
Let a(n) = -31*n**3 + 75*n**2 - 16*n. Let k(d) = -11*d**3 + 25*d**2 - 6*d. Let j(s) = 3*a(s) - 8*k(s). Determine x so that j(x) = 0.
0, 5
Let n(w) = 4*w**3 - 8*w**2 - 21*w. Let m(h) = -h**3 + h. Let p = 69 - 70. Let x(i) = p*n(i) - 5*m(i). Factor x(a).
a*(a + 4)**2
Let k(h) be the third derivative of 1/30*h**6 + 0 - 5/6*h**4 + 4/3*h**3 + 1/5*h**5 - h - 2/105*h**7 + 5*h**2. Find z, given that k(z) = 0.
-2, 1
Let g = -162 + 168. Suppose -5*y - 4*s - 12 = 0, 0 = 4*y + 4*s + g + 6. Determine r so that 0*r - 1/7*r**2 + 1/7*r**3 + y = 0.
0, 1
Let z(l) = -7*l**4 - l**3 - 8*l + 8. Let i be (-1)/(-4) + (-4)/32*26. Let v(n) = n**4 + n - 1. Let c(x) = i*z(x) - 24*v(x). Factor c(f).
-3*f**3*(f - 1)
Factor 58 + 0 - 123*p - 24*p + 92*p**2 - 3*p**3.
-(p - 29)*(p - 1)*(3*p - 2)
Let u(r) be the second derivative of -r**5/20 - 11*r**4/4 - 85*r**3/2 + 289*r**2/2 + 20*r - 2. Determine i so that u(i) = 0.
-17, 1
Let m be (248/(-20))/(-2*(-4)/(-200)). Let k = 312 - m. Factor -39/4*l**3 + 15/4*l**4 + 3/4*l + 27/4*l**k - 3/2.
3*(l - 1)**3*(5*l + 2)/4
Let y(p) = 5*p**2 - 5*p - 3. Let u(x) = 6*x**2 - 6*x - 4. Let q(c) = 4*u(c) - 5*y(c). Let g(a) = -7*a**2 + 12*a + 13. Let l(j) = -g(j) + 2*q(j). Factor l(t).
5*(t - 3)*(t + 1)
Let d(q) be the third derivative of q**6/100 - 13*q**5/150 + q**4/30 + 8*q**3/15 + 23*q**2 - 2*q. Factor d(n).
2*(n - 4)*(n - 1)*(3*n + 2)/5
Let q(y) = 7*y**4 + 32*y**3 + 78*y**2 + 91*y + 32. Let p(h) = -22*h**4 - 96*h**3 - 232*h**2 - 274*h - 96. Let i(l) = 3*p(l) + 10*q(l). Factor i(s).
4*(s + 1)**2*(s + 2)*(s + 4)
Let f(i) be the third derivative of i**9/151200 - i**8/50400 + 31*i**5/60 - 21*i**2. Let g(n) be the third derivative of f(n). Factor g(l).
2*l**2*(l - 1)/5
Factor -35*m - 8*m**2 + 10*m**2 + 13*m - 3*m**2 - 121 + 0*m**2.
-(m + 11)**2
Factor 16*a**2 + 8 + 30 - 86 - 14*a - 38*a.
4*(a - 4)*(4*a + 3)
Let l(u) be the first derivative of u**4 - 5 + 40/3*u**3 + 0*u + 50*u**2. Suppose l(n) = 0. What is n?
-5, 0
Let p be 1 - (0 + (-14 - -2)). Let a = -6 + p. Let -17*m**2 + a*m**2 - 2*m - 8*m**3 + 0*m**3 = 0. What is m?
-1, -1/4, 0
Let o be ((-14)/35)/(60/(-6250)). Factor 0*f + 20*f**3 + 0 - 8/3*f**2 - 50*f**4 + o*f**5.
f**2*(5*f - 2)**3/3
Let z(l) be the second derivative of -l**4/12 - 7*l**3/6 + 2*l**2 - 3*l. Let q be z(-7). Factor -6*h**5 + 2*h**3 + 4*h**5 - h**3 + h**q.
-h**3*(h - 1)*(2*h + 1)
Let u = -5311/8 + 664. Let s(z) be the second derivative of 1/12*z**3 + 0 - u*z**2 + 7*z - 1/48*z**4. Factor s(r).
-(r - 1)**2/4
Let y(s) be the third derivative of s**7/75 - 17*s**6/100 + 119*s**5/150 - 31*s**4/20 + 6*s**3/5 - 6*s**2 + 8*s. Determine p, given that y(p) = 0.
2/7, 1, 3
Let n = -65 + 60. Let d be (n/15)/((-5)/12). What is f in 0 + d*f**2 - 4/5*f**3 + 4/5*f - 4/5*f**4 = 0?
