
Let r(n) = n**3 - 6*n**2 - 8*n + 5. Let x be r(7). Let d = x + 4. Solve -17*a**3 + a**2 - 21*a**3 + 37*a**3 + d*a = 0 for a.
-1, 0, 2
Let i(s) = 4*s**5 - 20*s**4 + 8*s**2 + 4*s - 12. Let g(c) = -c**5 + 2*c**4 + c**3 - c + 1. Let p(q) = 8*g(q) + i(q). Factor p(y).
-4*(y - 1)**2*(y + 1)**3
Suppose -4*f + 18 = -3*g - 4, 5*f = -2*g + 16. Factor 2/13*n**f - 4/13*n**2 + 2/13*n**5 + 2/13*n - 4/13*n**3 + 2/13.
2*(n - 1)**2*(n + 1)**3/13
Let a = -220 - -144. Let u = -74 - a. Determine k, given that 16/3*k - 4/3*k**3 + u + 2*k**2 = 0.
-1, -1/2, 3
Find g such that 1957*g**3 - g + g - 972*g**3 + 2*g**4 - 975*g**3 + 8*g**2 = 0.
-4, -1, 0
Factor -4/9*i**3 + 0 + 16/9*i**2 + 0*i - 2/9*i**4.
-2*i**2*(i - 2)*(i + 4)/9
Let v(z) = 3*z**2 + 3*z - 10. Let d(a) = -4*a**2 - 3*a + 15. Let c(y) = -4*d(y) - 5*v(y). Let c(x) = 0. What is x?
-2, 5
Let v(j) = -3*j**3 + 5*j**2 + 18*j. Let x(t) be the second derivative of t**5/20 + t**4/12 - t**3/6 + 30*t. Let z(o) = -5*v(o) - 20*x(o). Factor z(q).
-5*q*(q + 2)*(q + 7)
Let f(s) be the first derivative of -4*s**5/15 + 17*s**4/3 - 44*s**3 + 162*s**2 - 288*s - 87. Factor f(r).
-4*(r - 8)*(r - 3)**3/3
Let y(o) be the second derivative of -o**4/66 + 2*o**3/3 - 11*o**2 - 277*o. Determine v, given that y(v) = 0.
11
Suppose 1 = -3*u + 10. Let p be 3*2*6/u. Let 4 - 6*f + 2*f**3 - 8 + 18*f + 2*f**3 - p*f**2 = 0. Calculate f.
1
Let r(f) be the first derivative of -f**5/30 + 23*f**4/24 - 10*f**3/3 - f**2/3 + 40*f/3 + 705. Determine a so that r(a) = 0.
-1, 2, 20
Suppose 73/5*m - 37/5 + 2/5*m**2 = 0. Calculate m.
-37, 1/2
Factor 102 - 39/2*b - 3/2*b**2.
-3*(b - 4)*(b + 17)/2
Let u be (-2 - (-16)/5)/(322/230). Let r = 205 + -1432/7. Solve -6/7*f**2 + r*f**5 - 3/7*f + u*f**4 + 0*f**3 + 0 = 0 for f.
-1, 0, 1
Suppose -1170*p = -1168*p - 6. Let b(x) be the second derivative of 1/150*x**6 + 0*x**4 + 2*x + 1/210*x**7 - 1/50*x**5 + 0 + 0*x**2 + 0*x**p. Factor b(f).
f**3*(f - 1)*(f + 2)/5
Let 36*p**3 - 20*p**5 - 11*p**5 + 12*p**2 - 27*p**4 + 10*p**5 = 0. What is p?
-2, -2/7, 0, 1
Let t(u) be the second derivative of u**4/18 + 11*u**3/9 - 2*u - 146. Let t(k) = 0. Calculate k.
-11, 0
Let z(i) be the second derivative of -i**9/25200 - i**8/33600 + i**7/6300 - 9*i**4/4 + 27*i. Let b(l) be the third derivative of z(l). Factor b(o).
-o**2*(o + 1)*(3*o - 2)/5
Let y be -2*(-3 + (1 - 1)). Suppose 5*h - y = 3*h. Determine w, given that 1 - h + w**2 + 8*w**3 - 8*w + w**2 = 0.
-1, -1/4, 1
Let t be 5 + 4/((-32)/28). Suppose -1/4*l - 3/4*l**3 - t + 5/2*l**2 = 0. What is l?
-2/3, 1, 3
Let z(s) be the second derivative of -s**4/20 + 28*s + 1. Factor z(h).
-3*h**2/5
Let b(q) be the second derivative of 15*q + 0*q**2 + 0 + 1/2*q**3 + 5/4*q**4. Factor b(l).
3*l*(5*l + 1)
Find p, given that -78/19*p**2 + 2/19*p**4 - 36/19*p**3 + 0 - 40/19*p = 0.
