 35*t - 35. Let k(p) = -35*b(p) - 2*l(p). Factor k(z).
-5*z**2*(z + 1)*(z + 2)
Let u(x) = 3*x + 21. Let r be u(-6). Suppose 25 = 2*o - 5*a, -a = r*o - 3 + 8. Factor o*n**5 + 108*n**3 - 5*n - 98*n**3 - 5*n**5.
-5*n*(n - 1)**2*(n + 1)**2
Factor -2/5*r**4 + 6/5*r**2 + 8/5*r - 8/5 - 4/5*r**3.
-2*(r - 1)**2*(r + 2)**2/5
Let o(k) = 19*k**3 - 84*k**2 - 145*k - 32. Let d(z) = -9*z**3 + 43*z**2 + 72*z + 16. Let i(b) = 5*d(b) + 2*o(b). What is l in i(l) = 0?
-1, -2/7, 8
Factor 3/2*y**3 + 9/2*y + 0 + 25/4*y**2 - 1/4*y**4.
-y*(y - 9)*(y + 1)*(y + 2)/4
What is r in -32/17*r - 14/17*r**2 - 2/17*r**3 - 24/17 = 0?
-3, -2
Let l(j) be the third derivative of j**6/300 - j**5/300 - j**4/120 + 2*j**2 + 34*j. Factor l(k).
k*(k - 1)*(2*k + 1)/5
Let j(i) = -38*i**3 - 2*i**2 + 184*i - 72. Let h(b) = -25*b**3 - 2*b**2 + 123*b - 48. Let m(a) = 8*h(a) - 5*j(a). Factor m(u).
-2*(u - 2)*(u + 3)*(5*u - 2)
Suppose t + 5*g + 25 = 0, -15*g = 2*t - 10*g + 25. Let a(i) be the first derivative of t*i + 8 - 1/15*i**3 + 0*i**2 + 1/5*i**4. Suppose a(k) = 0. What is k?
0, 1/4
Let h(u) = 112*u**3 + 742*u**2 + 320*u + 35. Let g(z) = -4*z**3 + z**2. Let n(y) = -3*g(y) - h(y). Solve n(m) = 0.
-7, -1/4, -1/5
Let m = 29 - 44. Let p(w) = -w**2 - 6*w + 2. Let g(u) = -6*u**2 - 42*u + 15. Let t(x) = m*p(x) + 2*g(x). Let t(l) = 0. What is l?
-2, 0
Let o(a) = -5*a**4 + 3*a**3 + 12*a - 12*a**3 + 0*a**4 - 4*a**4. Let j(d) = -8*d**4 - 9*d**3 + 12*d. Let p(u) = 6*j(u) - 5*o(u). Determine z so that p(z) = 0.
-2, 0, 1
Let z(x) = x**2 + 9*x - 6. Let k be z(-10). Suppose -k*c = -c - 9. Factor 0*s**2 + c*s**2 - 1 + 0*s**2 - 2.
3*(s - 1)*(s + 1)
Factor 32/13*u**2 - 800/13 + 2/13*u**3 + 40/13*u.
2*(u - 4)*(u + 10)**2/13
Let t(a) = -a + 1. Let u be -1 - 1/((-2)/6). Let m(s) = -s**2 - 13*s + 11. Let l = 144 + -166. Let k(r) = l*t(r) + u*m(r). Solve k(d) = 0.
-2, 0
Let b(m) be the first derivative of -m**4/18 + 13*m**2/9 + 8*m/3 + 110. Factor b(u).
-2*(u - 4)*(u + 1)*(u + 3)/9
Let c(r) be the second derivative of r**5/4 - 5*r**4/4 - 15*r**3/2 + 135*r**2/2 + 41*r. Factor c(h).
5*(h - 3)**2*(h + 3)
Let v be (3/(-9))/(5/(-45)). What is s in -13*s + 5 + 5*s**2 - v*s + 6*s = 0?
1
Let i = -68 - -70. Factor 0*s**i + 20*s + 0*s**2 - 7*s**2 + 15 + 12*s**2.
5*(s + 1)*(s + 3)
Let j(v) = 3*v + 70. Let p be j(-22). Let w(o) be the second derivative of -7*o + 1/72*o**p + 1/12*o**2 + 0 - 1/18*o**3. Determine x so that w(x) = 0.
1
Suppose -5*s = 3*f + 232, 0*f - 2*f = -4*s - 168. Let m be ((-23)/12 - -2)*(-198)/s. Factor -m*i**2 + 0 + 0*i.
-3*i**2/8
Let z be ((-196)/(2 - -12))/(-11). Find j such that -z*j + 4/11 + 6/11*j**2 = 0.
1/3, 2
Let x = 13484 - 148322/11. Determine w so that -x*w**2 + 0*w + 18/11 = 0.
