- 15/2*r**2 + 13. Let i(z) = 0. Calculate z.
-1/4, 1, 2
Let p(z) = -z**3 + 1. Let f(s) = 23*s**3 - 42*s**2 + 32*s - 13. Suppose -15*r + 4 = -17*r. Let c(m) = r*f(m) - 10*p(m). What is o in c(o) = 0?
2/3, 1
Suppose 0 = -0*i - 5*i. Suppose x + s - 27 = -2*s, s - 4 = i. Suppose 20*v**5 - 71*v**2 - 34*v**2 - x*v - 38*v - 135*v**4 + 265*v**3 + 8*v = 0. What is v?
-1/4, 0, 1, 3
Let s(z) = -z**3 + 7*z**2 + 7*z + 10. Let a be s(8). Factor -26*w**5 - 12*w**4 + 7*w**5 - 24 + 30*w**a + 13*w + 16*w**5 - 3*w**3 - w.
-3*(w - 1)**2*(w + 2)**3
Let m(v) be the second derivative of -5*v**4/12 - 10*v**3 - 175*v**2/2 - 124*v + 1. Factor m(k).
-5*(k + 5)*(k + 7)
Let -6/5*x**3 + 3/5*x**4 + 0*x - 24/5*x**2 + 0 = 0. What is x?
-2, 0, 4
Let t = -3865 + 7739/2. Factor 3/2*k**4 - 15/2*k**2 - 3/2*k**3 - t*k + 0.
3*k*(k - 3)*(k + 1)**2/2
Determine g, given that 15/7*g**3 - 30/7*g + 0 + 69/7*g**2 = 0.
-5, 0, 2/5
Let k(p) be the third derivative of -p**6/40 - 61*p**5/20 + 31*p**4/4 + 3*p**2 + 12*p. Find y such that k(y) = 0.
-62, 0, 1
Suppose -4*u - 7 - 7 = -2*g, -4*g + 28 = 5*u. Let h(w) = 4*w**2 + w + 1. Let i be h(-1). Determine o so that 5 + 2*o**2 - g*o**4 + 5*o**i - 5 = 0.
-1, 0, 1
Let z(a) be the first derivative of -16/9*a + 4*a**2 - 20/9*a**3 + 1 + 7/18*a**4. Find t, given that z(t) = 0.
2/7, 2
Let f(u) be the first derivative of 3*u**4/8 + 9*u**3/2 - 3*u**2/4 - 27*u/2 + 437. Determine k so that f(k) = 0.
-9, -1, 1
Let k(z) be the third derivative of 1/16*z**5 - 56*z**2 - 1/160*z**6 + 1/4*z**4 + 0 - 6*z**3 + 0*z. Factor k(q).
-3*(q - 4)**2*(q + 3)/4
Suppose 2*b + 3*c + 9 = 0, -31*b + 14 = -33*b - 4*c. Suppose -p - 5 = -7. Factor 8/3*y**b - 2/3 + 8/3*y - 4*y**p - 2/3*y**4.
-2*(y - 1)**4/3
Suppose 100 = -g + 6*g. Suppose 2*m = -3*m + 5*y + g, -14 = -3*m + 5*y. Factor -u**3 + 1 + 4*u**m - 3*u - 4 - 3*u**2 + 6.
3*(u - 1)**2*(u + 1)
Let w(h) = -1. Let t(y) be the second derivative of 0 + 1/6*y**4 + 0*y**3 - 8*y + 3*y**2. Let q(u) = t(u) + 6*w(u). Factor q(l).
2*l**2
Let 160/9*p**2 + 0 - 62/9*p**4 - 128/9*p + 4/9*p**5 + 74/3*p**3 = 0. Calculate p.
-1, 0, 1/2, 8
Suppose -14 = 2*k - k - 4*n, 2*k + 3*n = 16. Determine p, given that 4*p**3 + 8*p**4 + 7*p**5 - k*p**5 - p**5 = 0.
-1, 0
Let i(g) be the first derivative of g**6/6 - 3*g**5/5 - g**4/2 + 2*g**3 + g**2/2 - 3*g - 29. Factor i(r).
(r - 3)*(r - 1)**2*(r + 1)**2
Let i(t) = -t**3 - 7*t**2 + 17*t - 7. Let s(m) = -6*m + 3. Let l be s(2). Let a be i(l). Factor 2/11 + 10/11*q**a + 12/11*q.
2*(q + 1)*(5*q + 1)/11
Let k(b) = 3*b**4 + b**3 - b**2 + b + 1. Let t(d) = -3*d**4 - 26*d**3 - 7*d**2 + 76*d - 50. Let a(i) = 2*k(i) + t(i). Solve a(w) = 0 for w.
