. Factor -2/9*f**5 - 2/9*f + 0 + 8/9*f**q - 4/3*f**3 + 8/9*f**4.
-2*f*(f - 1)**4/9
Let r(v) be the second derivative of -v**7/14 - 2*v**6/5 - 3*v**5/5 + v**4/2 + 5*v**3/2 + 3*v**2 + 8*v + 4. Let r(n) = 0. What is n?
-2, -1, 1
Let d = -47513/7 + 6788. Factor 0*b**3 + 0 - 3/7*b**2 + d*b**4 + 0*b.
3*b**2*(b - 1)*(b + 1)/7
Let r = 1453/10710 + -5/2142. Solve -2/15*n**3 + 2/15*n**2 - 2/15 + r*n = 0.
-1, 1
Suppose 0 = n + 2 + 3. Let i = 6 + n. What is t in 17*t - 17*t - i + t**2 = 0?
-1, 1
Let w(n) be the first derivative of -7*n**6/36 - 8*n**5/15 + 59*n**4/24 + 16*n**3/9 - 13*n**2/3 - 8*n/3 + 597. Find t such that w(t) = 0.
-4, -1, -2/7, 1, 2
Let d(u) be the third derivative of u**6/600 - 7*u**5/150 + 13*u**4/24 - 10*u**3/3 + 2*u**2 - 14. Factor d(t).
(t - 5)**2*(t - 4)/5
Let w(f) be the second derivative of f**6/10 - 21*f**5/10 + 2*f**4 + 31*f**3 + 117*f**2/2 - 2*f + 50. Determine h, given that w(h) = 0.
-1, 3, 13
Let n = -1365 + 1367. Factor -7/2*l**2 + 8*l - n.
-(l - 2)*(7*l - 2)/2
Let b(r) be the second derivative of -r**4/4 - r**3/2 + 3*r**2 - 121*r. Solve b(u) = 0.
-2, 1
Let b = -91 + 60. Let l = b + 39. Let d(a) = -23*a**2 - 15*a + 30. Let t(h) = -15*h**2 - 10*h + 20. Let u(o) = l*t(o) - 5*d(o). Suppose u(f) = 0. What is f?
-2, 1
Let x(t) = -t**2 + 1. Let p(h) = -15*h**2 + 15. Let w = 89 + -71. Let z(n) = w*x(n) - p(n). Factor z(j).
-3*(j - 1)*(j + 1)
Let j(p) be the second derivative of -p**6/540 + p**5/30 - p**4/4 - 5*p**3/6 + 4*p. Let u(d) be the second derivative of j(d). Find i such that u(i) = 0.
3
Suppose 27*p + 254 = 956. Factor -p*b**2 - 8/9 + 80/9*b + 18*b**3.
2*(b - 1)*(9*b - 2)**2/9
Let d = 17 - -23. Let n be (-26)/(-6) + 20/(d/(-8)). Factor 1/6*s**2 - 1/6*s - n.
(s - 2)*(s + 1)/6
Let s(c) be the second derivative of -8*c**7/147 + c**6/105 - 92*c. Let s(p) = 0. What is p?
0, 1/8
Solve -700*s**3 - 281815*s - 609285*s - 36750*s**2 - 7503125 + 33600*s - 5*s**4 = 0.
-35
Suppose 3*d - 4*h = 5*d - 24, 3*d - 4*h + 14 = 0. Factor d*y - 5*y + 2*y**2 + y**2.
3*y*(y - 1)
Let b(p) be the third derivative of p**8/840 - p**7/175 + p**6/150 + p**2 + 5. Factor b(r).
2*r**3*(r - 2)*(r - 1)/5
Let q(d) be the first derivative of -d**7/210 - d**6/90 + d**5/15 + 2*d**3 + 4. Let a(r) be the third derivative of q(r). What is g in a(g) = 0?
-2, 0, 1
Solve 32/3*o**3 - 32/3*o - 8*o**2 + 4 + 4*o**4 = 0 for o.
-3, -1, 1/3, 1
Let d = 12/211 + 362/1055. Factor -4/5*x**4 + 0 + d*x + 2*x**3 - 8/5*x**2.
-2*x*(x - 1)**2*(2*x - 1)/5
Let k(p) be the second derivative of -p**7/273 + p**6/65 + p**5/13 + p**4/39 - 3*p**3/13 - 5*p**2/13 + 83*p. Suppose k(y) = 0. What is y?
-1, 1, 5
Let s(x) be the third derivative of 26*x**2 + 1/24*x**4 + 0 + 1/240*x**5 + 0*x + 1/8*x**3. Factor s(r).