-3, 3
Let k be (-180)/(-50) + (-3)/5. Find j such that -j + 5*j**3 - 2 - j**k - 3*j**3 + 5*j**2 - 3*j**2 = 0.
-2, -1, 1
Let f be 6/(-4)*(-72)/(-1). Let k be 4/14 - f/14. Factor -t**3 + 38*t**2 + 6*t**3 + 0 - 8*t + 15*t**3 - k.
2*(t + 2)*(2*t - 1)*(5*t + 2)
Let v(n) be the third derivative of n**8/56 - 17*n**7/105 + 19*n**6/60 + 3*n**5/10 - 11*n**4/6 + 8*n**3/3 - 36*n**2. Determine t so that v(t) = 0.
-1, 2/3, 1, 4
Let k be (-14)/(-4) + 3/(-2). Factor 91*x**3 + 4*x**4 - 2*x**2 + 4*x**2 - 83*x**3 + k*x**2.
4*x**2*(x + 1)**2
Suppose -42*u**2 - 50*u**3 + 45*u**3 - 40*u - 8*u**2 + 3*u**4 + 2*u**4 + 0*u**4 = 0. Calculate u.
-2, -1, 0, 4
Let z = -132 + 105. Let c be z/18 - (-1 - 1). Determine a so that 17/2*a**2 - 13/4*a - c = 0.
-2/17, 1/2
Factor -18/5*h**3 - 4*h**2 - 1/5*h**5 - 8/5*h + 0 - 7/5*h**4.
-h*(h + 1)*(h + 2)**3/5
Let s(z) = 2*z**2 + 4*z + 3. Let j(u) be the first derivative of u - 3 - 8 + 6. Let r(l) = j(l) - s(l). What is t in r(t) = 0?
-1
Let c(x) be the second derivative of -30*x + 0*x**4 + 1/60*x**6 - 1/4*x**2 + 0 + 1/20*x**5 - 1/6*x**3. What is d in c(d) = 0?
-1, 1
Factor 4*w**2 - 21*w**4 + 15 + 18*w**4 - w**5 - 15.
-w**2*(w - 1)*(w + 2)**2
Factor -2*y**3 - 5*y**3 + 52*y**3 + 80*y**2 - 20*y + 0*y.
5*y*(y + 2)*(9*y - 2)
Let d(v) be the third derivative of v**9/12096 - 7*v**5/10 + 28*v**2. Let h(s) be the third derivative of d(s). Factor h(a).
5*a**3
Let b = 2 - 5. Let p be 1*b/(3/(-2)). Find y such that -25*y**3 + 26*y**3 - y**p + 3*y**2 = 0.
-2, 0
Factor -923*w**3 - 648 - 180*w + 17*w**2 + 924*w**3 - 23*w**2.
(w - 18)*(w + 6)**2
Let d(c) be the first derivative of 3*c**3 + 0*c**2 - c + 1/10*c**5 + 10 - c**4. Let s(l) be the first derivative of d(l). Let s(w) = 0. Calculate w.
0, 3
Let c be (-4)/10 - (-17 + (-35696)/(-2160)). Let n(s) be the third derivative of 2*s**2 + 0*s + 16/27*s**3 + c*s**4 + 1/270*s**5 + 0. Factor n(w).
2*(w + 4)**2/9
Let t(k) = -5*k**2 + 55*k + 94. Let y(s) = 2*s**2 - 18*s - 32. Let q(m) = -6*t(m) - 17*y(m). Factor q(n).
-4*(n + 1)*(n + 5)
Find p such that -171*p**4 + 2*p**3 - 167*p**4 + 337*p**4 - 2*p + p**2 = 0.
-1, 0, 1, 2
Find n, given that -382/5*n + 8/5*n**2 - 96/5 = 0.
-1/4, 48
Let n be (-9)/((-36)/32)*2. Factor n*r + 0*r**4 - r**4 + 2*r**2 + 2*r**5 + 8 - 10*r**3 - r**4.
2*(r - 2)**2*(r + 1)**3
Suppose 5*h = j + 4 + 6, h = -j + 2. Determine n so that 0*n - 13*n - 3*n**h + 7*n = 0.
-2, 0
Let t(m) be the second derivative of m**7/14 - m**6/5 - 21*m**5/20 - m**4 + 2*m + 84. Determine r, given that t(r) = 0.
-1, 0, 4
Let l(t) be the first derivative of -4/5*t**3 - 4/5*t - 21 + 1/5*t**4 + 6/5*t**2. Factor l(y).
4*(y - 1)**3/5
Let h(l) = -3*l**3 - 2*l**2 - 14*l - 13. Let g be h(-1). Suppose 1/6 + 1/6*f**g + 1/3*f = 0. Calculate f.