-2, 1, 8
Let q(k) be the second derivative of k**6/45 + k**5/10 + k**4/18 - k**3/3 - 2*k**2/3 + k + 27. Solve q(r) = 0.
-2, -1, 1
Let b(k) = 5*k**3 - 5*k**2 + 3*k. Let v(p) = -p. Let u(o) = -o**2 + 13*o + 29. Let g be u(15). Let m(a) = g*b(a) - 3*v(a). Factor m(z).
-5*z**2*(z - 1)
Let x be (2 - 80/50) + 0. Factor 0 - 2/5*h + 3/5*h**2 + x*h**3.
h*(h + 2)*(2*h - 1)/5
Let m(w) be the first derivative of w**6/180 + w**5/40 + w**4/72 - w**3/12 - w**2/6 + 5*w + 22. Let a(o) be the first derivative of m(o). Factor a(y).
(y - 1)*(y + 1)**2*(y + 2)/6
Let f = -100 - -103. Let k(g) be the second derivative of 1/6*g**4 + 0 - g + 0*g**f - g**2. What is x in k(x) = 0?
-1, 1
Let p = 257/1143 + -1/381. Determine t, given that p*t**2 + 4/9*t + 0 = 0.
-2, 0
Let b(m) = -m**2 - 19*m + 36. Let q(o) = -2*o**2 - 38*o + 73. Let g(l) = 11*b(l) - 6*q(l). Factor g(r).
(r - 2)*(r + 21)
Let y be (-138)/(-24) + -5 + (-482)/(-40). Let z(g) be the first derivative of -4/15*g**3 - y*g - 6 + 16/5*g**2. Solve z(c) = 0 for c.
4
Let y be (-183)/(-36) - (-29)/(-348). Let -1/3*m**3 - 125/3 - y*m**2 - 25*m = 0. What is m?
-5
Let v(q) be the second derivative of q**7/42 + q**6/3 + 3*q**5/5 - 10*q**4/3 - 32*q**3/3 + 19*q + 2. Let v(x) = 0. Calculate x.
-8, -2, 0, 2
Let r(s) be the second derivative of s**4/48 + 31*s**3/24 + 15*s**2/4 - 3*s + 3. Factor r(g).
(g + 1)*(g + 30)/4
Let q(o) = -6*o**2 - o - 7. Let p(a) be the second derivative of -a + 0 - 5/2*a**2 - 1/6*a**3 - 1/3*a**4. Let x(h) = 7*p(h) - 5*q(h). Factor x(m).
2*m*(m - 1)
Let t(s) = 4*s**3 - 145*s**2 + 302*s - 146. Let l(i) = -i**3 - 2*i**2 - i - 1. Let j(c) = 3*l(c) + t(c). Find p, given that j(p) = 0.
1, 149
Let i(l) be the first derivative of -l**4/132 - 5*l**3/66 - 14*l - 15. Let v(x) be the first derivative of i(x). Factor v(c).
-c*(c + 5)/11
Let a(d) be the third derivative of -d**6/30 - d**5/15 + 2*d**4/3 + 8*d**3/3 - d**2 + 6. Determine k so that a(k) = 0.
-2, -1, 2
Factor 8*q**4 - q**5 + 28*q**2 - 17*q - 187*q**3 + 100*q**3 + 65*q**3 + 4.
-(q - 4)*(q - 1)**4
Let f(b) = b**3 + 15*b**2 - 75*b + 21. Let p be f(-19). Let y(g) be the first derivative of 2/21*g**3 - 6 + 8/7*g**p + 32/7*g. Determine j so that y(j) = 0.
-4
Suppose 4*u + 0*x = -4*x - 12, -4*u - x - 3 = 0. Let f be u/(-3) - (-5)/20. Find o, given that -1/4*o**3 + f + 1/4*o - 1/4*o**2 = 0.
-1, 1
Let a(z) be the first derivative of 0*z + 10/3*z**3 + 2*z**2 + 14 - z**4 - 2*z**5. Factor a(o).
-2*o*(o - 1)*(o + 1)*(5*o + 2)
Suppose 4*n - 3*m - 222 = 8*n, 5*n = 4*m - 293. Let r = n - -57. Factor r - 2/7*x**2 - 2/7*x.
-2*x*(x + 1)/7
Let f = -10635 + 116991/11. Factor 10/11*w**2 - f*w - 4/11.
2*(w - 1)*(5*w + 2)/11
Let q(x) be the third derivative of 1/357*x**7 + 0*x**3 + 2/255*x**5 + 38*x**2 + 0*x**4 + 2/255*x**6 + 0 + 0*x + 1/2856*x**8. Let q(r) = 0. Calculate r.
-2, -1, 0
Determine n, given that -1/4*n**2 + 71/4*n + 0 = 0.
