(1 - 2). Let k(z) = z**3 + 1. Let i be k(g). Factor i*r + r**3 + 5/2*r**2 + 1/2.
(r + 1)**2*(2*r + 1)/2
Let f(a) be the third derivative of -1/120*a**5 + 0 + 1/240*a**6 - 4*a**2 - 1/48*a**4 + 0*a**3 + 0*a + 1/420*a**7. What is d in f(d) = 0?
-1, 0, 1
Let f(m) = 2*m**2 - 5*m - 1. Let n(r) = -2*r**2 + 4*r + 2. Let c(o) = 4*f(o) + 6*n(o). Factor c(v).
-4*(v - 2)*(v + 1)
Suppose -h + 52 - 8 = 5*z, -3*z - 3*h = -36. Suppose -z = v - 5*i, -7 = -3*v - 4*i + 7. What is m in -2/7*m**3 + 2/7 - 2/7*m**v + 2/7*m = 0?
-1, 1
Let k(r) be the third derivative of -r**7/210 - r**6/120 + 4*r**2. Factor k(z).
-z**3*(z + 1)
Let a = -4 - -3. Let m be a + 6/(1/1). What is c in -3*c**3 - c**5 - 4*c**3 + 3*c**4 + m*c**3 = 0?
0, 1, 2
Let p be (-4)/18 + 152/36 + -4. What is d in 12/5*d**5 + p*d**2 + 28/5*d**3 + 2/5 - 34/5*d**4 - 8/5*d = 0?
-1/2, 1/3, 1
Let d(q) be the third derivative of q**5/135 - q**4/27 + 2*q**3/27 + 31*q**2. Factor d(u).
4*(u - 1)**2/9
Let t(x) be the second derivative of -8*x**2 - 7*x + 0 - 2/15*x**6 + 6/5*x**5 + 8*x**3 - 13/3*x**4. Determine s, given that t(s) = 0.
1, 2
Suppose -36*t - 16 = -40*t. Suppose 0 = -t*u + 12, -7 = 5*m - 5*u + 8. Factor m*b**2 + 2/9*b - 2/9*b**3 + 0.
-2*b*(b - 1)*(b + 1)/9
Suppose -24 + 6 = -5*h + 2*d, -16 = 2*h + 5*d. Factor 1/2 + h*c**3 + 3*c + 9/2*c**2.
(c + 1)**2*(4*c + 1)/2
Factor 12 + 3 + 1 + 144*m + 110*m**2 + 214*m**2.
4*(9*m + 2)**2
Let -81 + 69 - 3*v**2 - 10*v - 2*v = 0. Calculate v.
-2
Let b(d) be the first derivative of d**7/1680 - d**6/240 + d**5/120 - d**3/3 + 2. Let y(r) be the third derivative of b(r). Solve y(t) = 0 for t.
0, 1, 2
Let m(s) be the third derivative of -s**5/20 + s**4/4 - s**3/2 + 20*s**2. Factor m(u).
-3*(u - 1)**2
Factor 7/5*i**2 - 1/5*i**4 - 2/5*i**3 - 4/5*i + 0.
-i*(i - 1)**2*(i + 4)/5
Let c be (-10)/27*(-30)/25. Factor 10/9*g + 2/3*g**2 + c.
2*(g + 1)*(3*g + 2)/9
Let h(b) be the third derivative of b**8/126 - 11*b**7/315 - b**6/60 - 14*b**2. Factor h(q).
2*q**3*(q - 3)*(4*q + 1)/3
Suppose 0 + 39*t**2 + 0 - 35*t**2 + 16*t = 0. Calculate t.
-4, 0
Determine a, given that 6 + 4*a + 2/3*a**2 = 0.
-3
Let r be -18*3/((-36)/(-8)). Let p be ((-4)/10)/(r/20). Factor -2/3*a**5 - 4/3*a**2 + 2/3 + 2/3*a**4 + 4/3*a**3 - p*a.
-2*(a - 1)**3*(a + 1)**2/3
Let b(w) be the third derivative of 3*w**2 + 0 + 1/210*w**7 + 1/60*w**6 + 0*w + 1/6*w**3 - 1/336*w**8 - 1/24*w**4 - 1/30*w**5. Let b(n) = 0. What is n?
-1, 1
Let v(p) be the first derivative of 48*p**5/5 - 16*p**4 + 28*p**3/3 - 2*p**2 + 7. Factor v(q).
4*q*(2*q - 1)**2*(3*q - 1)
Let g(v) = -v - 2. Let p be g(-2). Let b = p - -5. Factor -2*a**5 + 4*a**4 + 6*a**b - 2*a**5 - 3*a**2 - 2*a - a**2.
2*a*(a - 1)*(a + 1)**3
Let l(w) = w**3 - 4*w**2 - 4*w - 2. Let p be l(5). Factor -u**p + u**2 + u**3 + 2*u**4 + 4*u**3 + u**2.
