 4. Let p(a) = a**2. Let d(f) = -i(f) + 2*p(f). Let d(r) = 0. Calculate r.
2/11, 1/3, 1
Let c(f) = 2*f**2 + 2*f + 10. Let k(u) be the third derivative of u**3/6 - 11*u**2. Let v(m) = c(m) - 10*k(m). Solve v(y) = 0.
-1, 0
Suppose 2*l = 5*y + 6 + 19, -40 = -5*l + 5*y. Let o(z) be the first derivative of 3/10*z**2 - 3/4*z**4 + 9/25*z**l - 5 + 1/5*z**3 + 0*z. Factor o(h).
3*h*(h - 1)**2*(3*h + 1)/5
Let t = -51 - -55. Let i be (t/2)/(4 + 2). Factor 1/3*o**2 + i*o + 0.
o*(o + 1)/3
Let i(k) be the second derivative of k**4/18 - 2*k**3 + 27*k**2 + 7*k. Factor i(m).
2*(m - 9)**2/3
Let d(i) = 12*i**4 + 59*i**3 + 84*i**2 + 16*i. Let b(t) = t**4 + t**3. Let h(z) = 3*b(z) - d(z). Factor h(a).
-a*(a + 2)*(a + 4)*(9*a + 2)
Let r(v) be the second derivative of 1/6*v**6 + 5/4*v**4 - 10/3*v**3 + 0 - 10*v**2 + v**5 + 12*v. Factor r(j).
5*(j - 1)*(j + 1)*(j + 2)**2
Let r(a) be the first derivative of -a**5/35 - 5*a**4/28 - 2*a**3/7 + 2*a**2/7 - a - 11. Let g(x) be the first derivative of r(x). Factor g(f).
-(f + 2)**2*(4*f - 1)/7
Let v = 901/819 - -1/91. Suppose v*h + 4/9*h**2 + 4/9 = 0. Calculate h.
-2, -1/2
Let d = 32 + -30. Factor -2*f**2 + 5*f**2 - 1 + 0*f**2 - f**4 - f**d.
-(f - 1)**2*(f + 1)**2
Let n(r) be the first derivative of 2*r**6/3 - 24*r**5/5 - 8*r**4 + 8*r**3 + 14*r**2 - 82. Let n(g) = 0. What is g?
-1, 0, 1, 7
Let 298 + 4600*g + 1702 + 4*g**5 + 3260*g**2 - g**5 + 102*g**3 + 620*g**3 + 64*g**4 - g**5 = 0. Calculate g.
-10, -1
Factor 13/9 - 40/9*u + 1/3*u**2.
(u - 13)*(3*u - 1)/9
Let r(k) = k**3 - 46*k**2 + 92*k - 47. Let m(p) = 4*p**3 - 230*p**2 + 462*p - 236. Let s(v) = 6*m(v) - 28*r(v). Find c such that s(c) = 0.
-25, 1
Let v(m) be the first derivative of m**6/21 + 2*m**5/35 - 2*m**4/7 - 8*m**3/21 - 80. What is x in v(x) = 0?
-2, -1, 0, 2
What is m in -2/19*m**2 + 36/19*m - 162/19 = 0?
9
Factor 30*q - 8*q**2 + 2 + 5 + 73 + 6*q**2 - 3*q**2.
-5*(q - 8)*(q + 2)
Let k(d) = -14*d**2 - 5*d - 4. Let u be k(-2). Let l = u + 50. Factor 2/5*x**2 + 2/5*x + l.
2*x*(x + 1)/5
Factor -1/4*k**4 + 45/2*k**2 + 0*k + 43/4*k**3 + 0.
-k**2*(k - 45)*(k + 2)/4
Let r be (-330)/(-14) + (-12)/(-28). Factor 76*l**2 - r + 4*l + 18*l**3 - 8*l**3 + 14*l**3.
4*(l + 3)*(2*l - 1)*(3*l + 2)
Let g be (1 + -1)*11/(-88)*4. Let d(q) = -q**3 + 5*q**2 + 3. Let k be d(5). Suppose g*u**2 + 1/4*u + 0 - 1/4*u**k = 0. Calculate u.
-1, 0, 1
Let t(h) = -2*h**3 + 5*h - 4*h**2 + 4*h**4 - 6*h - 4*h**3 + 4*h**5 + 6*h. Let d(u) = -u**5 - u**4 + u**3 + u**2 - u. Let b(v) = 3*d(v) + t(v). Factor b(f).
f*(f - 1)**2*(f + 1)*(f + 2)
Factor -17*m**2 + 11*m**2 - 5*m**4 + 4*m**2 + 4*m**2 + 3*m**2.
-5*m**2*(m - 1)*(m + 1)
Let g(h) be the third derivative of h**6/60 - h**5/10 - h**4/12 + h**3 + 46*h**2. Factor g(c).