-1, 0, 1
Let j(l) = l**2 + 293*l + 870. Let b be j(-3). Factor -2/5*t**4 + 0*t**2 + 2/5*t**3 + 0 + b*t.
-2*t**3*(t - 1)/5
Let s = -425 - -428. Let m(n) be the first derivative of n**2 - 1 + 4*n - 2/3*n**s. Factor m(g).
-2*(g - 2)*(g + 1)
Let j = -26 - -92. Let f be (j/55)/(2/5). What is i in -3/2*i**4 + 0 + i**f - i + 3/2*i**2 = 0?
-1, 0, 2/3, 1
Let z = -246 + 250. Let f(b) be the third derivative of -2/105*b**5 + 0*b - b**2 + 0*b**3 + 0*b**6 + 1/588*b**8 + 4/735*b**7 - 1/42*b**z + 0. Factor f(g).
4*g*(g - 1)*(g + 1)**3/7
Let d(f) be the third derivative of -f**7/630 + f**6/40 - 13*f**5/180 - 5*f**4/8 + 25*f**3/9 + 73*f**2. Find z, given that d(z) = 0.
-2, 1, 5
Let g(y) be the second derivative of y**4/60 - 2*y**3/5 + 18*y**2/5 - y - 3. Factor g(u).
(u - 6)**2/5
Let z(a) be the first derivative of -2*a**5/5 + a**4/2 + 302. Factor z(j).
-2*j**3*(j - 1)
Suppose -3*z - 71 = -4*p, 0 = -p + 5*p - 2*z - 70. Suppose -10*h = -p*h + 21. What is u in 0 - 12/5*u**4 + 8/5*u + 26/5*u**h + 2/5*u**5 - 24/5*u**2 = 0?
0, 1, 2
Let d(g) be the second derivative of -27*g**8/4480 - g**7/40 + 17*g**6/360 - g**5/30 - 5*g**4/12 - 5*g. Let l(k) be the third derivative of d(k). Factor l(t).
-(t + 2)*(9*t - 2)**2/2
Factor 8*w**4 + 4*w**2 + 50*w**3 - 2*w**5 - 107*w**3 + 47*w**3.
-2*w**2*(w - 2)*(w - 1)**2
Let z = 156 - 70. Let h = -86 + z. Determine n, given that -3/4*n - 3/4*n**3 - 3/2*n**2 + h = 0.
-1, 0
Let j = 27828 + -27826. Factor 3/2 + 3/2*u**3 + 9/2*u + 9/2*u**j.
3*(u + 1)**3/2
Let j(h) be the second derivative of 2*h**7/63 - 7*h**6/45 + 7*h**5/30 - h**4/9 + 13*h + 7. Let j(w) = 0. Calculate w.
0, 1/2, 1, 2
Suppose -8 - 1/2*d**2 - 5*d = 0. Calculate d.
-8, -2
Suppose -17*a = 49 - 304. Suppose 3*l + a = 21. Factor 2/3*q**3 + 2/3*q**l - 8/3*q - 8/3.
2*(q - 2)*(q + 1)*(q + 2)/3
What is a in 24*a**2 - 2/5*a**5 + 0 - 26/5*a**3 - 72/5*a - 4*a**4 = 0?
-6, 0, 1
Let f = 1 - 1. Let k be (6/(-18))/(3/(-33)) + 10/(-15). Factor f*o**2 + 0*o + 0 + 2/3*o**k - 2/3*o**5 + 0*o**4.
-2*o**3*(o - 1)*(o + 1)/3
Let f be -24 + 20 + 25/6. Let j be ((-1)/3 - (-4)/6) + 0. Factor 1/6*o**3 - j*o**2 + 0 + 0*o + f*o**4.
o**2*(o - 1)*(o + 2)/6
Let f(s) = 2*s**3 - 62*s**2 - 196*s - 150. Let o(c) = 3*c**3 - 61*c**2 - 192*c - 149. Let u(r) = 7*f(r) - 6*o(r). Factor u(m).
-4*(m + 1)*(m + 3)*(m + 13)
Let c(d) = -d**2 - 15*d - 28. Let v be c(-11). Let -10*g**4 - v*g**3 - 8*g - 11*g**4 + 17*g**4 - 20*g**2 = 0. Calculate g.
-2, -1, 0
Determine g so that -15/4*g**3 + 1/8*g**4 + 21/2*g**2 + 27/8 - 41/4*g = 0.
1, 27
Let f = 3/343 + 2043/1715. Suppose -1/5*t**2 - f - t = 0. Calculate t.
-3, -2
Suppose 3/2*m**3 + 190*m - 149/2*m**2 - 94 = 0. What is m?
2/3, 2, 47
Let q = -13632 + 13636. Let 58/3*h**2 + 16*h + 24/5 + 2/15*h**5 + 10*h**3 + 2*h**q = 0. What is h?