(r + 1)*(r + 3)/4
Suppose -3 = -2*b + 21. Let l be (-3)/(-20)*16/b. Let 0 + 0*k + 1/5*k**3 - 1/5*k**5 - 1/5*k**2 + l*k**4 = 0. What is k?
-1, 0, 1
Let n(z) be the first derivative of z**4 - 136*z**3/3 + 504*z**2 + 2592*z + 217. Factor n(r).
4*(r - 18)**2*(r + 2)
Let r(f) = -39*f**4 - 738*f**3 + 2448*f**2 - 2418*f + 819. Let t(m) = 11*m**4 + 211*m**3 - 699*m**2 + 691*m - 234. Let d(b) = -5*r(b) - 18*t(b). Factor d(g).
-3*(g - 1)**3*(g + 39)
Let m(b) be the first derivative of -b**2 - 3 + 3*b - 1/3*b**3 - 1/24*b**4. Let q(u) be the first derivative of m(u). Solve q(f) = 0.
-2
Suppose -3*y - 31 + 83 = -2*n, 3*y - 76 = -4*n. Factor -12*p - 4*p**2 + y + 8*p - 11*p - p.
-4*(p - 1)*(p + 5)
Let t(a) = -2*a**2 + 13*a + 22. Let j be t(8). Let i be (j - 12/(-8))/(-2). Factor -1 + i*f**2 + 3/4*f.
(f - 1)*(f + 4)/4
Let f(z) = -212*z**2 + 2 - 2*z + 213*z**2 + 6*z. Let m(d) = d + 1. Let p(w) = -3*f(w) + 6*m(w). Factor p(a).
-3*a*(a + 2)
Suppose 3*b - 48 = -2*v + 8, -3*b = -2*v - 40. Suppose -4 - 16*q**2 + b*q + 22*q**4 + 16*q**3 - 26*q**4 - 8*q**2 = 0. What is q?
1
Suppose -7*d = 110 + 79. Let n be (25 + d)/(1/(-1 - 0)). Factor -4/3*m**n - 2/3 + 5/3*m + 1/3*m**3.
(m - 2)*(m - 1)**2/3
Let y(z) be the first derivative of -6/5*z + 11 - 3/10*z**2 + 1/5*z**3. Find j, given that y(j) = 0.
-1, 2
Let t(m) be the second derivative of m**4/16 - 137*m**3/8 + 51*m**2 + 57*m + 6. Factor t(j).
3*(j - 136)*(j - 1)/4
Let h(f) be the first derivative of f**7/280 + f**6/24 + f**5/10 + 11*f**3 - 7. Let s(q) be the third derivative of h(q). Factor s(x).
3*x*(x + 1)*(x + 4)
Factor -3/2*u + 4/3 + 1/6*u**2.
(u - 8)*(u - 1)/6
Suppose 15*l + 41 = -13*l + 181. Factor -s**2 + 0*s + 0 + 0*s**4 - 3/2*s**3 + 1/2*s**l.
s**2*(s - 2)*(s + 1)**2/2
Let b(g) be the first derivative of 2*g**6/15 + 14*g + 11. Let x(l) be the first derivative of b(l). Factor x(r).
4*r**4
Solve 0 + 3*n**3 - 12*n - 19/2*n**2 + 1/2*n**4 = 0 for n.
-8, -1, 0, 3
Factor w**4 + w**5 - 16283*w**2 - 7*w**4 + 16297*w**2 - 9*w**3.
w**2*(w - 7)*(w - 1)*(w + 2)
Let v(t) be the second derivative of t**7/630 + t**6/270 - t**5/45 + 5*t**3/2 - 14*t. Let d(x) be the second derivative of v(x). Solve d(g) = 0.
-2, 0, 1
Let g = 17 - 2736/161. Let j = g - -158/483. Factor 1/6 - 1/3*d**3 + 0*d**2 - 1/6*d**4 + j*d.
-(d - 1)*(d + 1)**3/6
Let c(s) = 2*s**2 - 23*s - 28. Let o(b) = -b**2 + 5*b - 1. Let d(w) = -w**2 + 4*w - 1. Let j(t) = 6*d(t) - 5*o(t). Let r(h) = -c(h) + 3*j(h). Factor r(i).
-5*(i - 5)*(i + 1)
Let m = 2/1115 - -10702/1115. Solve 3/5*g**2 + 24/5*g + m = 0.
-4
Let k(u) = 5*u**5 - 10*u**3 - u - 6. Let m(a) be the third derivative of a**4/24 + a**3/6 + 5*a**2. Let j(t) = k(t) + 6*m(t). Solve j(s) = 0 for s.
-1, 0, 1
Let w(q) be the first derivative of q**4/3 + 10*q**3/3 + 8*q**2 + 12*q + 2. Let u(r) be the first derivative of w(r). Factor u(s).