2*(c - 3)*(c - 1)*(c + 1)
Let u(j) = -j**2 + 11*j - 2. Let p be u(11). Let l(n) = n**2. Let v(w) = w**2 - 6*w - 9. Let x(s) = p*l(s) + v(s). Factor x(a).
-(a + 3)**2
Let p(x) be the third derivative of x**6/60 + x**5/5 + 3*x**4/4 + 4*x**3/3 + 2*x**2 + 26. Determine h, given that p(h) = 0.
-4, -1
Let y(u) be the third derivative of u**5/30 - 7*u**4/12 - 8*u**3/3 + 5*u**2 - 5. Solve y(o) = 0 for o.
-1, 8
Suppose -2*o = 3*k - 63, -2*o = -4*k + o + 84. Let c be 4/6 - (k/9 + -2). Solve -1/3*u - c + 2/3*u**2 = 0.
-1/2, 1
Let f be (-2)/((-2 + -1)/3). Factor 8*x**2 + 18 - 3*x**2 + 12*x - 3*x**f.
2*(x + 3)**2
Let h = 66 + -66. Suppose h = 4*m + 20, 3*m + m = 4*d - 28. Suppose 4/7*c + 0 + 2/7*c**d = 0. What is c?
-2, 0
Suppose 0 = -5*v + 9 + 81. Suppose t - v = -4*g, 4*g + 0*g = 2*t. Factor x - 7 - 4*x**2 + t*x + 5 - 2*x + x**3.
(x - 2)*(x - 1)**2
Let l be (-90)/150 + 99/15. Let f(n) be the first derivative of 21/2*n**2 + 3 - 2*n**3 + l*n - 21/4*n**4. Factor f(q).
-3*(q - 1)*(q + 1)*(7*q + 2)
Factor -x + 0 - 1/3*x**3 + 4/3*x**2.
-x*(x - 3)*(x - 1)/3
Suppose 22 = -343*k + 354*k. Factor 2*f**k - 20/3*f**3 + 0*f + 0 + 2*f**4.
2*f**2*(f - 3)*(3*f - 1)/3
Let x be ((27/(-2))/(-9))/3. Determine k, given that 3/2 - x*k**2 + k = 0.
-1, 3
Let i(j) = -j**3 - 2*j**2 - j - 3. Let x be i(-3). Suppose -r + x = 6. Factor -2*c**3 - 3*c**3 + 3*c**4 - 5*c**3 + 7*c**r.
3*c**3*(c - 1)
Let r(n) = -n**4 - 23*n**3 + 121*n**2 - 303*n + 194. Let c(l) = 3*l**4 + 48*l**3 - 241*l**2 + 607*l - 387. Let p(b) = 6*c(b) + 15*r(b). Factor p(u).
3*(u - 7)**2*(u - 4)*(u - 1)
Suppose -9/2*m**2 - 3/2*m + 3/2*m**3 + 9/2 = 0. Calculate m.
-1, 1, 3
Let n(y) = 20*y - 3. Let t be n(2). Let -2*a - 2*a**4 + t*a**2 - a**2 - 22*a - 18*a**3 + 5*a**4 = 0. Calculate a.
0, 2
Let t(w) be the third derivative of 1/480*w**5 + 0*w**3 + 0 - 1/64*w**4 - 14*w**2 + 0*w. Factor t(a).
a*(a - 3)/8
Let x be 3/(-2)*(-8)/6. Suppose 0 = -4*s - x + 34. Suppose -4*d**4 + s*d**2 - 4 - 118*d**3 + 118*d**3 = 0. Calculate d.
-1, 1
Let m = -1/476 - -967/7140. Let f(c) be the second derivative of 0 + 4*c - m*c**5 + 1/3*c**2 + 1/45*c**6 - 4/9*c**3 + 1/3*c**4. Suppose f(a) = 0. Calculate a.
1
Let v be ((-18)/5)/(64/20 - 3). Let z be (-2)/(-6) + -4 + (-66)/v. Suppose -2*a**5 + z - 10/3*a**3 - 2/3*a**2 + 0*a - 14/3*a**4 = 0. Calculate a.
-1, -1/3, 0
Let n(v) = v - 3. Let j(b) = b - 4. Let x(s) = -2*j(s) + 3*n(s). Let t be x(4). Let 4*g**5 - g**4 - 3*g**5 + g**2 + g**2 - g**t - g**4 = 0. What is g?
-1, 0, 1, 2
Suppose 7 = -4*n + 55. Let -7 + 12*i + 6*i**2 + 2 + 3*i**4 + 3*i**2 - 7 - n*i**3 = 0. Calculate i.
-1, 1, 2
Solve -6/5*i**2 + 1/5*i**3 + 11/5*i - 6/5 = 0 for i.
1, 2, 3
Let q be (-9)/6 - 2589/270. Let h = q - -116/9. Solve -4/5*g**5 + h*g**4 - 2/5*g**3 - 1/5 + 6/5*g - 8/5*g**2 = 0.
