u**2*(u - 2)*(u - 1)/8
Let l be 6/15 + ((-74)/210 - 0). Let q(x) be the third derivative of 0 - l*x**4 + 0*x + 1/105*x**5 + 2/21*x**3 - x**2. Determine o so that q(o) = 0.
1
Suppose -45/2*j - 20*j**2 + 5/2*j**3 + 0 = 0. Calculate j.
-1, 0, 9
Let l(y) be the first derivative of y**3/12 - y**2/8 - 3*y - 98. Suppose l(w) = 0. What is w?
-3, 4
Find n, given that 1/2*n**2 + 3/2*n - 2 = 0.
-4, 1
Let f(s) be the first derivative of -7 + 15/2*s**2 - 5/3*s**3 - 10*s. Factor f(g).
-5*(g - 2)*(g - 1)
Let u be ((-4)/3)/(27 + 2 + -33). Factor -10/9*v**2 - u*v - 2/3*v**4 - 4/3*v**3 - 1/9*v**5 + 0.
-v*(v + 1)**3*(v + 3)/9
Let g(o) be the second derivative of -o**5/70 + o**3/3 + 6*o**2/7 + 49*o. Suppose g(t) = 0. What is t?
-2, -1, 3
Factor 11*a**4 + 134*a**2 + 72 - 15*a**4 + a**5 + 16*a**4 + 18*a**3 + 39*a**3 + 156*a.
(a + 2)**3*(a + 3)**2
Let d(a) be the third derivative of a**6/480 + 29*a**5/80 + 841*a**4/32 + 24389*a**3/24 + 2*a**2 - 4. Solve d(s) = 0.
-29
Factor 62/5*t**2 + 102/5*t + 2*t**3 + 18/5.
2*(t + 3)**2*(5*t + 1)/5
Let l be (12/(-9) - -2)*9. Solve -s**2 - 11*s**2 - l*s - 2*s**4 - 2 - 8*s**3 - 2*s = 0.
-1
Let 26228*r**2 - 4*r - 26223*r**2 + 75 - 36*r = 0. Calculate r.
3, 5
Determine o so that 14/5*o**3 - 42/5 - 118/5*o**2 + 146/5*o = 0.
3/7, 1, 7
Let u(a) = -6*a**2 - 3*a + 8. Let l(t) = 5*t**2 + 2*t - 7. Let z(r) = -5*l(r) - 4*u(r). Let b be z(3). Factor -2*v + 0*v**2 + b*v - 3*v**2 - v.
-3*v*(v + 1)
Let j = 9/7 + -283/231. Let n(b) be the first derivative of -2/11*b**2 - j*b**3 - 7 - 2/11*b. Find t such that n(t) = 0.
-1
Let a(y) = y**2 - 4*y + 1. Let r(m) be the third derivative of m**5/12 - m**4 + 5*m**3/6 - 22*m**2. Let u(c) = 34*a(c) - 6*r(c). Find n, given that u(n) = 0.
-1
Solve 2/3*p**2 + 2/3 - 4/3*p = 0 for p.
1
Let m(w) be the second derivative of 22*w - 1/4*w**2 + 3/20*w**6 + 0 + 1/8*w**3 + 1/6*w**4 - 11/40*w**5 - 5/168*w**7. Suppose m(b) = 0. Calculate b.
-2/5, 1
Let h(f) = 14*f**3 + 24*f**2 - 12*f. Let o(b) = -14*b**3 - 24*b**2 + 13*b. Let j(m) = -5*h(m) - 4*o(m). Factor j(a).
-2*a*(a + 2)*(7*a - 2)
Suppose r - 19 = -8. Let 7 - 6*x**2 + 20*x + r*x**2 + 13 = 0. What is x?
-2
Let a = 10811 + -32432/3. Suppose 0 - a*z**3 + 0*z + 1/3*z**2 = 0. What is z?
0, 1
Let q(r) = 6*r**3 + 12*r**2 + r - 5. Let a = -16 - -9. Let m(s) = -3*s**3 - 6*s**2 - s + 2. Suppose 4*u + 4 = -12. Let i(w) = a*m(w) + u*q(w). Factor i(d).
-3*(d - 1)*(d + 1)*(d + 2)
Let y(p) = -p**2 + 19*p - 6. Let j be y(19). Let i be (45/j - -7)*8/(-10). Factor -6/5*w + 6/5*w**3 - 2/5 + i*w**2.
2*(w - 1)*(w + 1)*(3*w + 1)/5
Let c(g) be the third derivative of 2*g**7/21 + g**6/15 - g**5 - 8*g**4/3 - 8*g**3/3 - g**2 + 10*g. Factor c(u).
4*(u - 2)*(u + 1)**2*(5*u + 2)
Let x be 592/111*(-1 - 10/(-4)). Let 3*u**3 - u**3 + 0*u**3 + 0*u**2 - 4*u**2 - 14*u - x = 0. Calculate u.
