40*-5*70/3. Let t(n) = -n**3 + 26*n**2 + 15*n + 6. Let j(p) = v*t(p) + 6*o(p). Factor j(l).
-5*l*(l + 1)*(l + 3)
Let m = 11 + -1. Suppose 0 = m*t + 1 - 31. Determine i so that 2/9*i**2 - 2/9 - 2/9*i**t + 2/9*i = 0.
-1, 1
Let i(n) = -n**3 + 23*n**2 + 2*n + 13. Let h be i(23). Let u = 61 - h. Determine f, given that 0 + 0*f + 3/2*f**3 - 3/2*f**4 + 0*f**u = 0.
0, 1
Let a(v) = 5*v**3 + 9*v**2 - 60. Let y(l) = 3*l**3 + 6*l**2 - 40. Let k(h) = -5*a(h) + 8*y(h). Let m(z) be the first derivative of k(z). Factor m(g).
-3*g*(g - 2)
Suppose -11 = -7*o + 17. Suppose -9*y = -o*y - 10. Factor 0*f + 3/4*f**5 - 3/4*f**4 + 0 + 3/4*f**y - 3/4*f**3.
3*f**2*(f - 1)**2*(f + 1)/4
Let h(t) be the first derivative of -2*t**5/5 - 2*t**4 - 10*t**3/3 - 2*t**2 - 165. Solve h(g) = 0 for g.
-2, -1, 0
Let r(m) = 6*m**2 + 5*m + 4. Let c be r(-1). Let b(i) be the first derivative of -c + 1/9*i**3 + 2/3*i - 1/2*i**2. Factor b(x).
(x - 2)*(x - 1)/3
Let g = -229 + 229. Factor -1/8*p**5 - 3/8*p**3 + 1/8*p**2 + 3/8*p**4 + 0 + g*p.
-p**2*(p - 1)**3/8
Suppose 64*x + 97*x = 139 + 505. Factor -16/11*a + 34/11*a**x - 56/11*a**3 + 4*a**2 + 2/11 - 8/11*a**5.
-2*(a - 1)**4*(4*a - 1)/11
Let f(l) be the second derivative of l**7/56 + l**6/4 + 9*l**5/8 + 5*l**4/2 + 25*l**3/8 + 9*l**2/4 - 37*l. Factor f(b).
3*(b + 1)**4*(b + 6)/4
Factor 1014/7*o + 0 - 72/7*o**3 + 351/7*o**2 + 3/7*o**4.
3*o*(o - 13)**2*(o + 2)/7
Factor 110 + 40*z**2 - 164*z + 5*z**3 + 135*z - 69*z - 57*z.
5*(z - 2)*(z - 1)*(z + 11)
Let -14*b**2 + 40*b - 35*b**3 + 6*b**2 + b**4 - 31*b**4 - 5*b**5 - 3*b**2 + 41*b**2 = 0. What is b?
-4, -2, -1, 0, 1
Let b(t) be the third derivative of -t**10/100800 - t**9/40320 + t**8/6720 + 7*t**5/15 - 32*t**2. Let u(k) be the third derivative of b(k). Factor u(s).
-3*s**2*(s - 1)*(s + 2)/2
Let l = 1635 + -1631. Let r(c) be the second derivative of 1/3*c**l + 2*c + 1/10*c**5 + 1/3*c**3 + 0*c**2 + 0. Factor r(y).
2*y*(y + 1)**2
Let r(o) be the second derivative of 17*o + 0 + 1/48*o**4 + 25/8*o**2 + 5/12*o**3. Factor r(h).
(h + 5)**2/4
Solve -5*r**4 + 47*r**3 - 2*r**3 - 51 - 135*r**2 + 155*r - 9 = 0.
1, 3, 4
Suppose -4*f + 16 = -2*p, 0 = -0*f - f + 4*p + 18. Factor -16*i + 132*i**3 + i**2 - 7*i**2 + 3*i**2 - 5*i**f - 126*i**4.
-2*i*(3*i - 2)**2*(7*i + 2)
Suppose -3*w + 17 = 4*p, 0 = 2*w + w + 3*p - 15. Suppose -3*a = 4*o - 7, -3*o + 29 = 2*o - w*a. Factor 8*q**o + 15*q**2 - 15*q**3 - 3*q - 6*q**3 + q**4.
3*q*(q - 1)**2*(3*q - 1)
Let b(f) be the second derivative of -f**5/50 - f**4/30 + 16*f**3/15 - 4*f**2 - 123*f. Factor b(w).
-2*(w - 2)**2*(w + 5)/5
Let r = 138 - 114. Let d be 2*2/r + (-33)/(-99). Factor d + 7/4*h + 5/4*h**2.
(h + 1)*(5*h + 2)/4
Let n(l) be the third derivative of -l**5/600 + 17*l**4/240 + 3*l**3/10 + 101*l**2. Factor n(t).