-1, 1/4, 1
Let h(b) be the third derivative of b**7/315 - b**6/180 - 7*b**5/30 + 5*b**4/4 + 315*b**2. Factor h(y).
2*y*(y - 3)**2*(y + 5)/3
Let w = -9666 - -9670. Factor 0 - 6/5*c**3 - 12/5*c - 21/5*c**2 + 3/5*c**w.
3*c*(c - 4)*(c + 1)**2/5
Factor r**2 + 291*r - 40*r - 117*r + 4489.
(r + 67)**2
Let s = -30 - -33. Suppose 12 = 5*p - s. Factor -3*x + 3*x**2 + 11*x**3 - 5*x + x**2 - 7*x**p.
4*x*(x - 1)*(x + 2)
Let k = -3134 - -3136. Factor -4/3*l + 16/3 - 2/3*l**k.
-2*(l - 2)*(l + 4)/3
Let n(g) = g**2 + 6*g + 1. Let q(b) = -2*b**2 - 13*b - 1. Let y(v) = -5*n(v) - 2*q(v). Factor y(c).
-(c + 1)*(c + 3)
Determine s so that 0 + 814/23*s**3 - 242/23*s**4 + 24/23*s - 272/23*s**2 = 0.
0, 2/11, 3
Factor -294 + 165/8*o**2 - 3/8*o**3 - 273*o.
-3*(o - 28)**2*(o + 1)/8
Let t(d) be the third derivative of -d**5/210 - 5*d**4/84 + 12*d**3/7 + d**2 - 20. Factor t(y).
-2*(y - 4)*(y + 9)/7
Factor 12/5*a**2 - 16/5 - 4*a + 4/5*a**4 + 4*a**3.
4*(a - 1)*(a + 1)**2*(a + 4)/5
Let b = -20143/15 - -1343. Suppose 0 + 0*f**2 + 0*f - b*f**4 - 4/15*f**3 = 0. What is f?
-2, 0
Factor -3195*n**3 - 10*n**4 + 13878 + 190*n**4 - 3*n**5 + 3618 - 27540*n + 15090*n**2.
-3*(n - 27)**2*(n - 2)**3
Let j(n) be the first derivative of n**4/4 - 239. Determine v, given that j(v) = 0.
0
Let i(h) be the first derivative of h**7/1050 + h**6/90 - 2*h**3 - 5. Let b(d) be the third derivative of i(d). Solve b(c) = 0.
-5, 0
Let j(n) = -n**4 - 43*n**3 - 91*n**2 - 49*n + 8. Let c(x) = 42*x**3 + 90*x**2 + 48*x - 6. Let m(y) = 4*c(y) + 3*j(y). Suppose m(a) = 0. What is a?
-1, 0, 15
Suppose -10*m + 2*m + 224 = 104*m. Find i, given that 4/3*i**5 + 0 + 0*i - 4/3*i**4 + 4/3*i**m - 4/3*i**3 = 0.
-1, 0, 1
Let 2*w**3 + 28*w**2 + 32*w**3 - 30*w**3 = 0. What is w?
-7, 0
Let j = -231 - -697/3. Let z = 11 + -8. Factor -j*l**z + 2/3 - 11/3*l + 13/3*l**2.
-(l - 2)*(l - 1)*(4*l - 1)/3
Suppose 0 = 3*t - 3*i - 9, 0 = -3*t + 6*i - i + 7. What is p in -2*p**2 - 14*p**4 - 5 + 12*p**2 + 7*p**4 + 2*p**t = 0?
-1, 1
Let s = -19 - -20. Let z be (13/(-4) - -3) + s. Factor -3/2 + z*l**4 - 9/4*l**2 + 3/4*l**3 - 15/4*l.
3*(l - 2)*(l + 1)**3/4
Let m(f) be the third derivative of f**8/40320 - f**7/5040 + f**6/1440 - f**5/30 - 2*f**2. Let n(o) be the third derivative of m(o). Factor n(r).
(r - 1)**2/2
Let k(p) = p**4 + p**2 - 3*p + 1. Let n(v) = 19*v**5 - 49*v**4 + 54*v**3 - 9*v**2 - 22*v + 7. Let l(w) = 21*k(w) - 3*n(w). Let l(f) = 0. Calculate f.
-1/19, 0, 1
Suppose -3/8*a + 0*a**4 + 0*a**2 + 3/4*a**3 + 0 - 3/8*a**5 = 0. What is a?
-1, 0, 1
Let o(l) be the second derivative of l**6/10 + 9*l**5/10 - 35*l**4/4 + 24*l**3 - 30*l**2 - 26*l - 8. Find i such that o(i) = 0.
-10, 1, 2
Factor -27*r**4 - 9*r**2 - 19*r**2 - 11*r**3 + 62*r**3 + 26*r - 22*r.
-r*(r - 1)*(3*r - 2)*(9*r - 2)
Let t =