-1, 4
Let j be -1 + 2 + 3/(6/2). Let s be -2*-1*(-1 + j). What is t in -s*t - 5/2*t**2 + 1/2 = 0?
-1, 1/5
Let -9*w - 114/7 - 3/7*w**2 = 0. What is w?
-19, -2
Let m(v) be the first derivative of -v**7/105 - 7*v**6/72 - 11*v**5/30 - v**4/2 + 4*v**3/3 + 24. Let x(c) be the third derivative of m(c). Solve x(p) = 0 for p.
-2, -3/8
Let w(l) = 67*l + 1275. Let g be w(-19). Factor -49/4*r**g - 9 + 21*r.
-(7*r - 6)**2/4
Let t(a) = -a**3 + 8*a**2 + 10*a - 6. Let v be t(9). Factor -150*o**v - 3*o + 9 + o**2 - 6*o**2 + 149*o**3.
-(o - 1)*(o + 3)**2
Solve 1/4*r**2 - 21/4 + 5*r = 0.
-21, 1
Suppose -4*l + 0*l + x + 7 = 0, 2*l + x = 5. Find j, given that 4/3*j**4 - 4/3*j**l + 2*j**3 - 2*j**5 + 0*j + 0 = 0.
-1, 0, 2/3, 1
Let z(j) be the first derivative of -2*j**3/3 + 6*j**2 + 80*j - 295. Factor z(y).
-2*(y - 10)*(y + 4)
Let p(l) = l**2. Let w = 33 + -32. Let k(h) = h**2 + 24*h - 20. Let m(u) = w*k(u) - 5*p(u). Find q, given that m(q) = 0.
1, 5
Let g = 50/237 + -7/158. Let k(r) be the first derivative of -4/9*r**3 + 0*r - g*r**4 + 0*r**2 + 10. Factor k(f).
-2*f**2*(f + 2)/3
Let g(j) = -2*j**2 + 43*j + 853. Let n be g(34). Determine c, given that 2/5*c**2 - 8/5 - 4/5*c + 1/5*c**n = 0.
-2, 2
Suppose -66*j + 65*j + 41 = 0. Suppose -4*s = -j + 29. Factor 2/3*o - 1/3*o**s + 0 + 1/3*o**2.
-o*(o - 2)*(o + 1)/3
Let n(p) be the second derivative of 3*p**5/80 + 7*p**4/16 + 15*p**3/8 + 27*p**2/8 + 40*p - 3. Factor n(u).
3*(u + 1)*(u + 3)**2/4
Factor 30 - 12 - 52*l + 4*l**2 + 21 + 9.
4*(l - 12)*(l - 1)
Suppose -5*w + 19 = 4*q, -4*w + 1 + 11 = 0. Let y = q + 2. Factor 3*c**2 - 5*c + 5*c + y*c.
3*c*(c + 1)
Factor 1/3*o**4 - 2/3*o**2 + 0 + 1/3*o**3 + 0*o.
o**2*(o - 1)*(o + 2)/3
Let y(j) be the first derivative of -105/4*j**4 + 16*j**5 - 10/3*j**6 + 15 + 0*j - 5*j**2 + 55/3*j**3. Determine f so that y(f) = 0.
0, 1/2, 1, 2
Determine f so that -39*f**3 + 3385*f**2 + 12*f**3 - 3280*f**2 - 69*f - 9 = 0.
-1/9, 1, 3
Let h(m) be the first derivative of -m**3/6 + 13*m**2/4 + 7*m + 3. Find u, given that h(u) = 0.
-1, 14
Suppose -3 = -s - 0. Let t be (s/3)/((-3)/(-6)). What is n in 2*n**2 + 3*n**4 + t*n**2 - 7*n**2 = 0?
-1, 0, 1
Let f(h) = 3*h**2 + 2*h - 5. Let o = -22 + 33. Let p(q) = -q**2 - q + 2. Let a(x) = o*p(x) + 4*f(x). Factor a(z).
(z - 2)*(z - 1)
Let d(q) = q**2 + 2*q - 14. Let p be d(4). Suppose -9*m + 16*m - p*m = 0. Find k, given that 2/9*k**4 - 2/9*k**2 + m + 0*k + 0*k**3 = 0.
-1, 0, 1
Let p be (1 + -1)/(-3 + (1 - -4)). Let k(q) be the second derivative of p*q**3 + 0 + 1/60*q**4 + 5*q + 0*q**2. Suppose k(i) = 0. Calculate i.
0
Let q(c) be the first derivative of -1 + 2*c**3 + 9/8*c**4 + 0*c - 3/10*c**5 + 0*c**2. Factor q(m).