2*u**2*(u + 1)**2
Find a such that 2/5*a**3 - 14/5*a**2 - 2/5*a + 12/5 + 2/5*a**4 = 0.
-3, -1, 1, 2
Let x(g) be the third derivative of 0*g**3 - 1/30*g**5 + 0*g + 0*g**4 + 3*g**2 + 0 + 1/120*g**6. What is d in x(d) = 0?
0, 2
Let y be (-7 + (-201)/(-21))/(6/4). Factor 3/7*z**3 - 15/7*z**2 + 24/7*z - y.
3*(z - 2)**2*(z - 1)/7
Let u be (-9)/(-12) + 1 - (22 + -21). Factor 0 + u*h**3 - 3/4*h**2 - 1/4*h**4 + 1/4*h.
-h*(h - 1)**3/4
Let z(q) be the third derivative of q**6/60 + 3*q**5/20 + 5*q**4/12 + q**3/2 - q**2. Factor z(p).
(p + 1)*(p + 3)*(2*p + 1)
Let 4/5 + 2/5*w - 2/5*w**2 = 0. What is w?
-1, 2
Let s(q) be the first derivative of 2/7*q**4 + 0*q - 3 + 2/7*q**3 - 1/7*q**2. Factor s(t).
2*t*(t + 1)*(4*t - 1)/7
Let j(f) be the first derivative of -2*f**6/25 - 3*f**5/100 + f**4/5 + f**3/10 - 2*f - 3. Let p(q) be the first derivative of j(q). Let p(o) = 0. Calculate o.
-1, -1/4, 0, 1
Let t(z) be the third derivative of -z**8/448 + z**7/140 - z**6/160 - 17*z**2. Factor t(r).
-3*r**3*(r - 1)**2/4
Let q = -877/5 + 176. Suppose -3/5*n**2 - q*n - 1/5 - 1/5*n**3 = 0. What is n?
-1
Suppose -6 = 3*d - 12. Let 0 + 0*m + 2/11*m**d = 0. What is m?
0
Let l(o) = -o**2 + 5*o + 3. Let b be l(5). Let r be (1/2)/(b/24). Determine c, given that c**4 - 2*c**r + 3*c**4 = 0.
0
Let q(k) = -1047*k**4 + 2628*k**3 - 2307*k**2 + 774*k - 84. Let j(s) = 299*s**4 - 751*s**3 + 659*s**2 - 221*s + 24. Let l(z) = -18*j(z) - 5*q(z). Factor l(u).
-3*(u - 1)**2*(7*u - 2)**2
Let l(h) be the first derivative of h**8/1680 + h**7/420 - h**6/360 - h**5/60 + 4*h**3/3 - 4. Let p(d) be the third derivative of l(d). Factor p(a).
a*(a - 1)*(a + 1)*(a + 2)
Let i(q) be the second derivative of -q**8/5040 - q**7/630 - q**6/180 - q**5/90 - q**4/72 + q**3/6 + q. Let d(x) be the second derivative of i(x). Factor d(t).
-(t + 1)**4/3
Suppose 4/7*l**4 - 4/7*l + 4/7*l**3 - 4/7*l**2 + 0 = 0. Calculate l.
-1, 0, 1
Let a(z) be the second derivative of z**5/100 - z**3/30 - 3*z. Solve a(t) = 0.
-1, 0, 1
Determine n so that -2/19*n**2 + 6/19 - 4/19*n = 0.
-3, 1
Let c(f) = f**3 + 1. Let u(k) = 5*k**3 + 35*k**2 - 80*k + 70. Let l(q) = 10*c(q) - u(q). Find m such that l(m) = 0.
2, 3
Let n(w) be the third derivative of 0*w + 0*w**3 + 8*w**2 - 11/60*w**6 - 1/6*w**5 + 1/4*w**4 - 1/35*w**7 + 0. Factor n(q).
-2*q*(q + 1)*(q + 3)*(3*q - 1)
Let t be 1 + 0 + -13 + 14. Let 0*l**2 + 4*l - t - 3*l**2 - 11*l = 0. What is l?
-2, -1/3
Find u, given that -3/2*u**3 + 3/2*u + 3 - 3*u**2 = 0.
-2, -1, 1
Let u(m) be the first derivative of m**4/32 + m**3/8 + 3*m**2/16 + m/8 - 1. Determine p so that u(p) = 0.
-1
Let g be 1 + (-5)/(5/(-2)). Let h(u) be the third derivative of -g*u**2 + 0 + 1/180*u**5 + 0*u - 1/72*u**4 + 0*u**3. Let h(c) = 0. Calculate c.
0, 1
Let r(j) be the second derivative of 3*j**5/20 - j**4/4 - 5*j**3/2 - 9*j**2/2 - 5*j. Let r(k) = 0. Calculate k.
