- 11. Let l(k) = n*u(k) - 3*h(k). Factor l(q).
-(q - 3)*(q + 1)
Determine b, given that 7*b + 0 + 1/2*b**2 = 0.
-14, 0
Let h(d) be the first derivative of d**3 - 15*d**2/2 + 29. Factor h(v).
3*v*(v - 5)
Solve 125*u**2 - 303 + 5*u**3 + 0*u**3 - 542 + 715*u = 0 for u.
-13, 1
Let v = -187 + 2807/15. Let c(h) be the first derivative of v*h**3 - 4 - 6/5*h**2 + 18/5*h. Suppose c(j) = 0. What is j?
3
Factor 0 - 1/3*l**3 - 10*l + 11/3*l**2.
-l*(l - 6)*(l - 5)/3
Suppose -6*s = 3*r - s + 8, 5*r - 4 = -4*s. Suppose 2 = 2*h, m - r = -m + 2*h. Factor -3 - 3*f**2 - m*f + 4*f - 5*f - 2*f.
-3*(f + 1)**2
Let x(s) be the third derivative of s**8/26880 + s**7/560 + 3*s**6/80 - s**5/3 - 6*s**2. Let p(j) be the third derivative of x(j). Determine f so that p(f) = 0.
-6
Let 17*t**4 + 10*t**3 + 780*t**2 + 235*t**3 + 14*t**4 + 180*t - 11*t**4 = 0. What is t?
-6, -1/4, 0
Let c be ((-4)/6)/(2/(-12)*1). Suppose 80*g**2 + 607*g**5 - 651*g**5 + 10 - 356*g**5 - 840*g**c - 425*g**3 + 75*g = 0. What is g?
-1, -1/4, 2/5
Solve 45/7*s**2 + 9/7*s**4 + 6/7 - 33/7*s**3 - 27/7*s = 0.
2/3, 1
Let 8/3*t + 0 - 2/3*t**3 - 5/2*t**5 + 22/3*t**2 - 41/6*t**4 = 0. Calculate t.
-2, -4/3, -2/5, 0, 1
Suppose -5*a + 12 + 8 = 0. Suppose a*f = 3*c + 11, 5 = -c - f + 13. Determine j, given that 2/3*j**c + 0 + 7/3*j**4 - 7/3*j**2 - 2/3*j = 0.
-1, -2/7, 0, 1
Let l(w) be the third derivative of w**9/16632 - w**8/9240 - w**7/2310 - 17*w**3/6 - 11*w**2. Let o(c) be the first derivative of l(c). Factor o(i).
2*i**3*(i - 2)*(i + 1)/11
Let f = -2/59595 - 5616497/19865. Let i = f + 283. Factor i*j - 2/15*j**2 - 2/15*j**3 + 0.
-2*j*(j - 1)*(j + 2)/15
Let c = 125/3 + -41. Let f = 26 - 77/3. What is k in c*k + 1/3 + f*k**2 = 0?
-1
Suppose -15 = -0*g - g - 5*l, 0 = g + l - 3. Let h = -89 - -447/5. Solve h*o**2 - 1/5*o + g - 1/5*o**3 = 0.
0, 1
Factor 2/3 + 4/9*v - 10/9*v**2.
-2*(v - 1)*(5*v + 3)/9
Let 3*h**2 + 21/2*h + 6 - 3/2*h**3 = 0. Calculate h.
-1, 4
Let k(c) be the third derivative of c**9/12096 - c**8/1008 + c**7/252 - c**5/30 - 14*c**2. Let t(u) be the third derivative of k(u). Factor t(o).
5*o*(o - 2)**2
Find l such that 8/11*l**3 + 6/11*l**2 + 2/11*l**4 + 0*l + 0 = 0.
-3, -1, 0
Let p(a) be the first derivative of 7/4*a**2 + 35 + 1/12*a**3 + 49/4*a. Determine s so that p(s) = 0.
-7
Let g(c) be the second derivative of c**4/114 + 52*c**3/57 + 100*c**2/19 + 15*c - 9. Factor g(w).
2*(w + 2)*(w + 50)/19
Let p be (-1500)/(-1050) + (-23)/21. Solve p*j**5 - 2/3*j**4 + 1/3*j - 2/3 - 2/3*j**3 + 4/3*j**2 = 0.
-1, 1, 2
Suppose -c - 4*c - 3*u = -34, 3*u = -3*c + 18. Let l(v) = -v**2 + 9*v + 6. Let i be l(c). Factor i*o - 23*o - 15*o**2 + 5 + 1.
-3*(o + 1)*(5*o - 2)
Suppose 1467*p - 2903*p + p**2 + 36 + 1448*p = 0. What is p?
