2*b + 19 = 0. Factor -62*r**2 - r + 45 + 5*r**p - 35*r**3 - 5*r**4 + 22*r**2 + 31*r.
-5*(r - 1)*(r + 1)*(r + 3)**2
Suppose -6*z + 476 = -1636. Let d be 172/z - (-1)/(-8). Determine t, given that -8/11*t**2 + d - 14/11*t = 0.
-2, 1/4
Factor 0*k**2 + 5/2*k**4 + 0*k - 15/2*k**3 + 0.
5*k**3*(k - 3)/2
Let w = -100 - -113. Suppose -w = 4*v - 3*n + 2, -20 = 4*v - 4*n. Solve 4/3*j**5 - 4/3*j**3 + v*j + 0 + 1/3*j**4 - 1/3*j**2 = 0.
-1, -1/4, 0, 1
Let n = 9401 + -46993/5. Factor 867/5*b**2 + n - 204/5*b.
3*(17*b - 2)**2/5
Let t(x) be the first derivative of 27*x**7/70 - 39*x**6/50 + 2*x**5/5 - x**4/15 + 19*x + 16. Let n(b) be the first derivative of t(b). Solve n(p) = 0 for p.
0, 2/9, 1
Factor 29*t**3 + 46*t**3 - 360 - 2655*t + 50*t**2 - 5*t**5 + 2355*t.
-5*(t - 3)**2*(t + 2)**3
Let p(d) = 4*d**3 + 104*d**2 + 204*d + 120. Let j(i) = i**3 + 35*i**2 + 68*i + 40. Let c(l) = -8*j(l) + 3*p(l). Suppose c(b) = 0. What is b?
-5, -2, -1
Let s(t) be the first derivative of t**4/10 + 52*t**3/15 + 71*t**2/5 + 92*t/5 - 10. Factor s(x).
2*(x + 1)*(x + 2)*(x + 23)/5
Let b(c) be the first derivative of -8/21*c**3 + 3/14*c**4 - 1 + 0*c - 1/21*c**6 + 4/35*c**5 - 4/7*c**2. Factor b(r).
-2*r*(r - 2)**2*(r + 1)**2/7
Let r(m) be the third derivative of -m**8/952 - 23*m**7/1785 - 29*m**6/1020 + 11*m**5/510 + 8*m**4/51 + 4*m**3/17 - 28*m**2. Let r(i) = 0. Calculate i.
-6, -1, -2/3, 1
Let t(x) be the second derivative of 21*x**5/20 + 19*x**4/4 - 66*x**3 + 54*x**2 + x + 37. Solve t(l) = 0.
-6, 2/7, 3
Let w(s) = 525*s**2 - 526*s**2 + 1 - s**4 - 2*s + s - s**3. Let p(n) = -n**4 - 3*n**3 - 5*n**2 - n + 4. Let i(u) = -5*p(u) + 10*w(u). Factor i(m).
-5*(m - 2)*(m - 1)*(m + 1)**2
Suppose -68 + 64 = -h + 5*w, 5*h - w - 20 = 0. Factor -8/5*x**3 - 2/5*x**h + 0*x - 8/5*x**2 + 0.
-2*x**2*(x + 2)**2/5
Let r(u) be the first derivative of -u**3/7 - 27*u**2/7 + 120*u/7 - 327. Factor r(w).
-3*(w - 2)*(w + 20)/7
Let y(k) be the third derivative of k**6/900 - 7*k**5/150 + k**4/10 + 8*k**3/9 - 24*k**2 + 6*k. Determine f so that y(f) = 0.
-1, 2, 20
Let j(n) = 3*n**2 + 290*n - 20437. Let a(q) = -q**2 - q - 3. Let i(d) = 4*a(d) + j(d). Factor i(u).
-(u - 143)**2
Let y(u) be the second derivative of -u**4/78 + 22*u**3/39 - 121*u**2/13 - 82*u. Solve y(w) = 0 for w.
11
Let b = 706/7 + -704/7. Factor -2/7*t**2 - 2/7*t + b + 2/7*t**3.
2*(t - 1)**2*(t + 1)/7
Let p be ((-23 - -20) + (-11)/(-5))*-5. Let w(z) be the second derivative of -27/2*z**2 - 1/4*z**4 + 0 + p*z + 3*z**3. Find c such that w(c) = 0.
3
Suppose 169*j - 5*z + 22 = 170*j, 0 = -4*j - z + 12. Factor 0 + 0*v**3 + 0*v - 2/15*v**j + 2/15*v**4.
2*v**2*(v - 1)*(v + 1)/15
Let y = -2/407 + 844/6105. Suppose 0 - 14/15*d**4 + 2/5*d**5 - 4/15*d + 14/15*d**2 - y*d**3 = 0. What is d?
