12 - h**3/6 + 7*h**2/2 + h. Let w(t) be the first derivative of j(t). Factor w(l).
-(l + 1)**2
Let s(h) be the first derivative of -h**4/8 - 11*h**3/2 - 363*h**2/4 - 1331*h/2 - 18. Factor s(u).
-(u + 11)**3/2
Suppose 0 = -23*k + 54*k - 155. Let u(h) be the first derivative of -1/5*h**3 - 1/25*h**k + 0*h - 1/10*h**2 - 3/20*h**4 + 9. Let u(z) = 0. What is z?
-1, 0
Let b(f) be the second derivative of 8*f**6/45 + 4*f**5/15 + f**4/6 - 7*f**3/3 + 9*f. Let j(r) be the second derivative of b(r). Factor j(n).
4*(4*n + 1)**2
Let j(r) = 24*r**5 - r**4 + 18*r**3 - 11*r + 11. Let g(a) = 13*a**5 + 9*a**3 - 6*a + 6. Let l(w) = -11*g(w) + 6*j(w). Let l(f) = 0. Calculate f.
0, 3
Find l such that 1/3*l**4 - 4*l**2 + 2/3*l**3 - 5/3 + 14/3*l = 0.
-5, 1
Let l(c) be the second derivative of -c**6/140 - 2*c**5/105 + 5*c**4/84 + 2*c**3/21 - 7*c**2/2 - 6*c. Let t(y) be the first derivative of l(y). Factor t(q).
-2*(q - 1)*(q + 2)*(3*q + 1)/7
Let n(b) be the third derivative of 16/39*b**3 - 2/195*b**6 + 4/39*b**4 + 28*b**2 + 0*b + 1/1365*b**7 - 4/195*b**5 + 0 + 1/2184*b**8. Find v such that n(v) = 0.
-2, -1, 2
Solve -4/3*o**2 - 5/3*o - 2/3 - 1/3*o**3 = 0 for o.
-2, -1
Suppose -1414 + 146*j - 42*j - 206 + 76*j - 5*j**2 = 0. What is j?
18
Let y(g) = -8*g**2 - 29*g - 33. Let c(s) = -13*s**2 - 57*s - 64. Let u(h) = -3*c(h) + 5*y(h). Factor u(j).
-(j - 27)*(j + 1)
Let i(a) be the third derivative of a**8/840 - 16*a**7/525 + 3*a**6/20 + 27*a**5/25 - a**2 + 59*a. Find t such that i(t) = 0.
-2, 0, 9
Let k(q) be the second derivative of -q**6/5 + 13*q**5/20 - 2*q**3/3 - 24*q. Suppose k(h) = 0. What is h?
-1/2, 0, 2/3, 2
Let w = 39223 + -38977. Find r, given that 330*r**3 + 0 + 75/2*r**4 + 48*r + w*r**2 = 0.
-8, -2/5, 0
Let c(f) be the first derivative of -f**6/240 - 3*f**5/160 + f**4/16 + f**3/6 + 14*f + 39. Let m(w) be the first derivative of c(w). Find b such that m(b) = 0.
-4, -1, 0, 2
Suppose -12830 + 27*b**3 - 66*b**2 - 12*b + 12902 + 3*b**4 + 3*b**4 - 3*b**5 = 0. What is b?
-3, -1, 2
Find o, given that -58*o - 5*o**3 + o**3 + 127*o - 17*o**4 - 9 + 50*o**2 - 45*o + 4*o**5 = 0.
-1, 1/4, 3
Let f(z) = -4*z**3 + 182*z**2 + 2168*z - 5046. Let r(y) = -y**3 + 60*y**2 + 723*y - 1682. Let t(d) = -4*f(d) + 14*r(d). Let t(v) = 0. What is v?
-29, 2
Let y(p) be the first derivative of -p**9/22680 + p**8/4200 - p**7/3150 - 4*p**3/3 + 10. Let h(s) be the third derivative of y(s). Factor h(t).
-2*t**3*(t - 2)*(t - 1)/15
Suppose r + 0 = -2. Let k(s) = -s**3 - s**2 - 1. Let g be k(r). Solve 0*v**3 + 3*v**4 + 0*v**5 - 6*v**3 + g*v**5 + 0*v**4 = 0.
-2, 0, 1
Let u(k) be the first derivative of 8*k**4 - 92*k**3/3 - 6*k**2 + 349. Factor u(j).
4*j*(j - 3)*(8*j + 1)
Let h = -16893 + 16896. Determine b so that 4 - 4/7*b**h + 20/7*b**2 + 52/7*b = 0.
-1, 7
Let k(c) = -2*c - 18. Let z be k(-14). Factor 5*s**2 + 12*s + s**2 - 9 - 7*s**4 + z*s**4 - 12*s**3.
