tive of 11 - y*f**2 - 6/7*f - 4/21*f**3. Factor r(j).
-2*(j + 1)*(2*j + 3)/7
Let 0*f + 0*f**3 - 1/3*f**4 + 4/9*f**2 - 1/9*f**5 + 0 = 0. What is f?
-2, 0, 1
Solve -54*t**3 + 12*t**4 - 145*t**2 + 8*t**4 - 25*t**4 - 70*t - 26*t**3 = 0 for t.
-14, -1, 0
Factor -3 + 9*p + 15 - 25*p + 4*p**2.
4*(p - 3)*(p - 1)
Factor 1444/11 + 2/11*d**3 + 874/11*d + 80/11*d**2.
2*(d + 2)*(d + 19)**2/11
Factor 0 + 7/6*h**2 + 1/2*h.
h*(7*h + 3)/6
Let x(d) be the first derivative of 2*d**3/15 + 14*d**2/5 + 48*d/5 + 70. Find z such that x(z) = 0.
-12, -2
Let o(c) be the first derivative of -c**5/5 + 7*c**4/3 - 16*c**3/3 - 32*c**2 - 9*c + 13. Let n(b) be the first derivative of o(b). Factor n(d).
-4*(d - 4)**2*(d + 1)
Let f(o) be the third derivative of o**8/1344 - o**7/105 + o**6/80 + o**5/6 + 25*o**4/96 + o**2 - 65. Factor f(p).
p*(p - 5)**2*(p + 1)**2/4
Solve -523*b**3 - 16*b**4 + 5000*b - 200*b**2 - 4709*b**3 + 234*b**3 - 2*b**5 + 216*b**4 = 0.
-1, 0, 1, 50
Let d(j) be the second derivative of 1/9*j**3 - 1/6*j**7 + 19/60*j**5 - 13/90*j**6 + 0*j**2 + 13/36*j**4 + 0 - 14*j. Let d(m) = 0. What is m?
-1, -1/3, -2/7, 0, 1
Let w(v) = 3*v**4 + 14*v**3 + 44*v**2 + 26*v + 13. Let a(k) = -3*k**4 - 15*k**3 - 42*k**2 - 27*k - 12. Let m(p) = -4*a(p) - 3*w(p). Factor m(x).
3*(x + 1)**3*(x + 3)
Let r(j) be the third derivative of 0*j**6 + 5/24*j**4 - 5/336*j**8 + 1/21*j**7 + 0 + 0*j**3 + 16*j**2 - 1/6*j**5 + 0*j. What is a in r(a) = 0?
-1, 0, 1
Let r be 12/45 - 0/7. Let j(n) be the first derivative of -4/5*n**2 - 4/15*n**6 + 10 + 4/5*n**4 - r*n**3 + 2/5*n + 2/25*n**5. Determine z, given that j(z) = 0.
-1, 1/4, 1
Suppose -4*m - 20 = -4*x, 0*x - 20 = 3*m - 2*x. Let w = m + 13. Factor -2*a**2 + 5*a + w*a**4 + 11*a - 5*a**4 + 6 + 14*a**2.
-2*(a - 3)*(a + 1)**3
Let p(k) = -4*k**4 - 47*k**3 + 41*k**2 + 45*k - 48. Let m(n) = -n**4 - 11*n**3 + 10*n**2 + 11*n - 12. Let s(d) = -26*m(d) + 6*p(d). Let s(r) = 0. Calculate r.
-3, -2, 1, 2
Suppose 3*w = v + 3, 0 = -4*v + 37*w - 42*w + 22. Solve 2*o + 4/5 + 2/5*o**v + 8/5*o**2 = 0.
-2, -1
Let k(u) be the first derivative of 6 - 4*u - 2/3*u**3 + 0*u**2 - 1/6*u**4. Let l(f) be the first derivative of k(f). Factor l(o).
-2*o*(o + 2)
Let f(m) be the second derivative of 1/10*m**6 + 0*m**4 - 16*m - 3/2*m**2 + 0 + 3/10*m**5 - m**3. Suppose f(o) = 0. What is o?
-1, 1
Let f = 3/5755 + 5743/23020. Factor -1/4*l**2 + 1/2 + f*l.
-(l - 2)*(l + 1)/4
Let y(x) be the second derivative of x**8/3360 + x**7/210 + x**6/30 + 2*x**5/15 - x**4/12 - 5*x. Let j(o) be the third derivative of y(o). Factor j(t).
2*(t + 2)**3
Let r(u) be the first derivative of -u**5 + 85*u**4/12 - 40*u**3/3 + 15*u**2/2 + 27*u - 20. Let f(d) be the first derivative of r(d). Let f(x) = 0. Calculate x.