-6
Let r(l) = -2*l + 4. Let d be r(-3). Let q = d + -6. Factor 4 + 39*b**4 + 5*b**5 + q*b**5 - 18*b**3 + 85*b**3 + 24*b + 57*b**2.
(b + 1)**3*(3*b + 2)**2
Let q(y) be the second derivative of y**5/50 - 8*y**4/15 - 58*y - 2. Solve q(k) = 0.
0, 16
Let y(t) = 4*t**3 + 4*t**2 + 2*t - 1. Let b(l) = 5*l**3 + 5*l**2 + 3*l - 1. Suppose 3*n + 13 - 4 = 0. Let s(a) = n*b(a) + 4*y(a). Factor s(f).
(f - 1)*(f + 1)**2
Factor 2/3*q**3 + 24 + 10/3*q**2 - 64/3*q.
2*(q - 2)**2*(q + 9)/3
Let x be (-39)/21 - 3/((-3)/2). Let d = 61/133 - 6/19. Find y such that 0 - d*y**2 + 0*y**3 + x*y**4 + 0*y = 0.
-1, 0, 1
Let y(q) be the second derivative of -q**7/84 + 2*q**6/45 - 5*q**4/36 + q**3/12 + q**2/6 - 3*q - 5. What is u in y(u) = 0?
-1, -1/3, 1, 2
Let u(w) = -126*w**2 - 380*w - 150. Let q(t) = 59*t**2 + 190*t + 75. Let s(m) = -7*q(m) - 3*u(m). Factor s(f).
-5*(f + 5)*(7*f + 3)
Let i(q) be the third derivative of 0*q - 3/10*q**3 + 1/600*q**6 + 35*q**2 - 7/300*q**5 + 0 - 17/120*q**4. Factor i(v).
(v - 9)*(v + 1)**2/5
Let f(i) be the third derivative of 0*i + 1/60*i**5 - 3*i**2 + 0 + 3*i**3 - 19/24*i**4. Let h(z) = z**2 - 10*z + 9. Let p(m) = -2*f(m) + 5*h(m). Factor p(y).
3*(y - 3)*(y - 1)
Factor -128/9 - 64*m + 88*m**3 - 296/9*m**2 - 242/9*m**4.
-2*(m - 2)**2*(11*m + 4)**2/9
Let d be 31 + 90/(-6) + -11. Let 0*b**2 - 2/15*b**d + 0*b + 4/15*b**3 - 2/15*b**4 + 0 = 0. What is b?
-2, 0, 1
Suppose -2*d - s + 14 = s, 0 = -4*s + 8. Suppose q + q = -d*w + 32, w = 5*q + 1. Determine c, given that -6*c**2 - 12*c**3 + w + 3*c**5 + 0*c**5 - c + 10*c = 0.
-1, 1, 2
Let s(g) = 14*g**2 - 6*g - 14. Let c(p) = 5*p**2 - 2*p - 5. Let d(z) = 11*c(z) - 4*s(z). Let t be d(1). Factor 1/4*v + 1/4 - 1/4*v**3 - 1/4*v**t.
-(v - 1)*(v + 1)**2/4
Let d(m) be the second derivative of m**8/7560 - m**7/3780 - m**6/810 - 3*m**3 - 32*m. Let x(q) be the second derivative of d(q). Factor x(n).
2*n**2*(n - 2)*(n + 1)/9
Let g(m) be the first derivative of 5*m**3/3 + 525*m**2 + 55125*m + 298. Find y, given that g(y) = 0.
-105
Let l(g) = 4*g**2 + 272*g + 537. Let b(v) = 28*v**2 + 1904*v + 3756. Let f(s) = 3*b(s) - 20*l(s). Suppose f(n) = 0. What is n?
-66, -2
Let y(t) be the second derivative of t**7/315 - t**6/90 + t**5/90 + 4*t**2 - 10*t. Let x(v) be the first derivative of y(v). Find q, given that x(q) = 0.
0, 1
Let n(x) be the second derivative of x**7/210 - 3*x**6/50 - 19*x. Suppose n(m) = 0. Calculate m.
0, 9
Let n(z) be the third derivative of z**8/1344 - z**7/56 + 5*z**6/32 - 25*z**5/48 - 3*z**2 - 5*z. Factor n(a).
a**2*(a - 5)**3/4
Find a, given that -1/5*a**2 - a - 2/5 + 2/5*a**3 = 0.
-1, -1/2, 2
Let q(r) = -12*r + 89. Let h be q(7). Let l(z) be the second derivative of 0*z**2 + 2*z + 0 + 1/9*z**3 - 1/9*z**4 + 1/30*z**h. Find i such that l(i) = 0.
0, 1
Find q, given that -104/5*q**2 - 106/5 + 1/5*q**3 - 211/5*q = 0.
