f) be the third derivative of 0*f - 1/120*f**5 - 1/160*f**6 + 0 - 1/840*f**7 + 0*f**4 + 0*f**3 + 6*f**2. Factor n(w).
-w**2*(w + 1)*(w + 2)/4
Let p(l) be the first derivative of -7*l**7/24 - 7*l**6/40 + 3*l**5/10 - l**4/12 - 4*l - 3. Let m(t) be the first derivative of p(t). Factor m(v).
-v**2*(v + 1)*(7*v - 2)**2/4
Factor 8*b**2 - 15*b**3 - 4/3*b + 25/3*b**4 + 0.
b*(b - 1)*(5*b - 2)**2/3
Let o be (46/8)/(60/(-48)). Let d = o - -227/20. Factor -1/2 - d*k**2 - 23/4*k**3 - 7/4*k**4 - 13/4*k.
-(k + 1)**3*(7*k + 2)/4
Let u = 9 - 17/2. Let g(f) be the first derivative of u*f**4 - 2/5*f**5 - f**2 + 2/3*f**3 + 0*f - 1. Determine t, given that g(t) = 0.
-1, 0, 1
Let t(i) be the second derivative of -3*i**5/140 + 3*i**4/28 + 9*i**3/14 + 15*i**2/14 + 22*i. What is o in t(o) = 0?
-1, 5
Suppose -2*k - 2*k = -8. Let x(d) be the first derivative of 0*d + 0*d**2 - 4/33*d**3 - k + 1/22*d**4. Find v, given that x(v) = 0.
0, 2
Let i be -4 - -5 - 2 - -3. Determine w, given that 0 - 2/9*w**i + 0*w = 0.
0
Let r(k) be the first derivative of 4*k**7/21 - k**6/15 + 3*k + 1. Let w(g) be the first derivative of r(g). Suppose w(u) = 0. What is u?
0, 1/4
Factor -1/2*k**2 - 1/2*k**4 + k**3 + 0*k + 0.
-k**2*(k - 1)**2/2
Let x(r) = -4*r**3 + 5*r**2 + 12*r - 13. Let w(v) = -12*v**3 + 16*v**2 + 36*v - 40. Let t(i) = 5*w(i) - 16*x(i). Let t(z) = 0. What is z?
-2, 1
Let i(p) be the third derivative of 0 + 0*p + 1/72*p**4 + 2*p**2 + 0*p**3 - 1/180*p**5. Factor i(d).
-d*(d - 1)/3
Let b(d) be the second derivative of -d**6/540 + d**5/45 - d**4/9 + d**3/3 + d. Let q(g) be the second derivative of b(g). Solve q(k) = 0.
2
Factor 0 - 2/5*x**4 - 2/5*x - 6/5*x**2 - 6/5*x**3.
-2*x*(x + 1)**3/5
Determine c so that 2*c**3 + 0*c**3 + 10*c**2 + 14*c + 6 + 0*c**2 = 0.
-3, -1
Let o = 27509/5 - 28118/5. Let q = 123 + o. Determine j so that -8/5*j**3 + 0*j**2 + q*j + 2/5 = 0.
-1/2, 1
Let d be 80/45 - (-2)/9. Let b = 1 + d. Factor n**2 - n**2 - b*n**3 - 3*n**2 + 3 + 3*n.
-3*(n - 1)*(n + 1)**2
Find p such that 28*p**2 - 8*p**3 - 28*p**4 + 16 - 16 + 8*p = 0.
-1, -2/7, 0, 1
Let h = 273 + -1907/7. Suppose 2/7*d**2 + h*d**3 - 2/7*d**4 + 0 - 4/7*d = 0. Calculate d.
-1, 0, 1, 2
Let y = -3 - -5. Find x, given that y*x**3 + 0*x + 0 - 2*x + 1 - x**4 = 0.
-1, 1
Let v(f) = -f**2 + 6*f - 2. Let o be v(5). Suppose q + s - o = 0, -3*q - 1 - 2 = -s. Factor -1/2*j**2 - 1/4*j + q - 1/4*j**3.
-j*(j + 1)**2/4
Let f(d) be the second derivative of -1/30*d**6 + 1/6*d**3 + d + 0*d**2 + 1/12*d**4 - 1/20*d**5 + 0. Solve f(h) = 0.
-1, 0, 1
Suppose -2*m + m = 4*u + 4, 16 = 5*u - 4*m. Let l(a) be the third derivative of 0*a + 0 + 1/60*a**6 + u*a**3 + 1/3*a**4 - 2*a**2 - 2/15*a**5. Factor l(v).
2*v*(v - 2)**2
Factor -2/7*z**2 + 18/7 + 0*z.