1/4, 1, 3
Let p(y) be the second derivative of -y**7/21 - 4*y**6/15 - 3*y**5/10 + 8*y + 24. Suppose p(c) = 0. Calculate c.
-3, -1, 0
Let s(d) be the second derivative of 5*d - 1/2*d**4 + 1/10*d**6 + 0 - 3/20*d**5 + 0*d**2 + 0*d**3. Solve s(f) = 0 for f.
-1, 0, 2
Let f be 15/(-75)*7*(-3 - 9/(-21)). Factor -3/5*c**2 + 21/5 + f*c.
-3*(c - 7)*(c + 1)/5
Let g(s) be the first derivative of 1/5*s**5 - 1/8*s**6 + 1/8*s**2 + 0*s + 1/8*s**4 - 1/3*s**3 + 9. Let g(u) = 0. Calculate u.
-1, 0, 1/3, 1
Suppose 16/3*y**2 - 16*y + 4/3*y**3 + 0 = 0. What is y?
-6, 0, 2
Let b(u) be the second derivative of -5*u**6/6 + 2*u**5 + 55*u**4/3 + 40*u**3/3 - 6*u - 1. Determine r, given that b(r) = 0.
-2, -2/5, 0, 4
Let i be ((-2)/4)/((-2)/16). Suppose -3*m**i - 2 - 1 + 0*m**4 - 64*m**2 + 70*m**2 = 0. Calculate m.
-1, 1
What is p in 70/11*p**4 + 2/11*p**2 + 0 + 76/11*p**3 - 4/11*p = 0?
-1, -2/7, 0, 1/5
Let q(k) be the second derivative of -5/42*k**7 + 0 + 0*k**4 + 0*k**2 - 1/4*k**5 + 1/3*k**6 + 3*k + 0*k**3. Factor q(d).
-5*d**3*(d - 1)**2
Let i(z) be the third derivative of -z**5/480 + 49*z**4/96 - 2401*z**3/48 + 2*z**2 + 74*z. Suppose i(g) = 0. What is g?
49
Let v be (-29 - -27) + (-18)/(1 + -4). Determine w so that 2/9*w + 2/9*w**v + 0 + 2/3*w**3 + 2/3*w**2 = 0.
-1, 0
Let n be (-3)/2 - (-66)/(36 - 3). What is x in -1/2 + 1/2*x**2 + 1/2*x - n*x**3 = 0?
-1, 1
Let a = -15 + 19. Solve 5*c**4 - 22*c**2 + 2 - 5*c**5 + 0*c**4 + 5*c + c**4 + 16*c**3 - 2*c**a = 0.
-2, -1/5, 1
Let n(m) be the second derivative of 2*m**6/15 + 2*m**5/5 - m**4 - 16*m**3/3 - 8*m**2 - 51*m - 1. Solve n(x) = 0.
-2, -1, 2
Let f be 2/12*-4 - (-800)/525. Let p = 262/91 - 30/13. Factor 2/7*m**4 - 10/7*m**2 + 0 + f*m**3 + p*m - 2/7*m**5.
-2*m*(m - 1)**3*(m + 2)/7
Let r(q) be the second derivative of -q**5/120 + q**4/16 + 29*q**2/2 - 17*q. Let y(p) be the first derivative of r(p). Find i such that y(i) = 0.
0, 3
Let v(h) be the first derivative of -h**6/12 + 11*h**5/10 + 15*h**4/8 - 35*h**3/6 - 7*h**2/2 + 12*h - 413. Let v(l) = 0. What is l?
-2, -1, 1, 12
Let b(z) be the second derivative of z**6/180 + z**5/12 + z**4/2 - 5*z**3/6 - 11*z + 2. Let f(v) be the second derivative of b(v). Factor f(t).
2*(t + 2)*(t + 3)
Let x(c) = -21*c**3 - 206*c**2 - 153*c + 35. Let s(v) = -64*v**3 - 620*v**2 - 460*v + 104. Let f(m) = 3*s(m) - 8*x(m). Let f(w) = 0. Calculate w.
-8, -1, 1/6
Factor -8/13*y**2 - 2/13*y**3 - 4/13 - 10/13*y.
-2*(y + 1)**2*(y + 2)/13
Let d be (25/10*(-8)/(-10))/1. Let v be (-1*d)/(176/(-22)). Solve -1/2 + v*j**2 - 1/4*j = 0 for j.
-1, 2
Factor 16/3*f**4 + 1024/9*f**2 + 128/3*f**3 + 0*f + 2/9*f**5 + 0.
2*f**2*(f + 8)**3/9
Let k(j) be the third derivative of 16*j**7/1575 - 62*j**6/225 - 127*j**5/450 - 4*j**4/45 - 633*j**2. What is z in k(z) = 0?
-1/4, 0, 16
Let m = 101 + -86. Suppose 8*w**2 + 12*w - 15 + 0*w**2 - 4*w**3 + m = 0. Calculate w.