-1, 0, 1/3, 1, 2
Let f(s) = -4*s + 31. Let v be f(9). Let d be -1 - (0 - 2) - v/(-7). Solve 2/7*q**2 - d*q - 4/7 = 0.
-1, 2
Let f(k) be the first derivative of k**6/320 - k**5/40 + 9*k**2 + 10. Let d(a) be the second derivative of f(a). Find o, given that d(o) = 0.
0, 4
Let y = -180 + 182. Suppose -5*s = -y*m - 4*s + 5, -4*m - 25 = 5*s. Factor m + 1/8*q + 1/8*q**2.
q*(q + 1)/8
Let z(t) = -t**2 - 10*t + 14. Let k be z(-11). Let p be 1/1 - (2 + -4). Find q such that 0*q**3 + 2*q**2 + 1 + 2*q**3 - p*q + q**5 + 0*q**3 - k*q**4 + 0 = 0.
-1, 1
Solve -40*c**4 - 810*c**2 + 120*c**3 - 565*c + 1445*c + 1815 + 35*c**4 = 0.
-1, 3, 11
Let q(b) = -4*b**2 - 57*b - 119. Let w(t) = -2*t**2 - 28*t - 60. Let h(y) = 4*q(y) - 7*w(y). Let h(c) = 0. What is c?
-14, -2
Suppose 18 - 58 = -10*g. Let t(d) be the second derivative of -1/15*d**6 + d + 5/42*d**7 + 0 + 1/6*d**g + 0*d**3 + 0*d**2 - 1/4*d**5. What is x in t(x) = 0?
-1, 0, 2/5, 1
Let k(y) = -y + 8. Let f be k(8). Let d(z) be the third derivative of 1/24*z**4 - 1/60*z**5 + 0*z + 2*z**2 + f + 0*z**3. Find o, given that d(o) = 0.
0, 1
Let g be (2/4)/(3 - 796/264). Let b = 36 + g. Factor 1/3*c**2 + 0*c + 0 - 1/3*c**b.
-c**2*(c - 1)/3
Let f = -266 - -1871/7. Let n be 3*(-4)/70*-5. Determine c, given that 0 + f*c**2 - n*c - 3/7*c**3 = 0.
0, 1, 2
Let z = -1469 + 1471. Let k(i) be the first derivative of -1/10*i**z - 1/15*i**3 + 0*i + 1/25*i**5 + 1/20*i**4 - 7. Factor k(a).
a*(a - 1)*(a + 1)**2/5
Let i(y) be the second derivative of -y**4/36 + 4*y**3/3 + 284*y. Factor i(o).
-o*(o - 24)/3
Suppose -66*y + 169 = 54*y - 71. Factor 1 - 1/6*s**y - 5/6*s.
-(s - 1)*(s + 6)/6
Let 0*w + w**2 + 0*w**4 - 3/2*w**3 + 0 + 1/2*w**5 = 0. What is w?
-2, 0, 1
Suppose -5*g + 13 = -2, 2*g = 2*x + 2. Let n(l) be the third derivative of 4*l**x + 0*l + 1/16*l**4 + 0 + 0*l**3 + 1/40*l**5. Suppose n(u) = 0. Calculate u.
-1, 0
Let p(m) be the second derivative of -2/21*m**3 + 0*m**2 + 0 + 0*m**5 - 13*m + 1/105*m**6 - 1/14*m**4. Solve p(z) = 0 for z.
-1, 0, 2
Factor 1/2 - 1/8*s**4 + 1/2*s**3 - 1/2*s - 3/8*s**2.
-(s - 2)**2*(s - 1)*(s + 1)/8
Solve 136 - 70*v + 20*v**2 - 170*v - 60*v - 48*v = 0 for v.
2/5, 17
Suppose 9/4*n**2 - 579/4*n - 195/2 = 0. Calculate n.
-2/3, 65
Let o be (-7)/63 + 333/81. Let y(k) be the first derivative of 2/9*k**2 - o - 2/3*k + 2/27*k**3. Factor y(p).
2*(p - 1)*(p + 3)/9
Let y(j) be the second derivative of j**6/75 + j**5/50 - j**4/30 - j**3/15 - 178*j. Factor y(r).
2*r*(r - 1)*(r + 1)**2/5
Let q(g) be the third derivative of 0*g**5 - 8*g**2 + 0 + 0*g**3 + 0*g - 1/252*g**8 + 0*g**4 + 0*g**7 + 1/90*g**6. Factor q(a).
-4*a**3*(a - 1)*(a + 1)/3
Let g = -47 - -50. Let v(q) be the third derivative of 0 + 0*q + 1/735*q**7 + 1/14*q**5 - 3*q**2 + 3/28*q**4 + 1/60*q**6 + 0*q**g. Factor v(t).