0, 71
Suppose 3 - 3 = 14*z. Let a be z - ((-25)/(-9) + 19 + -22). Let 0 + 0*d**4 - a*d**5 + 0*d + 2/9*d**3 + 0*d**2 = 0. What is d?
-1, 0, 1
Let t(p) be the first derivative of p**4/4 - 4*p**3 - p**2/2 + 16*p + 3. Let c be t(12). Find j such that -c*j**3 + 2*j - j**5 - 5*j + 5*j + 3*j**5 = 0.
-1, 0, 1
Let a(d) be the third derivative of -d**5/33 - d**4/44 + 90*d**2. Solve a(o) = 0.
-3/10, 0
Solve 104/15*f**2 + 64/5*f + 128/15 + 2/15*f**4 + 8/5*f**3 = 0.
-4, -2
Let w(i) be the third derivative of i**5/270 - 5*i**4/54 + 16*i**3/27 + 17*i**2 - 7*i. Factor w(z).
2*(z - 8)*(z - 2)/9
Let -1/3*n**2 - 10/3*n - 16/3 = 0. Calculate n.
-8, -2
Suppose -4*i = -3*p + 14, -7*p + 3*p = 5*i - 29. Suppose -p*w = -9*w. Factor 2*s**5 - 2*s - 4*s**2 + 4*s**4 + 4 - 4 + w*s**2.
2*s*(s - 1)*(s + 1)**3
Let w(l) = -l**5 + l**2 - 1. Let s(q) = 3644*q**5 - 540*q**4 - 10915*q**3 + 8911*q**2 - 1140*q + 39. Let v(p) = -s(p) + w(p). Suppose v(y) = 0. What is y?
-2, 2/27, 1
Let f(t) be the third derivative of 0*t**3 + 1/1995*t**7 - 1/57*t**4 + 0 - 1/228*t**6 + 0*t - 3*t**2 + 4/285*t**5. Factor f(a).
2*a*(a - 2)**2*(a - 1)/19
Let q(l) be the first derivative of -1/3*l**3 + 0*l + 1/4*l**4 - 1/15*l**5 - 16 + 1/6*l**2. Factor q(b).
-b*(b - 1)**3/3
Let y(r) be the third derivative of r**8/2016 - r**7/1260 - r**6/360 + r**5/180 + r**4/144 - r**3/36 + 81*r**2. Factor y(o).
(o - 1)**3*(o + 1)**2/6
Let i = 3131/9411 - -2/3137. Determine f so that -2*f**3 - i*f - 3/2*f**2 - 5/6*f**4 + 0 = 0.
-1, -2/5, 0
Let s(q) = -q + 24. Let c be s(8). Let y be 38/(-11) - c/(-4). Suppose -8/11*p**4 + 6/11*p - 2/11 + 10/11*p**2 - y*p**3 = 0. What is p?
-1, 1/4, 1
Let k(l) be the third derivative of -1/2*l**4 + 0*l + 0*l**3 - 13*l**2 + 0*l**5 + 1/40*l**6 + 0. Factor k(b).
3*b*(b - 2)*(b + 2)
Let -80/3 - 5/3*q**2 - 40/3*q = 0. Calculate q.
-4
Let z(p) be the third derivative of p**7/630 - 7*p**6/135 + 49*p**5/90 + 19*p**3/3 - 25*p**2. Let r(j) be the first derivative of z(j). Factor r(n).
4*n*(n - 7)**2/3
Suppose 52*b - 209 - 103 = 0. Let m(l) be the second derivative of 9*l + 0 - 108*l**2 - 51*l**4 - 2/3*l**b - 126*l**3 - 47/5*l**5. Solve m(n) = 0.
-3, -2/5
Determine u so that 1/2*u**3 - 3 - 7/4*u**2 + 1/4*u**4 - 5*u = 0.
-2, -1, 3
Let h(i) = 12 + 184*i + 0 + 4*i**3 + 20*i**2 - 164*i. Let q(o) = -4*o**3 - 21*o**2 - 20*o - 13. Let c(x) = 5*h(x) + 4*q(x). Factor c(a).
4*(a + 1)**2*(a + 2)
Let f = -77657/1370 - -217/137. Let k = 111/2 + f. What is r in 4/5 + 0*r**2 + k*r**3 - 6/5*r = 0?
-2, 1
Let k = 2953 - 2951. Factor 0*i + 0*i**k + 2/13*i**4 + 0 - 2/13*i**3.
2*i**3*(i - 1)/13
Factor -465*y + 63*y**2 - 306 + 66*y**2 - 138*y**2.
-3*(y + 51)*(3*y + 2)
Let x = -57 + 115. Suppose -5*y + 52 = -x. Factor -64/7*v**2 + y*v**3 - 14*v**4 + 8/7*v 