-1, 0, 3
Suppose -10 = -5*q + 10. Factor 35*w - 35*w + 3*w**q - 3*w**2.
3*w**2*(w - 1)*(w + 1)
Factor -2*u - 24/5 + 1/5*u**2.
(u - 12)*(u + 2)/5
Let j(z) be the first derivative of -1/4*z**4 - 2/9*z**3 + 8 + 0*z - 1/15*z**5 + 0*z**2. Factor j(y).
-y**2*(y + 1)*(y + 2)/3
Let b(x) be the second derivative of -4*x + 0 - 5/2*x**2 - 1/60*x**4 + 1/3*x**3. Determine f so that b(f) = 0.
5
Let c be 7 + (-189)/35 + (-4)/(-10). Suppose -5*t**2 - t**3 + t**c + 12*t**2 - 7*t**2 = 0. Calculate t.
0, 1
Let u(y) = -y**3 - 8*y**2 - 7*y - 12. Let f be u(-8). Suppose -5 = -7*i + f. Determine q so that -i*q - 4*q**3 + 7*q - q**5 - 5*q**3 - 6*q**4 = 0.
-3, 0
Let l(c) be the third derivative of c**9/13608 + c**8/7560 - c**7/1890 + 7*c**3/6 - 12*c**2. Let a(m) be the first derivative of l(m). Factor a(z).
2*z**3*(z - 1)*(z + 2)/9
Factor 3*j**3 - 4*j - 7*j**3 + 6*j**2 - 16*j**2 - 2*j**2 - 4*j.
-4*j*(j + 1)*(j + 2)
Let o(s) be the second derivative of -5*s**4/3 + 32*s**3/3 - 22*s**2 + 472*s. Factor o(l).
-4*(l - 1)*(5*l - 11)
Let z be 8/4*(92/8 - 3). Suppose 9*q - 1 = z. Factor 1/10*x**q + 1/5*x + 0.
x*(x + 2)/10
Suppose 56 = 11*t - 32. What is m in 3*m**2 + 5*m - t*m**4 - 3*m**3 + 5*m**4 + 2*m - 4*m = 0?
-1, 0, 1
Factor -686/3 - 588*h - 504*h**2 - 144*h**3.
-2*(6*h + 7)**3/3
Suppose 12*z = 13*z - 26. Let w = z + -24. Factor 0 + 0*p + 2/7*p**w + 2/7*p**4 + 4/7*p**3.
2*p**2*(p + 1)**2/7
Let p(m) be the third derivative of -m**6/24 + 17*m**5/6 - 200*m**4/3 + 1280*m**3/3 - 5*m**2 + 44*m. Let p(f) = 0. What is f?
2, 16
Let z(w) = -3*w**3 - 17*w**2 + 17*w + 3. Let l(s) = -s**3 - 9*s**2 + 9*s + 1. Let q(c) = -5*l(c) + 3*z(c). Factor q(k).
-2*(k - 1)*(k + 2)*(2*k + 1)
Let r = 10730 - 32189/3. Solve 3*o + r*o**2 + 0 = 0 for o.
-9, 0
Let t(n) be the third derivative of n**9/1512 + n**8/280 + n**7/420 - n**6/60 - n**5/30 + n**3 + 10*n**2. Let f(w) be the first derivative of t(w). Factor f(x).
2*x*(x - 1)*(x + 1)**2*(x + 2)
Let a(p) be the second derivative of p**5/100 - 3*p**4/10 + 27*p**3/10 - 43*p + 2. Solve a(o) = 0 for o.
0, 9
Let f(h) be the third derivative of -h**6/300 + 13*h**5/150 - 4*h**4/5 + 12*h**3/5 - 126*h**2. Factor f(v).
-2*(v - 6)**2*(v - 1)/5
Solve 40*k + 63*k - 23*k + 3*k**2 + 32*k**2 + 60 + 5*k**3 = 0 for k.
-3, -2
Let i be ((-25)/45)/(120/(-144)). Factor 0*m**3 - i*m**2 + 1/3*m**4 + 0*m + 1/3.
(m - 1)**2*(m + 1)**2/3
Suppose 8 = 6*c - 10. What is b in 17*b**3 - 85*b**2 + 80*b + 7*b**c + 4*b**3 - 7*b**2 - 16 = 0?
2/7, 1, 2
Let r(i) = i**3 - 10*i**2 - 11*i + 2. Let g = 11 - 0. Let b be r(g). Solve -7 - 12*o + 2 - 7 + 0 - 3*o**b = 0 for o.
-2
Let n be (1 - (-4)/(-3)) + (-232)/24. Let u = n - -41/4. Solve 0 + 0*s**3 - 3/4*s**2 + 