- 1)/7
Suppose -5*z - 19 = 3*w, w + 1 = 3. Let i(a) = 6*a + 34. Let m be i(z). What is d in -1/5*d**2 + 7/5*d**m + 0*d - 2/5*d**3 + 0 - 4/5*d**5 = 0?
-1/4, 0, 1
Let x = -24 + 27. Factor -14*h**2 + 4*h**x + 19*h**2 + 2*h - 10*h**2 - h**4.
-h*(h - 2)*(h - 1)**2
Let m(z) be the first derivative of -2*z**3/3 + 9*z**2 + 65. Factor m(o).
-2*o*(o - 9)
Let w(a) be the first derivative of -a**7/168 + 7*a**5/24 - 5*a**4/4 + a**3 + 3*a**2 - 5. Let r(m) be the third derivative of w(m). Factor r(c).
-5*(c - 2)*(c - 1)*(c + 3)
Let s be (-21)/14*(-5 + 3). Find u such that 2 - 2*u**4 - 10*u**s + 3*u**5 + 8*u + 2*u - 3*u = 0.
-1, -1/3, 1, 2
Let i(x) be the first derivative of x**6/480 - x**5/240 - x**4/48 - 5*x**2 + 3. Let a(z) be the second derivative of i(z). Factor a(u).
u*(u - 2)*(u + 1)/4
Let y(w) = w**3 + 12*w**2 + 51*w + 442. Let f be y(-11). Determine q so that 1/7*q**3 - 2/7*q - 1/7*q**f + 0 = 0.
-1, 0, 2
Let w = -9249 - -9254. Factor 0 - p - 3/2*p**3 + 1/2*p**4 - 5/2*p**2 + 1/2*p**w.
p*(p - 2)*(p + 1)**3/2
Suppose -47*o + 52*o + 2110 = 0. Let c = o + 3802/9. Factor c - 4/9*d**2 - 2/3*d.
-2*(d + 2)*(2*d - 1)/9
Factor -4/9*y**2 + 0 + 2/3*y - 2/9*y**3.
-2*y*(y - 1)*(y + 3)/9
Let g(n) be the third derivative of -1/8*n**3 - 1/240*n**5 - 18*n**2 + 0*n + 0 - 1/24*n**4. Find f such that g(f) = 0.
-3, -1
Factor -3/7*i**3 + 54/7*i**2 + 0 - 51/7*i.
-3*i*(i - 17)*(i - 1)/7
Let s = -308 + 310. Let v(t) be the first derivative of 0*t - 1/6*t**3 - s - 1/4*t**2. Factor v(o).
-o*(o + 1)/2
Let l = 58 + -58. Suppose l = 16*t - 20*t + 12. Factor 0 + 2/9*s - 2/9*s**t + 0*s**2.
-2*s*(s - 1)*(s + 1)/9
Let i = -31 + 67. Factor -3*o**4 - 3*o**3 - 36*o**2 - 2*o**4 - 12*o - 3*o**5 - i*o**3 - 13*o**4.
-3*o*(o + 1)**2*(o + 2)**2
Let s = -119250/7 - -17036. Suppose -2/7 + 4/7*h - s*h**2 = 0. Calculate h.
1
Let o = 1290 + -1285. Factor -2/7*t**3 - 1/7*t**o - 3/7*t**4 + 2/7*t**2 + 3/7*t + 1/7.
-(t - 1)*(t + 1)**4/7
Factor 144/13*k + 2/13*k**3 + 216/13 + 30/13*k**2.
2*(k + 3)*(k + 6)**2/13
Let k(z) be the first derivative of z**6/360 + 3*z**5/40 + z**4/3 - 9*z**3 - 9. Let m(o) be the third derivative of k(o). Determine l so that m(l) = 0.
-8, -1
Let -48*j - 132*j**3 - 204*j**2 - 9*j**4 + 57*j**4 - 69*j**4 = 0. Calculate j.
-4, -2, -2/7, 0
Suppose -5*t = -4*m - 0*t - 17, -m - 5*t + 27 = 0. Let g(z) be the first derivative of -4 - z**3 + 1/4*z**4 + 3/2*z**m - z. What is u in g(u) = 0?
1
Let i(q) be the third derivative of -q**6/450 - q**5/15 - 5*q**4/6 - 2*q**3 - 11*q**2. Let m(u) be the first derivative of i(u). What is a in m(a) = 0?
-5
Let i(p) = 4*p**5 + 6*p**4 + 62*p**3 + 131*p**2 + 144*p + 67. Let j(w) = w**5 - 2*w**4 + 2*w**3 + w**2 + 1. Let n(h) = i(h) - 3*j(h). What is x in n(x) = 0?