-2*(z - 3)*(z + 3)/7
Let q(x) be the third derivative of x**5/330 + x**4/66 - 19*x**2. Factor q(i).
2*i*(i + 2)/11
Let r(s) be the second derivative of 0*s**2 + s - 1/39*s**3 + 1/39*s**4 + 0 - 1/130*s**5. Determine x so that r(x) = 0.
0, 1
Let g be -2*(6/(-2) + 2). Solve -9*w + 81*w + 30*w**g - 93*w**2 - 12 - 147*w**3 = 0 for w.
-1, 2/7
Let z(o) be the third derivative of -3/20*o**4 + 4*o**2 - 1/900*o**6 + 0*o - 1/50*o**5 + 0 - 2/3*o**3. Let y(b) be the first derivative of z(b). Factor y(f).
-2*(f + 3)**2/5
Let k(q) be the first derivative of 3*q**6/25 - 8*q**5/25 + q**4/6 + 2*q**3/15 - 3*q - 1. Let y(c) be the first derivative of k(c). Let y(i) = 0. Calculate i.
-2/9, 0, 1
Suppose 3*k - 3 = 3. Factor 5/4*b**4 + 5/2*b**3 + 5/2*b**k + 1/4 + 1/4*b**5 + 5/4*b.
(b + 1)**5/4
Let s(d) = 3*d**2 - 2*d + 1. Let m be s(1). Let q(y) be the first derivative of y + 1/3*y**3 + m + y**2. Factor q(h).
(h + 1)**2
Let q(j) = 5*j**4 + 4*j**3 - 4*j**2 - 4*j. Let i(h) = h**4 + h**3 - h**2 - h. Let o(z) = -20*i(z) + 5*q(z). Determine f, given that o(f) = 0.
0
Let x(t) be the first derivative of -t**4/4 - 2*t**3 - 6*t**2 - 8*t + 9. Factor x(a).
-(a + 2)**3
Let w(h) = h**3 - 5*h**2 + 2. Let m(j) = -4*j**3 + 16*j**2 - j - 7. Let n(y) = 4*m(y) + 14*w(y). Find q, given that n(q) = 0.
-2, -1, 0
Let i(w) = 39*w**2 - w - 1. Let m be i(-1). Let c be (-285)/(-260) - (-6)/m. Factor -c*u**2 - 2*u + 1.
-(u + 2)*(5*u - 2)/4
Determine j so that -8 - 4*j**3 - 9 + 17 = 0.
0
Let k(z) be the first derivative of z**4/4 - z**3/3 + 8. Solve k(t) = 0 for t.
0, 1
Let n be (8/(-24))/(10/(-12)). Factor -2/5*i**4 - 8/5*i - 12/5*i**2 - n - 8/5*i**3.
-2*(i + 1)**4/5
Suppose 2*v = 7*v - 10. Suppose -2*x = -3*o - 7, 2*o = 4*o + v. Find k, given that -2*k + 2 - 1 + 2*k**2 + x*k**3 - 3 = 0.
-1, 1
Let o(t) be the third derivative of 5*t**8/336 + t**7/14 + t**6/12 - t**5/6 - 5*t**4/8 - 5*t**3/6 - 15*t**2. Factor o(z).
5*(z - 1)*(z + 1)**4
Let y(u) be the second derivative of u**7/5040 + u**6/360 + u**5/60 - u**4/12 - 3*u. Let t(b) be the third derivative of y(b). Factor t(c).
(c + 2)**2/2
Find r such that 0*r**3 + 0 - 2/13*r**5 + 2/13*r - 4/13*r**2 + 4/13*r**4 = 0.
-1, 0, 1
Let s(g) be the third derivative of g**6/90 + g**5/20 - g**4/6 + 2*g**3/3 + 2*g**2. Let h(q) be the first derivative of s(q). Factor h(d).
2*(d + 2)*(2*d - 1)
Determine b, given that -20 + 6*b**3 + 15*b**2 - 9*b**3 + 8*b**3 = 0.
-2, 1
Let g(x) = 11*x**2 - 21*x - 21. Let h(i) = -5*i**2 + 10*i + 10. Suppose a + 2*z = 15, -2*z + 3*z = -3*a + 40. Let w(t) = a*h(t) + 6*g(t). Solve w(q) = 0.
-2
Let u(g) be the third derivative of g**7/1680 + g**6/720 - g**3/3 + 5*g**2. Let q(r) be the first derivative of u(r). Factor q(y).
y**2*(y + 1)/2
Solve 39/2*m**2 + 6 + 24*m + 9/2*m**3 = 0.
-2, -1/3
Factor 98/11 + 2/11*q**2 + 28/11*q.
