) = k*a(q) + 12*u(q). Factor v(t).
3*(t - 1)**2*(t + 2)*(5*t + 2)
Let l(n) = 2*n - 12. Suppose -5*f - 53 = -0*c - 4*c, -2*c - f = -9. Let t be l(c). What is x in -4*x**3 - t*x**2 - 6*x**4 - x**2 + 5*x**3 - 10*x**3 = 0?
-1, -1/2, 0
Let p be ((232855/18)/7)/((-7)/14). Let z = p - -3707. Factor -16/3*s - 8/9 - 14/3*s**2 + z*s**3.
2*(s - 1)*(7*s + 2)**2/9
Let r(p) = -15*p**3 - 68*p**2 - 72*p - 12. Let m(q) = 178 - q**2 - 178. Let j(k) = 5*m(k) - r(k). Factor j(b).
3*(b + 2)**2*(5*b + 1)
Let i = -36 - -44. Determine o, given that 4 + 4*o**2 - 4*o**4 + 10*o - 2*o**5 + o**4 - 5*o**4 - i*o**3 = 0.
-2, -1, 1
Let f(r) be the first derivative of 21 + 0*r**2 + 5/4*r**4 + 0*r - 20/3*r**3. Factor f(m).
5*m**2*(m - 4)
Factor -16*i - 23*i**5 - 17*i**4 - 21 + 161*i**3 - 239*i**3 + 24*i**5 - 21*i - 46*i - 122*i**2.
(i - 21)*(i + 1)**4
Suppose -25 = -5*n + 5*g, 0 = -n - g + 4 - 3. Let 15*h**2 + 5 - 5*h**n + 10*h**3 - 89*h + 104*h = 0. What is h?
-1
Factor 3/5*w**4 - 12/5*w**2 + 6/5*w**3 - 6/5*w + 9/5.
3*(w - 1)**2*(w + 1)*(w + 3)/5
Suppose -2 = 36*u - 35*u, 4*n = 4*u + 8. Suppose -7/4*b + n - 3/2*b**2 + 1/4*b**3 = 0. Calculate b.
-1, 0, 7
Let i(s) be the second derivative of s**5/60 - s**4/24 - s**3/3 + 2*s**2 - 10*s. Let r(p) be the first derivative of i(p). Factor r(z).
(z - 2)*(z + 1)
Let k(a) be the second derivative of a**4/4 - 13*a**3/2 - 21*a**2 - 120*a. Factor k(h).
3*(h - 14)*(h + 1)
Find b such that 9*b**2 + 27*b**2 + 16 + 100*b + 48*b = 0.
-4, -1/9
Factor 55 + 29*y + 76*y + 20*y**2 + 16*y**2 + 9*y**2 - 5*y**3.
-5*(y - 11)*(y + 1)**2
Suppose 2*n - 2 + 4 = 0. Let d be n - -1 - (2 + 2)/(-20). Factor -2/5*y + 2/5*y**3 - 1/5 + d*y**4 + 0*y**2.
(y - 1)*(y + 1)**3/5
Let j be 0 - (8/24 + 14/(-6)). Solve -2*r + 0*r**4 - 6*r**3 + 217 - 6*r**2 - j*r**4 - 217 = 0 for r.
-1, 0
Let g be ((-1)/(-2))/(((-57)/(-90))/(-19)). Let u be 6/g - 4/(-5). Factor -u*q**2 - 4/5*q + 0.
-2*q*(q + 2)/5
Suppose 5*p - 4*o = 8, -4 = 93*p - 92*p + 2*o. Factor p + w**2 + 1/2*w + 1/2*w**3.
w*(w + 1)**2/2
What is z in 2/5 - 1/5*z**2 - 1/5*z**4 + 3/5*z**3 - 3/5*z = 0?
-1, 1, 2
Factor 10*h + 26 + 18*h - 2 + 82*h**2 - 78*h**2.
4*(h + 1)*(h + 6)
Let f(o) be the third derivative of o**9/574560 - o**8/63840 + o**7/23940 + o**5/15 + 18*o**2. Let d(y) be the third derivative of f(y). Factor d(j).
2*j*(j - 2)*(j - 1)/19
Let y(u) be the first derivative of u**5/35 - 33*u**4/28 + 85*u**3/7 + 289*u**2/14 + 100. Suppose y(r) = 0. Calculate r.
-1, 0, 17
Let j(v) be the first derivative of -v**3/3 + 4*v**2 + 13*v - 5. Let u be j(9). Solve u*h - 2*h + 4*h**2 - 5*h**2 = 0 for h.
0, 2
Determine m so that 2/9*m**3 + 4/3*m - 14/9*m**2 + 0 = 0.
0, 1, 6
Let a(x) be the first derivative of x**4/4 - x**3 + x**2/2 + 3*x + 14. Let v(t) = t**2 - t - 1. Let n(s) = -2*a(s) - 4*v(s). Factor n(j).