-(t - 18)*(t + 1)/10
Let m(a) = 11*a**3 - 27*a**2 + 4*a - 4. Let h(u) = 90*u**3 - 216*u**2 + 33*u - 33. Let v(x) = -4*h(x) + 33*m(x). Factor v(g).
3*g**2*(g - 9)
Let u = -4633135 + 6064774689/1309. Let c = -2/119 + u. Let -c*d + 2/11*d**2 + 6/11 = 0. What is d?
1, 3
Factor 1/3*y**3 - 125/3 + 5/3*y**2 - 25/3*y.
(y - 5)*(y + 5)**2/3
Let j(h) be the second derivative of 5/12*h**4 - 21*h - 10/3*h**3 + 0 + 10*h**2. Factor j(b).
5*(b - 2)**2
Suppose 7*i - 35 = -0*i. Suppose i*o - j = 24, 5*o - 16 = 2*o + j. Find r, given that -2/17*r**o + 4/17*r - 4/17*r**3 + 2/17 + 0*r**2 = 0.
-1, 1
Let w be (-896)/(-96)*(-3)/(-4). Let x(r) be the third derivative of -1/10*r**5 + 0 + 0*r**3 - 5*r**2 + 0*r + 1/6*r**4 + 1/105*r**w + 0*r**6. Factor x(d).
2*d*(d - 1)**2*(d + 2)
Let k = 30 - 26. Let g(l) be the second derivative of -l**3 + 3/4*l**k + 2*l - 9/40*l**5 + 0 + 0*l**2 + 1/40*l**6. Solve g(n) = 0 for n.
0, 2
Determine b so that 107*b - 5*b**3 - 20*b**2 - 50*b - 57*b = 0.
-4, 0
Determine l, given that 1979*l**3 - 2*l**4 - 25*l**2 - 1949*l**3 + 0*l**2 - 3*l**4 = 0.
0, 1, 5
Let m(l) be the third derivative of l**6/120 - l**4/4 - 9*l**2. Let y(k) = k**3 - 7*k. Let w(a) = -7*m(a) + 6*y(a). Factor w(d).
-d**3
Let a(q) = -2*q - 6. Let u(o) = o**2 + 9*o - 25. Let b be u(-11). Let s be a(b). Factor -1/3*t**2 + s + 0*t.
-t**2/3
Let w be 5/((10/(-3))/(4/(-3))). Factor 676*p**4 - 807*p**3 - 532*p**3 + 224*p**w - 16*p + 455*p**3.
4*p*(p - 1)*(13*p - 2)**2
Let q(d) be the first derivative of -d**3/8 + 3*d/8 + 21. Factor q(p).
-3*(p - 1)*(p + 1)/8
Let i(q) be the first derivative of q**5/5 + q**4/2 - 5*q**3 - 18*q**2 - 27. Factor i(s).
s*(s - 4)*(s + 3)**2
Suppose 747*n = 740*n. Let h(i) be the second derivative of -6*i**2 + 35/4*i**4 + 2*i**3 + 7*i + n. Suppose h(k) = 0. Calculate k.
-2/5, 2/7
Let a(h) = h**3 - 94*h**2 - 167*h. Let i(v) = -3*v**3 + 195*v**2 + 333*v. Let m(n) = -9*a(n) - 4*i(n). Find g such that m(g) = 0.
-19, -3, 0
Let i(h) = -h**2 - 4*h - 4. Let k(n) = 2*n**2 + 7*n + 7. Let z(w) = 7*i(w) + 4*k(w). Let c(v) = 7*v**2 + 18*v. Let x(p) = -c(p) + 4*z(p). Factor x(l).
-3*l*(l + 6)
Determine x, given that -14/5 - 18/5*x**2 + 6*x + 2/5*x**3 = 0.
1, 7
Let f be 4/1 - (-1 + 1). Let l = -10469/3 + 3490. Factor j**2 + l*j**f + 0 + 1/3*j + j**3.
j*(j + 1)**3/3
Let c be (55/15 - 3)*(9 - 6). Let x(m) be the third derivative of -3*m**c + 3/4*m**4 + 0*m + 0 - 1/20*m**5 - 9/2*m**3. Solve x(z) = 0.
3
Let a(i) = i**2 + 1. Let c(w) = -2 - 53*w + 0*w**2 + 58*w - w**2. Let y(j) = -4*a(j) - 2*c(j). Suppose y(u) = 0. What is u?
-5, 0
Let f = -281/1925 - -3/25. Let v = 223/308 - f. Solve -3/4*m**2 + 3/2*m - v = 0.
1
Let o(t) be the third derivative of 3/56*t**4 - 1/14*t**5 + 0 - 9*t**2 + 0*t**3 + 3/280*t**6 + 0*t. Factor o(f).