2*(q + 7)**2/11
Suppose 16 = -22*z + 26*z. Let v(s) be the third derivative of 1/18*s**3 + 0 - 1/24*s**z + 0*s - 3*s**2 + 1/90*s**5. Factor v(j).
(j - 1)*(2*j - 1)/3
Let h(d) be the first derivative of 3*d**4/4 - 9*d**2/2 + 6*d - 42. Factor h(o).
3*(o - 1)**2*(o + 2)
Let h be (20/12)/(-5) + (12 - 11). Solve h*u**2 + 2/3*u - 4/3 = 0.
-2, 1
Let v be (-9)/(-72)*8 - 1. Determine s so that 12*s**3 + 3/2*s**5 + 15/2*s**4 + 0*s + 6*s**2 + v = 0.
-2, -1, 0
Let g(j) be the first derivative of j**3/6 - 2*j**2 + 8*j + 20. Find i such that g(i) = 0.
4
Let h(k) be the second derivative of k**6/60 - k**5/15 - k**4/12 + 2*k**3/3 - 3*k**2/2 + 3*k. Let n(m) be the first derivative of h(m). Factor n(g).
2*(g - 2)*(g - 1)*(g + 1)
Let b be 46/(-14) + 12/42. Let i(d) = 6*d**2 - 9*d. Let k(t) = 6*t - 6*t**2 + 13*t + 1 - 7*t**2. Let m(f) = b*k(f) - 7*i(f). Suppose m(q) = 0. What is q?
1
Find z such that -4/3*z**3 + 0 - 2/3*z**4 - 2/3*z**2 + 0*z = 0.
-1, 0
Let y(c) = 7*c**2 - 13*c + 6. Let n(a) = -a**2 + 2*a - 1. Let s(q) = 39*n(q) + 6*y(q). Factor s(i).
3*(i - 1)*(i + 1)
Let m(a) be the second derivative of -a + 1/6*a**3 + 0*a**2 + 0*a**4 - 1/20*a**5 + 0. What is p in m(p) = 0?
-1, 0, 1
Suppose -16 = 3*h - 0*h - 4*q, 3*h = -4*q + 16. Let 0*m**4 + 2/7*m**5 - 6/7*m**3 + h*m + 0 - 4/7*m**2 = 0. What is m?
-1, 0, 2
Let a be (-3)/(-3)*(-6)/(-27). Solve -2/9*u + 0*u**3 + a*u**5 + 0 + 4/9*u**2 - 4/9*u**4 = 0.
-1, 0, 1
Let s = -31 - -43. Suppose 0 = t + s - 1. Let j(r) = -2*r**2 - 2*r + 8. Let c(d) = -5*d**2 - 7*d + 23. Let p(m) = t*j(m) + 4*c(m). Factor p(z).
2*(z - 2)*(z - 1)
Let h(b) be the first derivative of 2*b**6/3 + 12*b**5/5 + 3*b**4 + 4*b**3/3 - 13. Factor h(x).
4*x**2*(x + 1)**3
Let x = -10 + 52/5. Let c be (-1 - (-2 + 2))*0. Factor c - 2/5*d**5 - x*d**2 + 0*d + 2/5*d**4 + 2/5*d**3.
-2*d**2*(d - 1)**2*(d + 1)/5
Let d(p) be the first derivative of -1 - 1/6*p**3 + 0*p**2 + 0*p**4 + 1/20*p**5 - p. Let z(l) be the first derivative of d(l). Solve z(w) = 0 for w.
-1, 0, 1
Let u(d) = -d**3 - 5*d**2 + 7*d + 8. Let p be u(-6). Factor -5*s**2 + 2*s**4 + 3*s**2 + 6*s**3 - p*s**3 - 4*s.
2*s*(s - 1)*(s + 1)*(s + 2)
Let m(q) be the second derivative of q**4/16 - q**3 + 6*q**2 + q. Find t such that m(t) = 0.
4
Let y(d) be the second derivative of 1/21*d**7 + 0*d**4 + 0*d**2 + 0*d**3 + 0*d**5 - 1/15*d**6 + 0 + 2*d. Factor y(k).
2*k**4*(k - 1)
Let u = 31 + -21. Suppose d - u = -3*f, -d = -5*f + 17 + 5. Solve 8/7*v**2 - 4/7*v**3 - 6/7*v**f + 4/7*v - 2/7 = 0 for v.
-1, 1/3, 1
Suppose -a + 8 = 3*a. Let -9*x**3 + 2*x**2 - 5 + 2 + 9*x - x**2 + 2*x**a = 0. Calculate x.
-1, 1/3, 1
Suppose 0 = 3*a - 14 - 7. Factor -3*r**2 + 5*r**2 - a + 3 - 2*r.
2*(r - 2)*(r + 1)
Let w(h) = -13*h**4 - 4*h**3 + 13*h**2 