-4, -2
Let o(n) = -n**3 + 6*n**2 - 12*n + 11. Let a be o(3). Let t(c) be the first derivative of -125/22*c**4 - 16/11*c - 3 - 60/11*c**a - 100/11*c**3. Factor t(y).
-2*(5*y + 2)**3/11
Let o(p) = -p**2 - 4*p + 5. Let a be o(-5). Find h, given that -h**2 - h**5 + a*h**2 - 18*h + 3*h**3 + h**4 + 16*h = 0.
-1, 0, 1, 2
Let o(n) be the third derivative of n**6/45 - 13*n**5/9 + 238*n**4/9 + 578*n**3/3 + 30*n**2 + 4. Suppose o(t) = 0. Calculate t.
-3/2, 17
Let y(k) be the third derivative of -1/240*k**6 + 0*k**3 - 1/840*k**7 + 0*k - 6*k**2 + 1/240*k**5 + 0 + 1/48*k**4. Factor y(m).
-m*(m - 1)*(m + 1)*(m + 2)/4
Let p(o) be the first derivative of -5/7*o + 1/28*o**4 + 11/14*o**2 - 12 - 1/3*o**3. Factor p(c).
(c - 5)*(c - 1)**2/7
Let i(g) be the second derivative of -1/66*g**4 + 0 + 1/11*g**2 + 0*g**3 - 14*g. Factor i(z).
-2*(z - 1)*(z + 1)/11
Let c(s) be the second derivative of 3*s**5/5 + 19*s**4/6 + s**3 + s - 10. Factor c(n).
2*n*(n + 3)*(6*n + 1)
Suppose -25 = 5*o, 0 = 4*r - o - 18 + 1. Factor 6*u**2 + 3/2*u**r + 3 + 15/2*u.
3*(u + 1)**2*(u + 2)/2
Suppose -17 - 63 = -2*j. Determine y, given that -6*y + 10 - 29*y - 2*y**4 - 10*y**3 - 8*y**4 + j*y**2 + 5*y**5 = 0.
-2, 1
Factor -32*l + 2/9*l**2 + 1152.
2*(l - 72)**2/9
Let s(c) be the third derivative of -3*c**8/616 + 2*c**7/35 + 47*c**6/660 + 4*c**5/165 - 3*c**2 - 6*c. Suppose s(k) = 0. What is k?
-1/3, 0, 8
Suppose 0 = -14*t + 9*t + 10. Suppose 0 = t*i - 11 + 5. Let 10/7*u**4 - 4/7*u + 0 - 10/7*u**2 + 4/7*u**i = 0. What is u?
-1, -2/5, 0, 1
Solve -1/12*h**3 - 1/6 - 5/12*h - 1/3*h**2 = 0 for h.
-2, -1
Let q(v) be the first derivative of -8 + v**3 + 3/2*v**2 - 36*v. Find d, given that q(d) = 0.
-4, 3
Let z = -14021 - -14023. Factor 15/2*h**z - 3*h - 12 - 3/2*h**3.
-3*(h - 4)*(h - 2)*(h + 1)/2
Let v(k) be the first derivative of 3*k**4 + 5 + 0*k**2 + 36/5*k**5 + 0*k**3 + 0*k + 9/2*k**6. Factor v(u).
3*u**3*(3*u + 2)**2
Let l(w) = w**2 - w + 1. Let t(h) = 3*h - 3*h - 3*h + 5*h. Let q(z) = -2*l(z) - 3*t(z). Factor q(p).
-2*(p + 1)**2
Let x(f) be the third derivative of f**5/15 - f**4/6 - 2*f**2 - 90. Factor x(r).
4*r*(r - 1)
Let i(x) be the second derivative of -2/225*x**6 + 0*x**3 + 0 - 16*x + 1/315*x**7 - 2/75*x**5 + 4/45*x**4 + 0*x**2. Find k such that i(k) = 0.
-2, 0, 2
Let k(p) = 6*p**3 + 2*p**2 - 32*p - 24. Let c(x) = 19*x**3 + 7*x**2 - 98*x - 72. Let t(v) = 2*c(v) - 7*k(v). Factor t(a).
-4*(a - 3)*(a + 1)*(a + 2)
Solve -18/7*h**3 + 60/7*h**2 + 2/7*h**4 + 48/7 - 88/7*h = 0.
2, 3
What is o in 48/7 + 106/7*o**2 - 18/7*o**4 - 2/7*o**3 - 134/7*o = 0?
-3, 8/9, 1
Let a(p) = -3*p**2 - 8*p + 2. Let d(n) = 16*n**2 + 42*n - 11. Let f(l) = 11*a(l) + 2*d(l). Factor f(g).