3*f*(f - 3)*(3*f - 1)/7
Solve -69192/11 - 67706/11*j**2 - 2/11*j**4 - 137640/11*j + 740/11*j**3 = 0 for j.
-1, 186
What is z in -5*z**4 - 15/2*z**3 + 0*z - 10/3*z**2 - 5/6*z**5 + 0 = 0?
-4, -1, 0
Suppose 9*t - 11*t - 10 = 0. Let o be ((-1)/(-2))/((-12)/t + -2). Suppose -1/2 - w**2 + o*w + 1/4*w**3 = 0. What is w?
1, 2
Factor 156*w**2 - 6*w + 156*w**2 - 487*w**2 + 7*w**3 + 156*w**2.
w*(w - 3)*(7*w + 2)
Let f(g) = 2*g**3 - 50*g**2 + 384*g - 1026. Let z(d) = -5*d**2 - 29 + 30 + 6*d**2. Let n(w) = f(w) + 2*z(w). Factor n(p).
2*(p - 8)**3
Suppose -5*s - 2*f = -6*f - 75, -3*f + 30 = 2*s. Let t be 8/(6 - 4) - 48/s. Determine i so that -12/5*i**2 - 4/5 - t*i**3 - 12/5*i = 0.
-1
Let g(i) = -i**2 + 7*i - 4. Let t be g(6). Factor -4*l - 4*l + l**2 + 16 + t*l**2 - 2*l**2.
(l - 4)**2
Let v be 0/(1/(4 - (3 + 0))). Suppose -5 = -b - 2*q + 4, v = 3*b - 5*q + 6. Factor 15/4*w**4 - 3/4*w**3 + 0*w**2 + 0 + 0*w - b*w**5.
-3*w**3*(w - 1)*(4*w - 1)/4
Let k(o) be the first derivative of 8*o**3/27 + 61*o**2/9 + 10*o/3 + 352. Factor k(w).
2*(w + 15)*(4*w + 1)/9
Let y be 1/2*0/2. Let h(o) be the second derivative of 1/4*o**3 - 6*o + 0*o**2 + y - 1/8*o**4. Factor h(x).
-3*x*(x - 1)/2
Factor -10*o - 2/5*o**2 + 0.
-2*o*(o + 25)/5
Let y(m) be the first derivative of m**6/42 + m**5/7 + m**4/7 - 113. Factor y(h).
h**3*(h + 1)*(h + 4)/7
Suppose -6 = -5*o - d, -4*d - 15 - 7 = -3*o. Suppose o*c**2 + 91*c - 3*c**2 - 90*c = 0. Calculate c.
0, 1
What is s in -2/3*s**4 + 8*s**3 + 0 + 0*s - 24*s**2 = 0?
0, 6
Let c(r) be the third derivative of 0 + 0*r**3 + 27*r**2 - 1/245*r**7 - 1/14*r**4 + 1/70*r**6 + 0*r + 1/70*r**5. Factor c(j).
-6*j*(j - 2)*(j - 1)*(j + 1)/7
Let j be 6/(-1) - ((2 - 11) + (-176)/(-112)). Let -38/7*v**3 - 4*v**2 - 16/7 + 8*v + 16/7*v**4 + j*v**5 = 0. What is v?
-2, 2/5, 1
Suppose 0 = 112*x - 105*x - 21. Suppose -1/5*c**x + 3/5*c**2 - 3/5 + 1/5*c = 0. Calculate c.
-1, 1, 3
Let g(c) = -4*c**5 - 20*c**4 - 112*c**3 - 128*c**2 - 100*c - 20. Let a(o) = -o**4 + o**3 - 2*o**2 - o - 1. Let h(r) = -12*a(r) - g(r). Factor h(u).
4*(u + 1)**2*(u + 2)**3
Let q = -11 - -14. Suppose -3*o = -0*o - 6. Factor 2*b - 15 - o*b - 9*b + q*b**3 + 9.
3*(b - 2)*(b + 1)**2
Let z be (4/6)/(2/27). Suppose -13*l + z*l = 0. Let l*f**3 - 7*f**3 + 5*f**4 + 7*f**3 = 0. What is f?
0
Let h(j) be the first derivative of j**4/16 + j**3/6 - 3*j**2/8 + 100. Factor h(m).
m*(m - 1)*(m + 3)/4
Let r(h) = -h**3 - 6*h**2 - 6*h - 24. Let u be r(-7). Let l = u - 199/3. Factor -l*j**3 + 0*j**2 + 1/3*j**4 - 1/3 + 2/3*j.
(j - 1)**3*(j + 1)/3
Let b(h) be the second derivative of h**7/5460 + h**6/780 + h**5/390 + 9*h**3/2 + 2*h. Let r(z) be the second derivative of b(z). Suppose r(s) = 0. Calculate s.
-2, -1, 0
Let g(q) be the second derivative 