4*(s + 1)*(s + 4)
Let s(c) be the second derivative of -2/15*c**6 + 14*c - c**4 + 2/3*c**3 + 3/5*c**5 + 0*c**2 + 0. Determine t so that s(t) = 0.
0, 1
Let a(d) be the second derivative of -d**5/10 + 2*d**4/3 + 17*d**3 + 90*d**2 + 44*d. Find y, given that a(y) = 0.
-3, 10
Let q be (5 - -3)*(252/135)/14. Determine s so that 2/15 + q*s + 32/15*s**2 = 0.
-1/4
Let b(x) be the third derivative of 1/3*x**3 + 3/8*x**4 - 1/30*x**5 - 3/40*x**6 + 0 + 28*x**2 + 0*x. Factor b(t).
-(t - 1)*(t + 1)*(9*t + 2)
Factor 4/7*u - 2/7 - 2/7*u**2.
-2*(u - 1)**2/7
Let x be (-3 + -27)/6 + (-10)/(-1). Find t such that 2/7*t**3 - 2/7*t**x - 2/7*t**2 + 0 + 2/7*t**4 + 0*t = 0.
-1, 0, 1
Let w(u) = u**2 + u - 5. Let k be 0 + 5/(15/21). Let x = k - 3. Let j(l) = l**2 + l - 4. Let q(g) = x*w(g) - 6*j(g). Factor q(a).
-2*(a - 1)*(a + 2)
Let n(a) be the third derivative of -a**7/105 + 17*a**6/30 - 107*a**5/10 + 136*a**4/3 - 256*a**3/3 + 4*a**2 - 3. Factor n(k).
-2*(k - 16)**2*(k - 1)**2
Let d = -90 - -98. Let i = -8 + d. Factor 4/5*g**4 + i*g + 4/5*g**3 + 0 + 0*g**2.
4*g**3*(g + 1)/5
Let l(d) be the second derivative of -d**5/20 - d**4/4 + 3*d**3/2 - 8*d**2 - 25*d. Let p(r) be the first derivative of l(r). Find w, given that p(w) = 0.
-3, 1
Find u such that 0 + 6/17*u**2 + 70/17*u = 0.
-35/3, 0
Factor 12/7 + 4/7*k**3 + 4/7*k**2 - 20/7*k.
4*(k - 1)**2*(k + 3)/7
Let -1/2*q + 4/3*q**2 - 1/3 - 1/2*q**3 = 0. Calculate q.
-1/3, 1, 2
Let s(x) be the second derivative of -7*x + 0 + 0*x**3 - 1/18*x**4 + 1/30*x**5 + 0*x**2. Let s(u) = 0. Calculate u.
0, 1
Let d(v) be the second derivative of -v**9/22680 + v**7/1890 - v**5/180 + v**4 - 8*v. Let t(x) be the third derivative of d(x). Factor t(b).
-2*(b - 1)**2*(b + 1)**2/3
Suppose -38*u**2 - 67 - 9*u + 13 + 41*u**2 = 0. Calculate u.
-3, 6
Let a = 103 + -938. Let n = a - -3361/4. Factor -27/4*f**2 - n*f - 3/2 - 3/4*f**4 - 15/4*f**3.
-3*(f + 1)**3*(f + 2)/4
Let v(o) be the first derivative of -o**7/105 - o**6/30 - o**5/30 - 3*o**2/2 - 12. Let d(g) be the second derivative of v(g). Factor d(w).
-2*w**2*(w + 1)**2
Let x(u) = -3*u**4 - 2*u**3 - 7*u**2 + 7*u - 7. Let h = 52 - 46. Let s(v) = -3*v**4 - 3*v**3 - 6*v**2 + 6*v - 6. Let a(d) = h*x(d) - 7*s(d). Factor a(j).
3*j**3*(j + 3)
Suppose 5 = i - l - 3, -3*i - 3*l = 0. Let m(a) be the first derivative of -8*a**2 + 40/3*a**3 + 2*a - 5*a**i - 42/5*a**5 - 13 + 6*a**6. What is z in m(z) = 0?
-1, 1/3, 1/2, 1
Suppose -5*c + 5*l = 15, -3*c + 0*l + 5*l = 15. Let j(z) be the first derivative of 3/2*z**4 - 1/2*z**6 - 3/2*z**2 + c*z + 0*z**5 + 3 + 0*z**3. Factor j(k).
-3*k*(k - 1)**2*(k + 1)**2
Let m(b) be the third derivative of 3*b**7/70 - b**6/40 - b**5/4 + b**4/8 + b**3 - 2*b**2 - 116*b.