-1, 0, 20
What is j in -4*j**4 + 105*j**2 - 17*j**3 - 10 - 213*j**2 - 66*j - 22 - 34*j - 27*j**3 = 0?
-8, -1
Factor 2048/7 + 2/7*t**2 - 128/7*t.
2*(t - 32)**2/7
Let x(b) be the second derivative of b**6/420 - b**5/70 + b**2 + 9*b. Let j(n) be the first derivative of x(n). Solve j(t) = 0 for t.
0, 3
Let q(k) be the second derivative of 27*k**7/14 + 12*k**6 - 19*k**5/4 - 775*k**4/6 - 110*k**3 - 36*k**2 - 390*k. Let q(u) = 0. Calculate u.
-3, -2/9, 2
Factor -1/2*h + 1/6*h**2 + 0.
h*(h - 3)/6
Let r(b) = b**3 + 9*b**2 + 9*b - 8. Let h be r(-2). Let u(l) be the first derivative of 26/3*l**3 + 8*l - 6 - 12*l**h + 2/5*l**5 - 3*l**4. Factor u(y).
2*(y - 2)**2*(y - 1)**2
Suppose -64/5*j + 3/5 - 80*j**3 + 76*j**2 = 0. What is j?
1/10, 3/4
Solve 65*l**2 + 19*l - 37*l**2 - 38*l**2 - 5*l**3 - 4*l = 0 for l.
-3, 0, 1
Suppose 0 = -90*z + 92*z + q, -3*z + 10 = -q. Factor 0 - 10/19*p**4 + 4/19*p + 2/19*p**5 - 14/19*p**z + 18/19*p**3.
2*p*(p - 2)*(p - 1)**3/19
Let s(y) be the third derivative of -2*y**7/105 + 29*y**6/30 + y**5/5 - 89*y**4/6 + 116*y**3/3 - 131*y**2. Suppose s(a) = 0. Calculate a.
-2, 1, 29
Let z(b) be the second derivative of 2*b**6/45 + 2*b**5/15 - 11*b**4/9 - 8*b**3/3 + 24*b**2 - 11*b - 3. Solve z(t) = 0 for t.
-3, 2
Let n(j) be the first derivative of 0*j**4 + 2 + 1/360*j**6 - 4/3*j**3 + 1/120*j**5 + 0*j + 0*j**2. Let u(h) be the third derivative of n(h). Factor u(v).
v*(v + 1)
Let r(o) = 35*o**2 + 795*o + 275. Let x(n) = 31*n**2 + 796*n + 273. Let h(b) = 4*r(b) - 5*x(b). Determine y, given that h(y) = 0.
-53, -1/3
Let -176/5*x**2 - 2/5*x**5 + 0 - 102/5*x**3 - 24/5*x**4 - 96/5*x = 0. Calculate x.
-4, -3, -1, 0
Let p be 57/(-38)*32/(-3). Suppose -5*u - p = -9*u. Solve -18/5*y**2 - 4/5 + 14/5*y + 2*y**3 - 2/5*y**u = 0.
1, 2
Let d(g) be the second derivative of -g**7/504 + g**5/6 + g**4/4 + 24*g. Let q(p) be the third derivative of d(p). Suppose q(f) = 0. What is f?
-2, 2
Factor 2*x + 6*x**4 - 5*x + 3*x**3 - 2140*x**2 + 2134*x**2.
3*x*(x - 1)*(x + 1)*(2*x + 1)
Let r(y) = -44*y**4 - 176*y**3 - 292*y**2 - 136*y. Let i(s) = 2*s**4 + s**3 - s**2 - s. Let h(n) = -24*i(n) - r(n). Factor h(c).
-4*c*(c - 40)*(c + 1)**2
Let h = -955/148 - -248/37. Factor -1/8*v**4 - 1/8*v**3 + 0*v + h*v**2 + 0.
-v**2*(v - 1)*(v + 2)/8
Let w = -13 - -8. Let t(p) = 0*p**3 - 2*p**2 + 0*p + 5*p**3 + 6*p - 3*p**3. Let k(z) = -2*z**3 + z**2 - 5*z. Let d(r) = w*t(r) - 6*k(r). Factor d(u).
2*u**2*(u + 2)
Determine a, given that 78*a - 268/3*a**2 - 4*a**4 - 2/3*a**5 - 24 + 40*a**3 = 0.
-12, 1, 3
Let s(f) = -5*f + 3*f - 12 - 6*f - f**2 - 7*f. Let o be s(-14). Factor -167*i**3 - i**4 + 167*i**3 + 3*i**2 + o*i.
-i*(i - 2)*(i + 1)**2
Suppose 2*n = -2*q - 0*n + 12, -5*n = 3*q - 14. Let t be 26/6 - (-4 + q). Factor -2/3*c**2 - t*c - 1/3*c**3 + 0.