3*(s - 3)*(s - 1)**2*(s + 1)
Let o = 9 + -5. Let i be (4 - 4)/(0 - 1). Factor -c + c**o - 1 - c + 2*c**3 + i + 0.
(c - 1)*(c + 1)**3
Let j(u) be the first derivative of u**3/2 + 75*u**2/2 - 153*u/2 - 297. What is x in j(x) = 0?
-51, 1
Let r be (36/(-24))/(6/(-20)). Find d such that 2*d - 1694*d**r - 16 - 10*d**3 + 356*d**2 - 1095*d**3 - 205*d**3 + 86*d - 3256*d**4 = 0.
-1, -2/7, 2/11
Suppose 10*r - 2 = 18. Factor -6*c + 6 + c - 18 - 5*c + r*c**2.
2*(c - 6)*(c + 1)
Suppose -11*r + 18 = -4. Suppose 3*p + 5 = -2*q - 3, 0 = 5*q + 2*p - r. Let -2/7*b**q + 2/7*b + 0 = 0. What is b?
0, 1
Let q(c) be the first derivative of c**4/2 + 130*c**3/3 - 227. Find d such that q(d) = 0.
-65, 0
Let k(t) be the first derivative of -t**8/672 + t**6/120 - t**4/48 - 7*t**2 + 3. Let v(r) be the second derivative of k(r). Factor v(s).
-s*(s - 1)**2*(s + 1)**2/2
Let q(y) = -2*y - 2 + 0*y - 4. Let i be q(-4). Suppose 3*k + i - 3*k + 55*k**2 + 2*k**4 - 59*k**2 = 0. What is k?
-1, 1
Let t(c) = -7*c**3 + 29*c**2 + 2*c - 9. Let q be t(4). Suppose 2*v = 4*v + f - 3, -5*f = v - q. Factor -4/3*o**2 + 0 - 4/3*o**3 + v*o.
-4*o**2*(o + 1)/3
Let t(c) = 0*c**2 - 2 + 11*c - 7*c + 4*c**2 + 6. Let m(k) = k. Let x(s) = 12*m(s) - t(s). Determine h so that x(h) = 0.
1
Factor -751*d**2 + 1502*d**2 - 6 - 746*d**2 - 13*d.
(d - 3)*(5*d + 2)
Let z(n) be the second derivative of -9*n**6/40 + 603*n**5/20 - 4621*n**4/4 + 2948*n**3 - 2904*n**2 - 656*n. Factor z(u).
-3*(u - 44)**2*(3*u - 2)**2/4
Let w = -74 - -77. Suppose -4*t = y - 16, -w*t + 32 = t + 5*y. Factor 0 + 0*s**t + 2/11*s**4 + 0*s + 0*s**2 - 2/11*s**5.
-2*s**4*(s - 1)/11
Let c be (1/6)/(3/12). Let r(t) be the first derivative of -c*t**3 - t**2 + 0*t + 2/5*t**5 + 3 + 1/2*t**4. Factor r(b).
2*b*(b - 1)*(b + 1)**2
Let w be 3/4 + 1 + -1. Suppose 242 + 112 = 177*q. Suppose w*v**q + 0 - 1/2*v = 0. Calculate v.
0, 2/3
Let g(d) be the first derivative of d**2/2 + 9*d - 6. Let u be g(-5). Factor -41*j**5 - 11*j**5 - 2*j**2 - 66*j**u - 28*j**5 + 8*j**5 - 20*j**3.
-2*j**2*(3*j + 1)**2*(4*j + 1)
Determine x, given that 11/9*x**2 + 0 - 2/9*x - 19/9*x**3 + 13/9*x**4 - 1/3*x**5 = 0.
0, 1/3, 1, 2
Suppose -38*r = 28*r. Factor r*s**2 + 0*s - 45/2*s**3 + 15*s**4 + 0 - 5/2*s**5.
-5*s**3*(s - 3)**2/2
Let g(x) be the third derivative of x**5/15 - 7*x**4/6 + 4*x**3 - 104*x**2. Let g(n) = 0. What is n?
1, 6
Let n = 14 - 9. Suppose -4*x = -b - 0*x - 8, x = 5*b - 17. Factor -2*r**3 + 9*r**2 - n*r**2 - r**b - 5*r**2.
-r**2*(r + 1)**2
Solve -165*a + 5445/2 + 5/2*a**2 = 0 for a.
33
Let o be (-14)/(-49) - 36/(-21). Find j such that 9/5 + 1/5*j**o + 6/5*j = 0.