-3*m**2*(m - 4)*(m + 1)/2
Let m(g) = 7*g**4 + 144*g**3 - 347*g**2 + 240*g - 50. Let d(p) = p**3 - p**2 - 1. Let a(f) = 30*d(f) - 5*m(f). Find w, given that a(w) = 0.
-22, 2/7, 1
Let o(z) = -2*z + 26. Let d be o(12). Factor 2 - 4*g**2 - 91*g**3 + 90*g**3 - g**4 + 5*g + 7*g**d.
-(g - 2)*(g + 1)**3
Let t be (-237)/(-33) + -3 - (-10)/(-55). Let b(r) be the first derivative of 1/5*r**5 + 3/4*r**t + 2 + 1/2*r**2 + 0*r + r**3. Find j such that b(j) = 0.
-1, 0
Let v(x) be the second derivative of x**7/21 - x**6/15 - 2*x**5/5 + 2*x**4/3 + 33*x - 2. Factor v(u).
2*u**2*(u - 2)*(u - 1)*(u + 2)
Suppose -355*d**3 + 24*d - 32*d**2 + 60*d**4 + 302*d**2 - 14*d + 15*d = 0. What is d?
-1/12, 0, 1, 5
Let s = 2981 + -2976. Find w such that -2/7*w**s + 0 - 2/7*w**4 + 0*w + 2/7*w**3 + 2/7*w**2 = 0.
-1, 0, 1
Let o(z) = -4*z**3 + z**2 + 2*z + 1. Let q be (-3)/(-7) + (-10)/7. Let s be o(q). Suppose s*k + 3 - 3 - 2*k**3 + 2*k**2 = 0. Calculate k.
-1, 0, 2
Determine z, given that 15/2*z**3 + 3/2*z + 21/2*z**4 - 21/2*z**2 - 9*z**5 + 0 = 0.
-1, 0, 1/6, 1
Suppose -7*z - 15 = -2*z, -4*v - 2*z = 746. Let n = v - -189. Solve 4/5*l - 3/5 - 4/5*l**3 + 1/5*l**n + 2/5*l**2 = 0 for l.
-1, 1, 3
Let s(l) be the first derivative of -3*l**4/2 + 128*l**3/3 - 319*l**2 - 484*l - 108. Factor s(x).
-2*(x - 11)**2*(3*x + 2)
Solve -16/3*z**3 + 88/3*z**2 - 10/3*z**4 + 0 - 32/3*z = 0 for z.
-4, 0, 2/5, 2
Let h(w) = -5*w**2 - 4*w + 9. Let c be ((-3)/(-6))/(5/(-10)). Let m(q) = q - 1. Let r(j) = c*m(j) + h(j). Solve r(d) = 0 for d.
-2, 1
Let i = -32 + 16. Let g be (4 + 0)*(-8)/i. Determine b, given that -4/3*b - 2/3 - 2/3*b**g = 0.
-1
Let w(y) be the second derivative of -1/6*y**3 + 0*y**2 + 0 + 1/24*y**4 - y. Factor w(k).
k*(k - 2)/2
Let q(i) be the first derivative of 5*i**4/4 - 125*i**3 + 9375*i**2/2 - 78125*i + 5. Factor q(s).
5*(s - 25)**3
Let w(v) = -v - 33. Let p be w(-38). Let c(u) be the first derivative of -4/9*u**3 + 4 + 4/15*u**p - 1/6*u**4 + 0*u + 1/3*u**2. Find s, given that c(s) = 0.
-1, 0, 1/2, 1
Let d(n) = n**5 - 4*n**4 + 2*n**3 + n**2 + 3*n. Let y(u) = 2*u**5 - 12*u**4 + 6*u**3 + 4*u**2 + 8*u. Let f(j) = 8*d(j) - 3*y(j). Factor f(a).
2*a**2*(a - 1)*(a + 1)*(a + 2)
Suppose p - 6 - 30 = -g, 2*g - p = 72. Let q be (-15)/(-4) - (-9)/g. Suppose -1/2*h - 3*h**3 + 2*h**2 + 0 + 2*h**q - 1/2*h**5 = 0. What is h?
0, 1
Let l(v) be the first derivative of 2*v**3/9 + 17*v**2/3 - 40*v + 849. Determine f so that l(f) = 0.
-20, 3
Factor -5/2*o**2 + 37/2*o - 27.
-(o - 2)*(5*o - 27)/2
Let i be (-1 - 2 - -8) + -5. Let a(l) be the third derivative of 0*l + 0*l**3 + 0*l**4 + 0 + i*l**6 + 5*l**2 - 1/945*l**7 + 1/270*l**5. Solve a(c) = 0.
-1, 0, 1
Let f(t) be the third derivative of -t**6/40 - 3*t**5/20 + 336*t**2. Find g such that f(g) = 0.
-3, 0
Let d(z) = -3*z**3 - 3*z**2