-c*(c + 1)**2/3
Let a be -12 + -3 + 11 + (4 - (-2 + 0)). Factor -1/6 - 1/3*f - 1/6*f**a.
-(f + 1)**2/6
Let l = 153 + -152. Let w(s) be the first derivative of 15/2*s**2 + l + 10*s - 5/4*s**4 + 0*s**3. Suppose w(o) = 0. Calculate o.
-1, 2
Suppose -12 = 3*c - 6*c. Suppose 0 = c*m + 3*d - 6, 4*d + 20 = 4*m. What is k in 3*k - 27*k**4 + 27*k**2 - m*k - 3*k + 21*k**5 - 15*k**3 - 3*k = 0?
-1, 0, 2/7, 1
Factor -128/13*t**3 - 46/13*t**4 - 32/13*t - 144/13*t**2 - 6/13*t**5 + 32/13.
-2*(t + 2)**4*(3*t - 1)/13
Let q be (-22)/(3*2/(-3)). Let d = q - 7. Find k such that 3*k**5 + 4*k**4 + 12*k - 9*k - d*k**3 - 6*k**2 - 2*k + 2 = 0.
-1, 2/3, 1
Let f be -33*3*1/9. Let b = 13 + f. Factor 4 + 6*t - 6*t**3 - 4*t**2 - 3*t**b - t**4 + 5*t**2 - t**4.
-2*(t - 1)*(t + 1)**2*(t + 2)
Let n(d) be the third derivative of -13/240*d**4 + 0 + 0*d + 7/60*d**3 - 29*d**2 + 1/120*d**5 + 1/1200*d**6. Suppose n(v) = 0. What is v?
-7, 1
Let o(n) be the first derivative of -n**6/90 + n**5/10 - n**4/3 - 2*n**3/3 + 4. Let r(t) be the third derivative of o(t). Factor r(j).
-4*(j - 2)*(j - 1)
Let y(r) = -63*r + 20*r + 16*r - 36 + 24*r. Let b be y(-13). Determine i, given that 6/7*i + 0 - 2/7*i**b + 4/7*i**2 = 0.
-1, 0, 3
Let d = -74 - -21. Let l = d + 161/3. Factor 0*b - l*b**2 + 0 + 1/3*b**3.
b**2*(b - 2)/3
Let c(j) be the third derivative of 0*j**5 + 0*j**3 + 33*j**2 - 1/112*j**8 + 0*j**6 + 0*j**4 + 0*j + 0*j**7 + 0. Factor c(x).
-3*x**5
Let n(l) = -l**2 - 21*l - 28. Let w be n(-19). Let j be 2/(-1) + w/4*2. Factor 2/13 + 2/13*i - 2/13*i**2 - 2/13*i**j.
-2*(i - 1)*(i + 1)**2/13
Suppose 0 = -2*x - 0*x + 24. Let -2*v**2 + v**2 + 5*v**2 - x*v + 4*v = 0. Calculate v.
0, 2
Let n(l) = 4*l**2 + 16*l + 12. Let f(k) = -k**2 - k. Let j(w) = -2*f(w) - n(w). Factor j(s).
-2*(s + 1)*(s + 6)
Factor 15*x**5 + 2*x**2 + 14*x**2 - 16*x**5 - 7*x**4 - 8*x**3.
-x**2*(x - 1)*(x + 4)**2
Factor 9446*f + 188*f**2 + 196*f**4 + 4*f**5 - 9446*f + 380*f**3.
4*f**2*(f + 1)**2*(f + 47)
Let w(v) = 0 - 162*v - 4 + 167*v + 2*v**2. Let q(g) be the first derivative of 7*g**3/3 + 19*g**2/2 - 15*g + 2. Let t(m) = -6*q(m) + 22*w(m). Factor t(b).
2*(b - 1)**2
Let o be -2 - 20/15*-3. Factor -3*b**3 - 21*b**2 - b + 24*b**o + b.
-3*b**2*(b - 1)
Suppose -m + 4 = 5*d, -3*m + 2*d + 11 = -1. Suppose 2*p**2 + 9*p - 4*p - p**m - 7*p**2 - 6*p**2 + 7*p**3 = 0. What is p?
0, 1, 5
Let i(q) be the second derivative of -2*q**6/15 - 4*q**5/5 - q**4 + 8*q**3/3 + 8*q**2 - 29*q. Find l, given that i(l) = 0.
-2, -1, 1
Let 676/5*b - 4/5*b**4 - 20*b**3 - 572/5*b**2 + 0 = 0. Calculate b.
-13, 0, 1
Let k(j) = 2*j**2 + 51*j - 46. Let q be k(-26). Let o be (-52)/q - (-3 + (-26)/(-10)). Factor 0*d**2 + 5*d - 5/3*d**o + 10/3.
-