-1
Let r be 606/30 - 2/10. Factor -4 - 7*d - 4*d**4 + r*d**3 - 4 - 36*d**2 + 26*d + 9*d.
-4*(d - 2)*(d - 1)**3
Let x(o) be the first derivative of 0*o + 14 + 10/3*o**3 - 5/2*o**2 - 5/4*o**4. Find k such that x(k) = 0.
0, 1
Let c(x) be the first derivative of -2*x**3 - 25*x + 2*x**4 - 1/5*x**5 - 20*x**2 + 44. Suppose c(u) = 0. Calculate u.
-1, 5
Determine a so that 4725/2*a + 3375/2 + 343/2*a**3 + 2205/2*a**2 = 0.
-15/7
Let y(z) be the first derivative of 3*z**4/4 + z**3/3 - z**2/2 - z + 9. Let o be y(1). Determine k, given that k + 3*k + 498*k**o - 502*k**2 = 0.
0, 1
Let r = 2844 + -2844. Factor 0*k + 0*k**3 + 1/2*k**4 + r - 1/2*k**2.
k**2*(k - 1)*(k + 1)/2
Let q(g) be the second derivative of 27*g**4/10 - 48*g**3/5 + 64*g**2/5 + 329*g. Let q(j) = 0. What is j?
8/9
Let j(s) be the third derivative of -s**6/144 - 7*s**5/24 + 25*s**4/16 - 115*s**3/36 - 42*s**2. Determine q, given that j(q) = 0.
-23, 1
Let c(o) = 21*o - 1320. Let p be c(63). Suppose 0 + 3/4*d**2 - 1/2*d + 1/2*d**p = 0. Calculate d.
-2, 0, 1/2
Let c(a) be the first derivative of -2*a**3/15 - 13*a**2/5 - 72*a/5 + 230. Determine h, given that c(h) = 0.
-9, -4
Suppose -1 + 15 = h - 3*u, -2*u = 4*h. Let i(c) be the first derivative of -1/6*c**4 + 4 + 0*c**h - 2/15*c**5 + 1/9*c**6 + 0*c + 2/9*c**3. Solve i(m) = 0 for m.
-1, 0, 1
Let c = -298 + 301. Let k(a) be the third derivative of 0*a**c + 0*a + 0 - 1/90*a**5 + 3*a**2 - 1/180*a**6 + 0*a**4. Factor k(n).
-2*n**2*(n + 1)/3
Let w(k) = k**3 + 2*k**2 - 8*k + 3. Let v be w(2). Let g(x) be the second derivative of -1/9*x**2 + 2*x + 1/27*x**v + 0 + 1/27*x**4. Solve g(q) = 0 for q.
-1, 1/2
Solve 0 - 1/2*y - 2*y**2 = 0 for y.
-1/4, 0
Let q = 3025/6 - 504. Let k(l) be the second derivative of l + 0 + 0*l**2 + 1/9*l**3 + 1/10*l**5 - 1/45*l**6 - q*l**4. Factor k(z).
-2*z*(z - 1)**3/3
Let k(i) be the third derivative of -i**5/12 + 5*i**4/2 - 30*i**3 - i**2 + 1. Find w, given that k(w) = 0.
6
Let f = 131129/8 + -16391. Factor f*q**2 + 1/8*q**3 - 1/8 - 1/8*q.
(q - 1)*(q + 1)**2/8
Let k be 8/(2 + -34) - 82/(-8). Determine l so that -k*l**3 + 10*l + 14*l**2 + 8*l**4 - 19*l**2 - 3*l**4 = 0.
-1, 0, 1, 2
Factor 14*c**2 + 55/2*c**3 + 13*c**4 + 0*c + 0 - 1/2*c**5.
-c**2*(c - 28)*(c + 1)**2/2
Let d(f) = -f**3 - 4*f**2 + 8*f. Let u be d(-6). Factor 4*r**3 + 47*r + 18*r - 32 - 17*r - u*r**2.
4*(r - 2)**3
Let u be 8/(-1) - (27 + -37). Let -16/23*v**u - 4/23*v + 2/23 = 0. Calculate v.
-1/2, 1/4
Let r(f) = f**5 - 9*f**4 + 6*f**3 - 5*f**2 - 7*f. Suppose 2*n + 17 + 25 = 0. Let g(y) = -y**4 + y**3 - y**2 - y. Let j(u) = n*g(u) + 3*r(u). Factor j(p).
3*p**2*(p - 2)*(p - 1)*(p + 1)
Suppose 0*h - 5*h = 85. Let w = 20 + h. Factor -s**2 + 0*s**3 - 2*s**w + 2*s**2 + s**3.
-s**2*(s - 1)
Factor 54*g + 27/2 - 144*g**2 - 59/2*g**4 + 103*g**3 + 3*g**5.
(g - 3)**3*(g - 1)*(6*g + 1)/2
Supp