2*t*(t + 1)*(t + 3)**2/7
Solve -8/7*y - 9/7 + 1/7*y**2 = 0.
-1, 9
Let l(u) = -17*u**2 + 10*u - 38. Let i(p) = 8*p**2 - 4*p + 18. Let x(v) = 13*i(v) + 6*l(v). Factor x(y).
2*(y + 1)*(y + 3)
Let a(t) be the second derivative of -t**7/231 + 12*t**6/55 - 323*t**5/110 - 6*t**4/11 + 108*t**3/11 - 3*t - 28. Let a(x) = 0. Calculate x.
-1, 0, 1, 18
Let v(j) be the first derivative of j**6/2 + 12*j**5/5 + 9*j**4/4 - 84. Factor v(p).
3*p**3*(p + 1)*(p + 3)
Let y(s) = 5*s + 5. Let b(u) = -u - 1. Let x(w) = 2*b(w) + y(w). Let v(l) = l**2 - l - 1. Let j(n) = 3*v(n) + x(n). Factor j(p).
3*p**2
Let u(x) be the second derivative of -x**7/1260 + x**6/72 - x**5/15 - x**4/6 - 3*x. Let t(m) be the third derivative of u(m). Factor t(d).
-2*(d - 4)*(d - 1)
Factor 0 - 2/9*h**3 - 32/9*h + 34/9*h**2.
-2*h*(h - 16)*(h - 1)/9
Let p(k) be the first derivative of -4*k**3/9 + 7*k**2 + 22*k/3 - 44. Let p(y) = 0. What is y?
-1/2, 11
Let m(y) = y**2 + y - 4. Let z be m(2). Find g such that 3*g**5 + g**4 + g**4 - z*g**5 - 3*g**5 = 0.
0, 1
Factor 6*z**4 + 1054*z**3 - 40*z**2 + z + 23*z - 1052*z**3.
2*z*(z - 2)*(z + 3)*(3*z - 2)
Let x = 23 - 17. Find n such that 45*n**3 + 2*n - x*n - 49*n**3 + 8*n**2 = 0.
0, 1
Let c(x) be the third derivative of x**7/315 - 7*x**6/180 - x**5/18 + 25*x**4/12 + 151*x**2. Factor c(n).
2*n*(n - 5)**2*(n + 3)/3
Suppose 0 = 61*c - 211 + 36 - 69. Let 4/9*o**3 + 2 - 2/3*o + 2/9*o**5 + 10/9*o**c - 28/9*o**2 = 0. What is o?
-3, -1, 1
What is m in -66 - 131/2*m + 1/2*m**2 = 0?
-1, 132
Let g = 3494 - 3486. Factor 4/3*j**2 - 2*j**3 - 16/3 + g*j.
-2*(j - 2)*(j + 2)*(3*j - 2)/3
Let c(o) = o**2 - 5. Let k(s) = -s**2 + s + 6. Let y(n) = -4*c(n) - 3*k(n). Let g be y(-3). Factor -6*t**3 + 2*t**3 - g*t**5 - 6*t + 8*t + 4*t**5.
2*t*(t - 1)**2*(t + 1)**2
Let w(o) be the first derivative of 7/6*o**4 - 2*o**3 + 2/3*o**2 + 0*o - 4. Find p such that w(p) = 0.
0, 2/7, 1
Let r be ((20/(-180))/((-1)/6))/4. Let m(n) be the second derivative of 0*n**3 - n**2 - 2*n + 0 + r*n**4. Solve m(l) = 0.
-1, 1
Let t(h) be the first derivative of 1/10*h**6 - 6/5*h + 2/5*h**3 + 0*h**5 + 10 - 3/5*h**4 + 9/10*h**2. Solve t(f) = 0 for f.
-2, -1, 1
Let t = -61 + 61. Find v, given that t*v**2 + 0*v**2 - 15*v + 10 + 3*v**2 + 2 = 0.
1, 4
Let g = 0 - -3. Let i = 27 - 18. Determine c so that -9*c**3 + 0*c**4 + 6 - 3*c**4 + 0 - 6*c**2 + i*c + g*c**2 = 0.
-2, -1, 1
Let x(v) = v**4 + 5*v**3 - 3*v**2 + 2*v - 5. Let b(m) be the third derivative of m**6/120 - m**3/6 + m**2. Let o(w) = -15*b(w) + 3*x(w). Solve o(c) = 0 for c.
-2, 0, 1
Let x = -5777 + 5780. Factor 0 + 2/5*l**2 - 2/5*l + 2/5*l**x - 2/5*l**4.
-2*l*(l - 1)**2*(l + 1)/5
Let y(r) be the third derivative of -r**8/3360 + r**6/720 - 7*r**3/3 - 6*r**2. Let v(k) be the first d