-g*(g + 4)
Let w = -10 - -8. Let x be (0 + w + (-20)/(-12))*0. What is f in -2/9*f**3 + 0 + 0*f**2 + x*f = 0?
0
Let w be ((-98)/(-441))/((-2)/(-18)). Let u(x) be the first derivative of 0*x + 5/22*x**4 - 1 - 4/55*x**5 + 1/11*x**w - 8/33*x**3. Factor u(p).
-2*p*(p - 1)**2*(2*p - 1)/11
Let y(g) be the second derivative of 1/110*g**5 + 0*g**2 + 9*g + 1/33*g**3 + 0 - 1/33*g**4. Let y(c) = 0. What is c?
0, 1
Suppose 0 = 5*w + 40 - 45. Let d be 4*(w/(-18) + 4/18). Find x such that -2/3*x - d*x**2 + 0 = 0.
-1, 0
Let m = -234173/7 + 33461. Suppose 486/7*k + 2/7*k**3 + 1458/7 + m*k**2 = 0. Calculate k.
-9
Let d(s) be the first derivative of s**7/28 - s**6/20 - 3*s**5/40 + s**4/8 + 15*s + 8. Let g(y) be the first derivative of d(y). Find c, given that g(c) = 0.
-1, 0, 1
Solve -5*x**2 + 2*x - 5*x**3 - x + 8*x + x = 0 for x.
-2, 0, 1
Let a(p) be the third derivative of -p**6/240 + p**5/30 - p**4/48 - p**3/2 + 2*p**2 + 12. Find k, given that a(k) = 0.
-1, 2, 3
Let n = -3/145 + 18/29. Let g(b) be the third derivative of n*b**5 - 5/12*b**4 + 0*b - 16/105*b**7 + 0 - 1/15*b**6 - 2/3*b**3 + 3/56*b**8 - 2*b**2. Factor g(s).
2*(s - 1)**3*(s + 1)*(9*s + 2)
Let 3*b**5 + 8*b + 6*b**4 + 20*b - 44*b - 6*b**3 + 6 - 12*b**2 + 19*b = 0. Calculate b.
-2, -1, 1
Let c(w) = -3*w**2 + 14*w - 15. Let n be c(3). Find x such that 0 - 1/3*x**3 + n*x + 2/3*x**2 = 0.
0, 2
Let d(q) be the third derivative of -q**5/12 - 15*q**4/8 + 25*q**3/3 + q**2 - 16*q. Suppose d(k) = 0. What is k?
-10, 1
Let k(n) be the first derivative of n**4/6 - 16*n**3/9 + 7*n**2 - 12*n - 106. Determine l so that k(l) = 0.
2, 3
Let w(a) be the second derivative of -7*a**8/1920 - a**7/240 + a**6/60 - a**5/60 + 11*a**4/4 + 40*a. Let m(s) be the third derivative of w(s). Factor m(p).
-(p + 1)*(7*p - 2)**2/2
Let b be -1 - 520/78*(-12)/70. Find j such that -b*j**2 + 1/7*j**4 + 1/7*j + 0 - 1/7*j**3 = 0.
-1, 0, 1
Let f(v) = -4*v**2 - 18*v + 39. Let k be f(-6). Let m(a) be the second derivative of -3*a**2 + 3*a + 5/6*a**4 + 0 + 2/3*a**k. Solve m(p) = 0 for p.
-1, 3/5
Let l(r) be the first derivative of -r**3/6 - 13*r**2/2 + 27*r/2 - 35. Find n, given that l(n) = 0.
-27, 1
Suppose -4*f + 3*a = -8, 3 = -4*f - 2*a + 11. Determine w, given that -2*w + w**5 - 10*w**3 + 20*w**f + 4*w**5 - 10*w**4 - 10 + w + 6*w = 0.
-1, 1, 2
Factor 184*l**2 + 2 - 4*l**5 + 356*l**4 - 8*l**3 - 320*l**4 + 34 - 132*l - 112*l**3.
-4*(l - 3)**2*(l - 1)**3
Let x(p) = -5*p**3 + 19*p**2 + 20*p + 20. Let j(g) = 2*g**3 - g**2 + g - 2. Let f(b) = 4*j(b) + x(b). Factor f(t).
3*(t + 1)*(t + 2)**2
Let q(t) be the third derivative of t**6/480 + 19*t**5/240 - 25*t**4/12 + 18*t**3 - 729*t**2. Let q(p) = 0. What is p?
-27, 4
Determine x so that -729*x**3 - 704*x**3 - 23*x**5 + 132*x**4 - 101*x**2 - 43*x**4 + 12 + 80*x + 1376*x**3 = 0.
-1, -3/23, 1, 2
Let l = 703/105 + -33/5. Let z(k) be the first derivative 