(h) = 0.
0, 1
Let t(b) be the second derivative of b**6/30 - b**4/12 + b**2/2 - b. Let k(f) = 3*f**4 + 2*f**3 - 5*f**2 - 4*f + 6. Let y(w) = -k(w) + 2*t(w). Factor y(z).
-(z - 1)**2*(z + 2)**2
Let z(w) be the first derivative of -3*w**2 - 2*w - 9/4*w**4 - 1 - 11/2*w**3. Let p(m) be the first derivative of z(m). Factor p(b).
-3*(b + 1)*(9*b + 2)
Let k(q) be the first derivative of -1 + 0*q**5 - 1/12*q**4 + 0*q**2 + 1/180*q**6 - 1/3*q**3 + 0*q. Let g(n) be the third derivative of k(n). Factor g(y).
2*(y - 1)*(y + 1)
Let b(j) be the second derivative of j**4/8 - 3*j**3/4 + 3*j**2/2 + 29*j. Factor b(l).
3*(l - 2)*(l - 1)/2
Let r = -16 + 22. Let x = -1 + r. Solve 0 + 0*k - 2/5*k**3 + 2/5*k**4 - 2/5*k**2 + 2/5*k**x = 0 for k.
-1, 0, 1
Let q(s) be the third derivative of 1/480*s**6 + 0 + 0*s**3 - 1/840*s**7 + 0*s**4 + 0*s**5 + 0*s - 4*s**2. Factor q(f).
-f**3*(f - 1)/4
Factor 0*h + 0*h**3 - 2/3*h**4 + 0 - 5/3*h**5 + 0*h**2.
-h**4*(5*h + 2)/3
Suppose 0 = z + 3*y + 1, 5*z - 2*z - 4*y - 62 = 0. Let k = 18 - z. Determine i, given that 8*i**2 - 9/2*i - 7*i**3 + 3*i**k + 1 - 1/2*i**5 = 0.
1, 2
Let q(w) be the first derivative of -w**4/12 - 2*w**3/3 - 3*w**2/2 - 4*w/3 + 1. Factor q(r).
-(r + 1)**2*(r + 4)/3
Let i(o) = o**2 - 2*o - 1. Let c be i(4). Factor 0*s**2 - s**2 - c*s**2 + 4*s + 4*s**3.
4*s*(s - 1)**2
Let d(l) be the first derivative of l**4/2 + 4*l**3/3 - 3. Factor d(r).
2*r**2*(r + 2)
Let a(i) = -i**2 + 6*i + 9. Let m be a(7). Let z = 5 - m. Let 2 + 8*j - z*j**2 + 5*j**2 + 6 = 0. What is j?
-2
What is g in 3/2*g**4 + 0*g + g**5 - 2*g**2 - g**3 + 1/2 = 0?
-1, 1/2, 1
Let u(f) be the second derivative of f**5/110 + f**4/33 + f**3/33 + 6*f. Suppose u(d) = 0. Calculate d.
-1, 0
Let v(u) = 6*u**2 + 6*u - 21. Let j(x) = -3*x**2 - 3*x + 11. Let h(g) = -9*j(g) - 5*v(g). Solve h(k) = 0.
-2, 1
Let d(y) be the third derivative of -y**9/1512 - y**8/420 - y**7/420 - 5*y**3/6 + y**2. Let i(w) be the first derivative of d(w). Factor i(t).
-2*t**3*(t + 1)**2
Let c(j) be the first derivative of -j**5/20 + j**4/6 + j**3/6 - j**2 - 2*j + 3. Let z(k) be the first derivative of c(k). Let z(f) = 0. What is f?
-1, 1, 2
Let z(x) be the first derivative of -5*x**6/3 - 8*x**5 - 125*x**4/8 - 95*x**3/6 - 35*x**2/4 - 5*x/2 + 54. Factor z(o).
-5*(o + 1)**3*(2*o + 1)**2/2
Let l(t) be the third derivative of t**6/30 - t**5/5 + t**4/2 - 2*t**3/3 + 33*t**2. Let l(a) = 0. Calculate a.
1
Let w = 2 + 0. Suppose m = -w*m. Factor 2*z**4 + 0 + m*z + 4/3*z**3 + 0*z**2.
2*z**3*(3*z + 2)/3
Let z(d) = d**3 - 4*d**2 + d. Let o be 4*2/(-6)*3. Let j(l) = 0 + 3*l**3 + 4*l + 34*l**2 - 47*l**2 - 1. Let y(g) = o*j(g) + 14*z(g). Let y(k) = 0. Calculate k.
-1, 1, 2
Let i be -5 + 115/25 + 18/15. Factor i*g + 2/5*g**2 + 0.
2*g*(g + 2)/5
Let j(n) = n**5 - n - 1. Let m(q) = 12*q**5 - q**4 - 2*q**3 + 2*q**2 - 10*q - 12. Let i(h) = -44*j(h) + 4*m(h). Determine p, given that i(p) = 0.
-1, 1
Let w(n) be the third derivative of 11/60*n**5 + 3*n**2 - 1/20*n**6 + 1/6*n**4 - 3/70*n**7 + 0*n + 0 - 2/3*n**3. Let w(o) = 0. What is o?
-1, 2/3
Suppose 4*g**2 + g**3 + 2*g**2 - 3*g**3 - 2*g**2 - 2*g = 0. Calculate g.
0, 1
Let y(l) be the second derivative of l**6/30 + 3*l**5/10 + 13*l**4/12 + 2*l**3 + 2*l**2 + 4*l. Find d, given that y(d) = 0.
-2, -1
Suppose 50 - 53 = -p. Suppose 1/2*r**p + 0 + r**2 + 1/2*r = 0. Calculate r.
-1, 0
Let w(u) be the second derivative of u**4/78 - 2*u**3/39 - 13*u. Solve w(s) = 0 for s.
0, 2
Let s(g) = g**3 - g - 1. Let v = 5 + -13. Let c(k) = -12*k**3 - 48*k**2 - 44*k - 16. Let q(h) = v*s(h) + c(h). Solve q(j) = 0.
-1, -2/5
Let d(m) be the third derivative of m**7/3360 + m**6/960 - m**4/4 - 3*m**2. Let w(f) be the second derivative of d(f). Suppose w(y) = 0. Calculate y.
-1, 0
Let v = 8 - 5. Suppose 3*g**2 + 6*g**3 - g**2 - 8*g**v = 0. What is g?
0, 1
Suppose -1 = -d + 2. Factor -4*x**d + 0*x**3 + x**4 - 6*x**4 + 2*x**3.
-x**3*(5*x + 2)
Suppose 0 = 2*l - 4*l. Let d(h) be the first derivative of 1/3*h**3 + l*h**2 + 3 + 0*h. Suppose d(q) = 0. What is q?
0
Let h(n) = n**3 + 4*n**2 + n - 6. Let w(z) = z**3 + 3*z**2 - 5. Let m(d) = -3*h(d) + 4*w(d). Solve m(s) = 0.
-1, 2
Let n(y) be the first derivative of -y**2 + 0*y**3 + 0*y + 1/300*y**5 + 0*y**4 - 1. Let f(b) be the second derivative of n(b). Factor f(m).
m**2/5
Let o(s) = -2*s - 7. Let d be o(-5). Factor 66 - 66 - 4*l - d*l**3 + 8*l**2.
-l*(l - 2)*(3*l - 2)
Let j(q) be the third derivative of q**6/60 - q**5/10 + q**4/6 - 10*q**2. Facto