-1, 3
Let s(f) = f**2 - 1. Let r(q) be the first derivative of 3*q**3 + q**2/2 - 10*q + 2. Let x(t) = -3*r(t) + 24*s(t). Determine u so that x(u) = 0.
-2, 1
Factor -2 - 8*k - 4 - 17*k**2 + 19*k**2 - 4.
2*(k - 5)*(k + 1)
Let h be (0/(1 - -1) - 1) + 5. Solve -14/5*u - 2/5*u**h - 18/5*u**2 - 4/5 - 2*u**3 = 0.
-2, -1
Let v(z) be the second derivative of -7/30*z**5 + 1/3*z**3 - 1/6*z**4 - 1/2*z**2 + 0 - 1/15*z**6 - z. Let l(q) be the first derivative of v(q). Factor l(f).
-2*(f + 1)**2*(4*f - 1)
Suppose 2*t - 43 = t. Let -1 - t*d - d**2 + 25*d + 16*d = 0. What is d?
-1
Let c be (-3 - 0)*112/(-24). What is i in 16*i - 2 - i**2 + 1 - c*i = 0?
1
Suppose 0 = -a, -6 = -2*w + 4*a - 0*a. Factor -2*t**4 + 4*t**3 + 0*t**4 - 8*t**w.
-2*t**3*(t + 2)
Suppose 2*u + 8 = 12. Factor 4/3 + u*x + 2/3*x**2.
2*(x + 1)*(x + 2)/3
Suppose -k + 6 = 2*k. Solve -m**3 + 30 - 30 - m**3 - k*m**4 + 4*m**2 = 0 for m.
-2, 0, 1
Let z = 2/107 - -313/428. Factor 5/4*f**3 + 0 + 0*f + z*f**5 + 7/4*f**4 + 1/4*f**2.
f**2*(f + 1)**2*(3*f + 1)/4
Let y be 0 + 0 + 10/5. Let v = 1 + y. Determine u so that 8/5*u**5 - 16/5*u**v - 4/5*u**2 + 2/5*u**4 + 8/5*u + 2/5 = 0.
-1, -1/4, 1
Let r(b) be the first derivative of 4*b**5/15 + 5*b**4/3 + 4*b**3 + 14*b**2/3 + 8*b/3 - 4. Factor r(m).
4*(m + 1)**3*(m + 2)/3
Let f(y) be the first derivative of -5*y**4/16 - 5*y**3/6 - 5*y**2/8 + 13. Factor f(v).
-5*v*(v + 1)**2/4
Suppose -32 = -8*a + 32. Suppose -z - 3 + a = 0. Suppose -9/5*x**4 + 0 + 0*x**3 + 0*x - 3/5*x**z + 12/5*x**2 = 0. What is x?
-2, 0, 1
Solve -1/5*s - 2/5 + 1/5*s**2 = 0.
-1, 2
Let l be 74/280 - (-2)/7. Let w = -1/20 + l. Factor 1/2*t**2 + w - t.
(t - 1)**2/2
Let h = 11/25 + -1/25. Find j, given that 4/5*j + 0 - 6/5*j**3 - 2/5*j**4 + h*j**2 + 2/5*j**5 = 0.
-1, 0, 1, 2
Let o(b) be the first derivative of -6 - 8/7*b**2 - 1/14*b**4 + 10/21*b**3 + 8/7*b. Factor o(z).
-2*(z - 2)**2*(z - 1)/7
Let i(d) be the second derivative of d**7/21 - d**6/3 + 3*d**5/5 + 2*d**4/3 - 8*d**3/3 + 6*d. Factor i(q).
2*q*(q - 2)**3*(q + 1)
Suppose 10*b = 14*b - 36. Suppose 3*k - b = -3. Solve 0 - 2/11*i - 2/11*i**3 + 4/11*i**k = 0 for i.
0, 1
Let -4*m**3 + 8/3*m**5 + 0 - 14/3*m**2 + 14/3*m**4 + 4/3*m = 0. What is m?
-2, -1, 0, 1/4, 1
Let y(c) be the first derivative of -4 - 5*c**4 + 0*c + 0*c**2 - 12/5*c**5 - 8/3*c**3. Let y(r) = 0. Calculate r.
-1, -2/3, 0
Let t = -54 - -57. Find g such that 1/5*g**t - 1/5 + 1/5*g**2 - 1/5*g = 0.
-1, 1
Let s be -1 + -15*(-14)/36. Let x = 389/78 - s. Factor x*l**2 + 2/13 + 4/13*l.
2*(l + 1)**2/13
Let p(q) be the first derivative of 1/12*q**4 + 0*q**3 + 1 - 1/2*q**2 + 2/3*q. Suppose p(r) = 0. Calculate