-3
Let g be -3 - (-5 + 2) - -3. Let q(k) be the second derivative of 0 + 4*k + 1/2*k**g + k**2 + 1/12*k**4. Factor q(n).
(n + 1)*(n + 2)
Determine c so that 2/9*c**3 - 2662/9 + 242/3*c - 22/3*c**2 = 0.
11
Let r(q) be the second derivative of 3*q**5/20 + 13*q**4/6 + 37*q**3/6 + 7*q**2 + 86*q + 1. Factor r(o).
(o + 1)*(o + 7)*(3*o + 2)
Let x(o) = 7*o**3 + 3*o**2 + 5*o - 9. Let y(k) = 4*k**3 + 2*k**2 + 2*k - 4. Let f be (-6)/(-7)*(-7 + 14) - 2. Let d(h) = f*x(h) - 9*y(h). Factor d(s).
-2*s*(s + 1)*(4*s - 1)
Find h, given that 107*h + 2/3 - 323/3*h**2 = 0.
-2/323, 1
Suppose -52*z**3 + 9*z**4 - 26 - 28*z + 78*z + 2*z**5 + 13*z**4 + 4*z**2 = 0. What is z?
-13, -1, 1
Let i(g) be the second derivative of -g**4/12 + 4*g. Let c(h) = -h**5 - 2*h**4 - h**3 - h**2. Let w(l) = 3*c(l) - 3*i(l). Factor w(s).
-3*s**3*(s + 1)**2
Let p = -1953264/283 - -6902. Let b = p - -841/1132. Let -3/4*i**3 + 3/4*i**2 - 3/4 + b*i = 0. What is i?
-1, 1
Factor -3*a + 3*a**4 - 137*a**3 + 0*a + 5*a + 144*a**3 - 6*a.
a*(a + 1)*(a + 2)*(3*a - 2)
Let y(v) be the third derivative of -v**6/3960 - v**5/330 - v**4/66 + v**3/6 + 13*v**2. Let w(h) be the first derivative of y(h). Factor w(d).
-(d + 2)**2/11
Let q(b) be the first derivative of 5*b**5/12 + 5*b**4/3 - 10*b**3/3 - 5*b**2 + 19. Let d(n) be the second derivative of q(n). Factor d(s).
5*(s + 2)*(5*s - 2)
Let p(j) be the third derivative of -7921*j**5/150 + 89*j**4/15 - 4*j**3/15 - 16*j**2 + 6. Factor p(g).
-2*(89*g - 2)**2/5
Suppose -2/9*p**2 - 20/3 - 34/9*p = 0. Calculate p.
-15, -2
Let k be 8 + (-6)/162*201. Let b(z) be the second derivative of -17/60*z**5 - 2/9*z**3 + 0*z**2 + 2/45*z**6 - 5*z + 0 + k*z**4. What is m in b(m) = 0?
0, 1/4, 2
Let j be (-189)/(-9) + 805/(-45). Factor -98/9 - 2/9*b**2 - j*b.
-2*(b + 7)**2/9
Let u be (-3 + 0)*(51 + -50). Let p be 4/(-12)*0/u. Factor z + p + 1/2*z**2.
z*(z + 2)/2
Let u(r) be the third derivative of 1/5*r**3 + 1/450*r**5 + 17*r**2 + 0 + 0*r + 1/30*r**4. What is n in u(n) = 0?
-3
Factor 0 + 4/5*o**2 - 2/5*o**3 + 6/5*o.
-2*o*(o - 3)*(o + 1)/5
Let f be 1 - (-4)/(12/27). Solve 10 - 15*u**3 - 2 - f*u - 2*u**4 + 7*u**3 + 18*u**3 - 6*u**2 = 0 for u.
-1, 1, 4
Let x(d) = -9*d**2 + d**3 + 16 - 8 + 4*d + 2 + 3*d. Let f be x(8). Solve -1/5*t**3 - 2/5*t**f + 0*t + 0 = 0.
-2, 0
Let g(y) be the second derivative of y**7/84 - y**6/90 - 11*y**5/60 + 4*y**4/9 - 5*y**3/36 - y**2/2 - 247*y. Solve g(j) = 0.
-3, -1/3, 1, 2
Let r(p) = -p**2 - 10*p + 32. Let k be r(-10). Suppose -15*d**2 - 19*d**2 - 1 - 3 - 6*d + k*d**2 = 0. What is d?
-2, -1
Find g, given that -176*g - 432*g**3 + 22 - 15 + 504*g**2 + 13 - 108*g**4 = 0.
-5, 1/3
Let r(f) be the third derivative of -3/80*f**4 - 7/600*f**5 - 1/30*f**3 + 0*f + 0 + f**2. Factor r(l).
-(l + 1)*(7*l + 2)/10
Let s(d) be the second 