-2*(j - 1)**2*(j + 1)
Let q(j) be the first derivative of 1/12*j**3 + 0*j - 1/72*j**4 - 9/2*j**2 - 1/360*j**5 - 2. Let w(t) be the second derivative of q(t). Factor w(m).
-(m - 1)*(m + 3)/6
Let f(s) be the third derivative of 1/240*s**5 + 1/96*s**4 + 0*s - 1/12*s**3 - 29*s**2 + 0. Solve f(x) = 0 for x.
-2, 1
Let g(a) be the third derivative of -1/60*a**6 + 0*a**5 + 1/210*a**7 + 0*a - 1/6*a**3 + 1/12*a**4 - 2*a**2 + 0. Solve g(b) = 0 for b.
-1, 1
Let u(n) be the first derivative of n**4 + 260*n**3 + 25350*n**2 + 1098500*n + 224. Determine x, given that u(x) = 0.
-65
Let g = -25 - -28. Factor -15*a**4 + 32*a**5 - 35*a**5 - 22*a**g + a**3 - 9*a**2.
-3*a**2*(a + 1)**2*(a + 3)
Let r(s) be the second derivative of 11*s + 0*s**2 + 1/6*s**4 + 0*s**3 + 0 + 0*s**5 - 1/15*s**6. Determine f so that r(f) = 0.
-1, 0, 1
Let b(j) = 6*j**4 + 8*j**3 - 12*j**2 - 10. Let k(d) = -2*d**4 - 3*d**3 + 4*d**2 + 4. Let t(c) = -3*b(c) - 8*k(c). Factor t(o).
-2*(o - 1)**2*(o + 1)**2
Let n(f) be the third derivative of 1/4*f**4 + 0 + 0*f - 1/120*f**6 - 1/40*f**5 + 7/6*f**3 - 5*f**2. Let o(r) be the first derivative of n(r). Factor o(d).
-3*(d - 1)*(d + 2)
Suppose -5*x - 4*o - 6 + 0 = 0, 22 = 5*x - 3*o. Factor x - 710*k**5 + 5*k**3 - 2 + 705*k**5.
-5*k**3*(k - 1)*(k + 1)
Suppose 0*f + 8 = 4*f. Factor 32*n**3 - 47*n**3 - 3*n**5 + n**4 - 6*n**f - 13*n**4.
-3*n**2*(n + 1)**2*(n + 2)
Factor 0 - 13/4*t**2 + 7/2*t - 1/4*t**3.
-t*(t - 1)*(t + 14)/4
Let q(s) = s + 3. Let v be q(2). Suppose v*a = 2*a. Factor -3 - 45*p**2 - 3*p**5 + 9*p + a*p**4 + 9*p**4 - 6*p**3 + 39*p**2.
-3*(p - 1)**4*(p + 1)
Suppose 4*l + 3*l - 49 = 0. Let s(p) be the third derivative of 0*p**4 + 0 - 4/315*p**l + 4*p**2 + 0*p + 0*p**5 - 1/180*p**6 + 0*p**3 - 1/168*p**8. Factor s(o).
-2*o**3*(o + 1)*(3*o + 1)/3
Let r(m) be the first derivative of -2*m**5/5 - m**4 - 2*m**3/3 - 459. Find t such that r(t) = 0.
-1, 0
Let z(m) = -m**5 - m**4 - m**3 + m**2. Let j(q) = 8*q**5 + 16*q**4 + 76*q**3 + 68*q**2. Let k(g) = -j(g) - 12*z(g). Let k(b) = 0. Calculate b.
-2, 0, 5
Let u(x) be the second derivative of 2*x**6/75 + 6*x**5/5 + 253*x**4/15 + 56*x**3 + 392*x**2/5 + 54*x. Suppose u(n) = 0. What is n?
-14, -1
Let m(i) be the third derivative of 7*i**8/16 + 117*i**7/5 + 285*i**6 - 9668*i**5/5 + 2394*i**4 - 1296*i**3 - 52*i**2 - 2. Solve m(h) = 0.
-18, 2/7, 2
Factor 0 + 3/2*v**2 - v - 1/2*v**3.
-v*(v - 2)*(v - 1)/2
Let k(y) = y**2 - 77*y + 1107. Let o be k(58). Factor 15/2*m - 5*m**3 - 5/2*m**o - 15/2*m**4 + 5/2 + 5*m**2.
-5*(m - 1)*(m + 1)**4/2
Find d, given that 230496*d - 2400738 - 7749689 - 2209007 - 1176*d**2 - 2699638 + 2*d**3 = 0.
196
Let j be (28 + (-13 - 27))/(-6). Factor 9*y**j + 3/2*y - 3/2*y**3 - 9.