-1, 106
Solve -16/7*a**3 - 8/7 + 12/7*a + 0*a**4 + 4/7*a**5 + 8/7*a**2 = 0 for a.
-2, -1, 1
Factor -3/4*z**4 - 3*z + 6 + 15/4*z**3 - 9/2*z**2.
-3*(z - 2)**3*(z + 1)/4
Determine r, given that 161 + 5*r**2 + r + 7*r**2 - 161 = 0.
-1/12, 0
Let o(q) = q**2 + 23*q - 8. Let j be o(-22). Let m = j - -32. Factor 1/2 - 1/4*d**4 - 5/4*d + 1/4*d**3 + 3/4*d**m.
-(d - 1)**3*(d + 2)/4
Suppose -2*u - 282 = 4*f, 0 = 4*u + 3*f - f + 570. Let g = 146 + u. Suppose 3/4*x**2 - x**g + 1/4*x + 0 = 0. What is x?
-1/4, 0, 1
Let l(w) be the first derivative of -w**4/12 - w**3/9 + 38. Determine n, given that l(n) = 0.
-1, 0
Let h(j) be the first derivative of 9*j**5/25 - 97*j**4/10 + 476*j**3/5 - 1911*j**2/5 + 343*j + 18. Find d such that h(d) = 0.
5/9, 7
Let h(t) be the second derivative of -t**6/6 - t**5/4 + 5*t**4/4 + 5*t**3/6 - 5*t**2 - 30*t + 2. Let h(r) = 0. What is r?
-2, -1, 1
Let m(q) be the third derivative of q**7/84 - 11*q**6/90 + 7*q**5/15 - 2*q**4/3 + 5*q**3/6 + 4*q**2. Let a(t) be the first derivative of m(t). Factor a(h).
2*(h - 2)**2*(5*h - 2)
Let q(u) be the first derivative of u**7/2940 + u**6/315 + u**5/105 + 8*u**3/3 + 7. Let l(k) be the third derivative of q(k). What is d in l(d) = 0?
-2, 0
Suppose 3*a - 10 - 2 = 0. Let b = -1 - -3. Let 6*f**a + 8*f**3 - 8*f**3 - 6*f**b + 3*f**5 - 3*f**3 = 0. Calculate f.
-2, -1, 0, 1
Suppose -2*p - 2*k = -20 - 28, 0 = -2*p + 4*k + 18. Let q = -16 + p. Factor -q*s**5 + s**5 + 2*s**3 - 3*s**3 + s**4 - s**2 + 3*s**5.
s**2*(s - 1)*(s + 1)**2
Let q(f) = -5*f**2 + 5. Let d(b) = 1 - b**2 + 154*b - 154*b. Let r(k) = -33*d(k) + 6*q(k). Factor r(t).
3*(t - 1)*(t + 1)
Factor 72/13*q**2 + 2/13*q**3 + 0 - 74/13*q.
2*q*(q - 1)*(q + 37)/13
Let s(t) be the first derivative of -29 + 1/30*t**4 - 4/15*t**3 - 8/15*t + 3/5*t**2. Find r such that s(r) = 0.
1, 4
Let s = -153 - -155. Determine k so that -12/5 - 3/5*k**3 + 21/5*k**s + 0*k + 3/5*k**5 - 9/5*k**4 = 0.
-1, 1, 2
Let a = 27284 + -81850/3. Solve 4/3 - 2/3*v**5 + 4/3*v**4 - a*v + 4/3*v**3 - 8/3*v**2 = 0 for v.
-1, 1, 2
Let k be 1/(-1)*0/3. Let q be ((-3)/6 - k)*-4. Find w, given that 5 - 20*w - 3*w**q + 1 + 23*w = 0.
-1, 2
Suppose -106 = 4*i - 1026. Let -10*t - 8*t + i - 220 + 6*t**2 + 2*t**3 = 0. What is t?
-5, 1
Suppose 2*n = 40 - 24. Suppose 0 = m - 4*j - 7, -4*m - 20 = -9*m + 5*j. Factor -7*y**4 - 58*y**2 + 14*y**2 - 23*y**4 + 70*y**m + n*y + 5*y**4.
-y*(y - 2)*(5*y - 2)**2
Let c(k) be the second derivative of k**4/72 + k**3/36 - 3*k - 19. Find t, given that c(t) = 0.
-1, 0
Suppose 3*y - n - 2 = 8, 4*y - 15 = 3*n. Let b(c) be the first derivative of c**2 + 0*c - 2 - 4/9*c**y + 1/18*c**4. Factor b(p).
2*p*(p - 3)**2/9
Let q(p) be the second derivative of p**7/42 + 19*p