-6, -1
Let y(i) = i + 27. Let f be y(-24). Factor -10*r**2 + f*r**3 + 0*r**3 - r**3 + 1 - 7 + 14*r.
2*(r - 3)*(r - 1)**2
Suppose 0 = 16*x - 9*x - 42. Let m(p) be the first derivative of 0*p - 6/5*p**5 + 1 - 2/5*p**3 + 0*p**2 - 3/10*p**x - 27/20*p**4. Let m(t) = 0. What is t?
-2, -1, -1/3, 0
Let u(p) = -p**2 + 31*p + 2. Let a be u(31). Let l(c) be the first derivative of 0*c - 2/3*c**3 + 4 + 0*c**a. Determine x, given that l(x) = 0.
0
Let n(k) be the second derivative of 0 - 5*k**2 - 27*k + 5/6*k**3 + 5/4*k**4. Suppose n(r) = 0. What is r?
-1, 2/3
Suppose 18 = 3*g + 9. Suppose -10976 + 43*n**2 + 2352*n - 63*n**2 + 4*n**g - 79*n**2 - 69*n**2 = 0. Calculate n.
14
Let c = 26 + -24. Let x(w) be the first derivative of 0*w - 8/33*w**3 + 1/22*w**4 - 5 + 4/11*w**c. What is v in x(v) = 0?
0, 2
Let n(z) = -z**2 - 11*z + 24. Let t be n(-12). Let c = -7 + t. What is u in -1/2*u**3 + 0*u**2 + 1/4*u + 0 + 1/4*u**c + 0*u**4 = 0?
-1, 0, 1
Let -9*n + 10 - 5*n - 30*n**3 - 15*n**3 - 43*n**2 - n**5 - 10 - 17*n**4 = 0. What is n?
-14, -1, 0
Let q(k) be the first derivative of k**8/672 + k**7/105 + k**6/48 + k**5/60 - k**2/2 - 14. Let b(n) be the second derivative of q(n). Factor b(t).
t**2*(t + 1)**2*(t + 2)/2
Let m(d) be the first derivative of 7*d**4/12 - 16*d**3/9 - 17*d**2/6 + 2*d - 66. Factor m(t).
(t - 3)*(t + 1)*(7*t - 2)/3
Let s(y) be the first derivative of -27 + 25/4*y**4 + 0*y + 10*y**2 - 20*y**3. What is k in s(k) = 0?
0, 2/5, 2
Let h be 20/8*2 - 0. Suppose h*l = l + 12. Factor 4/7 - 2/7*b**l + 8/7*b**2 - 10/7*b.
-2*(b - 2)*(b - 1)**2/7
Suppose 5*i + 2*i - 14 = 0. Let y(n) = n**2 - 4. Let z be y(4). Factor -2*q + 2*q + q**2 + z*q + i*q**2.
3*q*(q + 4)
Let b(v) be the first derivative of 9/5*v + 3/5*v**2 - 23 - 1/5*v**3. Suppose b(m) = 0. What is m?
-1, 3
Solve 84*n**2 + 10*n**5 + 9*n**5 - 23*n**5 + 128*n + 26*n**4 + 120*n**3 + 6*n**5 + 140*n**2 = 0.
-4, -1, 0
Let l(k) = 9*k**3 - 12 + 5*k**2 - 21*k + 4*k**2 - 3*k**2. Let t(v) = -8*v**3 - 6*v**2 + 20*v + 13. Let h(j) = -5*l(j) - 6*t(j). Solve h(o) = 0 for o.
-3, -1, 2
Suppose 3*c + 6 = 0, 2*z + c = 5*c - 42. Let g be (12 + -7)*(-4)/z. Determine f so that -2/5*f**4 + g*f**2 - 12/5*f**5 + 0 + 0*f + 2*f**3 = 0.
-2/3, -1/2, 0, 1
Let a(q) be the first derivative of 0*q + 4/33*q**3 - 1 - 1/22*q**4 + 3/11*q**2. Factor a(d).
-2*d*(d - 3)*(d + 1)/11
Let 0 - 32/7*x**2 + 24/7*x**3 + 0*x - 4/7*x**4 = 0. Calculate x.
0, 2, 4
Determine k, given that 7786*k**2 + 65 - 70*k + 7782*k**2 - 15563*k**2 = 0.
1, 13
Factor -68*a**2 - 111*a**3 + 114*a**3 + 4 + 61*a**2.
(a - 2)*(a - 1)*(3*a + 2)
Let p(x) = 3*x**4 + 115*x**3 - 4111*x**2 + 50657*x - 4. Let m(w) = -w**4 - w**3 + w**2 - w + 1. Let v(u) = -20*m(u) - 5*p(u). Factor v(k).
5*k*(k - 37)**3
Let k(v) = 