-3*(y - 6)*(y - 1)*(y + 1)/2
Let g(t) be the third derivative of 1/150*t**5 + 0 + 0*t**3 + 13*t**2 + 0*t - 1/30*t**4. Determine s so that g(s) = 0.
0, 2
Let u(b) be the third derivative of -12*b**2 - 8/3*b**3 - 2/3*b**4 - 1/15*b**6 + 7/15*b**5 + 0*b + 0. Factor u(z).
-4*(z - 2)**2*(2*z + 1)
Let f(c) be the second derivative of -c**5/120 + c**3/12 - 3*c**2 + 13*c. Let m(i) be the first derivative of f(i). Determine s so that m(s) = 0.
-1, 1
Let h = -32 + 36. Factor -34*s**2 - 3*s**3 + 42*s**2 - h - 5*s**3 + 4*s - 4*s**4 + 4*s**5.
4*(s - 1)**3*(s + 1)**2
Factor 49*l**2 + 19 + 76*l + 61 - 10*l**2 - 20*l**2 - 23*l**2.
-4*(l - 20)*(l + 1)
Suppose 31 = z - 3*p - 10, 2*z + 3*p - 37 = 0. Let f = z + -16. Factor -3*y**5 + 0 - 2*y + 7*y + 10*y**3 + 4*y**5 - f*y**2 - 5*y**4 - 1.
(y - 1)**5
Let z = 123 + -222. Let i be 275/z - (-3 + 0). Factor -32/9 - i*s**2 - 16/9*s.
-2*(s + 4)**2/9
Let w(j) be the second derivative of -10*j**4/21 + 17*j**3/21 + 3*j**2/7 + j - 9. Factor w(x).
-2*(x - 1)*(20*x + 3)/7
Let f(r) = -r**3 + 56*r**2 - 209*r + 6. Let z be f(4). Factor 0*a + 6/7*a**z + 0 - 2/7*a**3.
-2*a**2*(a - 3)/7
Let c(a) be the third derivative of 0*a + 0*a**3 - 1/60*a**5 + 4*a**2 - 1/80*a**6 + 1/48*a**4 + 0. Suppose c(h) = 0. What is h?
-1, 0, 1/3
Let g(k) = -k**4 + k**3 - k**2 - k + 1. Let n(o) = 16*o**4 - 12*o**3 + 32*o**2 + 4*o - 36. Let u(c) = -20*g(c) - n(c). Factor u(q).
4*(q - 2)**2*(q + 1)**2
Let o(f) be the third derivative of -f**8/420 - 4*f**7/525 + 2*f**5/75 + f**4/30 + 208*f**2. Suppose o(h) = 0. Calculate h.
-1, 0, 1
What is m in 3*m**3 - 21*m**2 - 2 - 6*m + 18*m + 21*m - 13 = 0?
1, 5
Let q(a) be the third derivative of a**7/1155 + a**6/132 + 7*a**5/330 + a**4/44 + 268*a**2. Factor q(o).
2*o*(o + 1)**2*(o + 3)/11
Let b = -34 + 33. Let k be 1/(b + (-18)/(-15)). Suppose 7*n**3 - 8*n**4 + 10*n + 3*n**4 + k*n**2 - 17*n**3 = 0. What is n?
-2, -1, 0, 1
Let w(a) be the first derivative of 2*a**3/39 - 58*a**2/13 + 1682*a/13 - 126. Factor w(i).
2*(i - 29)**2/13
Let m(b) = 13*b**2 + 4*b - 2. Let i(f) = f**2 + 6*f - 20. Let a(q) = -2*q + 7. Let n(o) = -17*a(o) - 6*i(o). Let t(c) = 3*m(c) + 7*n(c). Factor t(g).
-(g + 1)*(3*g - 1)
Let b(a) = -a**3 - 26*a**2 + 276*a + 49. Let v be b(8). Factor -1/3*r**3 + 243 + 9*r**2 - v*r.
-(r - 9)**3/3
Let o be -250*(-3)/195 + 2/13. Let r(d) be the first derivative of -3*d**3 + 5 - 1/5*d**5 + 7/2*d**2 - 2*d + 5/4*d**o. Factor r(i).
-(i - 2)*(i - 1)**3
Let g(d) = 9*d**2 + 21*d + 7. Let y(t) = -14*t**2 + 40*t**2 + 8 - 18*t**2 + 20*t. Let c(q) = -4*g(q) + 5*y(q). Factor c(m).
4*(m + 1)*(m + 3)
Let r(x) be the first derivative of 35/24*x**4 + 2 + 5/3*x**3 + 13/2*x**2 + 0*x + 5/12*x**5. Let w(d) be the second derivative of r(d). Factor w(o).
5*(o + 1)*(5*o + 2)
Let b = -10 + -5.