et l(f) = f - 1. Let h(c) be the third derivative of c**5/60 - 29*c**4/24 + 253*c**3/6 - 46*c**2. Let y(x) = -h(x) + 3*l(x). Determine v, given that y(v) = 0.
16
Suppose -2/7*k**3 - 68/7*k**2 - 72/7 + 142/7*k = 0. Calculate k.
-36, 1
Let n(t) = -t**3 - 4*t**2 - 12*t - 16. Let g be n(-2). Let m(c) be the first derivative of 14 + 0*c**2 + 21/20*c**4 + g*c - 2/5*c**3. Factor m(w).
3*w**2*(7*w - 2)/5
Suppose -5 - 4 = -3*n - 3*j, 4*n - 3*j - 47 = 0. Suppose -5*k = 2*z - n, 3*k - 1 = -0*k - 5*z. Let -3*u**3 + 723 + 12*u - 12*u**k - 727 + 7*u**3 = 0. What is u?
1
Let v(q) = -21*q**4 - 45*q**3 - 131*q**2 - 91*q - 16. Let z(w) = -4*w**4 - 9*w**3 - 26*w**2 - 18*w - 3. Let a(d) = -9*v(d) + 48*z(d). Factor a(f).
-3*f*(f + 1)*(f + 3)*(f + 5)
Let n(l) be the first derivative of -2*l**6/3 + 2*l**5 - 3*l**4/2 - 2*l**3/3 + l**2 + 3499. Find x, given that n(x) = 0.
-1/2, 0, 1
Let a(x) = 47*x + 300. Let o be a(-20). Let g = 1281/2 + o. Find q, given that 1/6*q**3 + 1/2*q**2 - g - 1/6*q = 0.
-3, -1, 1
Suppose 20*k + 20680 + 15680 = 0. Let q be (5*2/6)/((-1010)/k). Factor 5/4*n**q - 5/2 + 0*n**2 - 15/4*n.
5*(n - 2)*(n + 1)**2/4
Let z(v) be the first derivative of -v**4/6 + 9*v**3 + 28*v**2 - 54*v - 85. Let n(j) be the first derivative of z(j). Solve n(r) = 0.
-1, 28
Let v(i) = i**3 + 9*i**2 - 3*i - 18. Let t be v(-9). Solve 30*h**3 + 255*h**2 - 369*h**2 + 6 + 69*h + t*h**3 = 0.
-1/13, 1, 2
Let j be -10 + (-5410)/(-790) + 3. Let m = j - -434/1817. Find w, given that 0 + 2/23*w + m*w**2 = 0.
-1, 0
Let y(p) be the third derivative of -p**6/40 - p**5/20 + p**4/8 - 71*p**3/6 - 48*p**2. Let j(c) be the first derivative of y(c). Suppose j(i) = 0. Calculate i.
-1, 1/3
Let i(k) = 4*k**3 - 24*k**2 + 46*k - 16. Let j(z) = 114*z - 60*z**2 + 2*z**3 + 8*z**3 + 74 - 114. Let q(g) = -12*i(g) + 5*j(g). What is l in q(l) = 0?
1, 4
Let r(h) be the first derivative of 2*h**6/3 + 216*h**5/5 - 6*h**4 - 1264*h**3/3 + 858*h**2 - 648*h - 3179. Determine c so that r(c) = 0.
-54, -3, 1
Let n(v) = v**2 - v + 2. Let z(l) = 25*l + 14. Let p(j) = -2*n(j) - z(j). Let d(s) = -6*s**2 - 68*s - 54. Let o(g) = -3*d(g) + 8*p(g). Factor o(m).
2*(m + 1)*(m + 9)
Let t(r) = r. Suppose -11*n = -n + 230. Let y = -18 - n. Let p(o) = 2*o**2 + 2*o + 1. Let d(j) = y*t(j) - p(j). Determine g, given that d(g) = 0.
1/2, 1
Let r = 535 - 3744/7. Let -5/7*q**3 + 0 - 3/7*q**2 - r*q**4 + 9/7*q = 0. What is q?
-3, 0, 1
Let c(i) be the first derivative of -i**6/210 - 137*i**5/280 - 17*i**4/28 + 83*i**3/3 - 35. Let s(f) be the third derivative of c(f). Factor s(n).
-3*(n + 34)*(4*n + 1)/7
Let t be 5 + (13 - 12) + -2*1. Let g be (40/32*8)/t. Determine x, given that 0 + 5*x + g*x**2 = 0.
-2, 0
Suppose j = 2*p + 18, -7*p + 13 = j - 8*p. Factor -57*r - 162*r + 379*r - 4*r**2 + 1600 + j*r**2.
4*(r + 20)**2
Let z(v) be the first derivative of -2*v**3/57 - 101*v**2/19 + 204*v/19 + 1661. Factor z(b).
-2*(b - 1)*(b + 102)/19
Let h(s) = -11*s**4 + 9*s**3 + 62*s**2 + 20*s - 56. Let c(j) = -21*j**4 + 18*j**3 + 123*j**2 + 39*j - 114. Let n(z) = -8*c(z) + 15*h(z). Solve n(r) = 0 for r.
-2, 1, 6
Let a(p) be the second derivative of 5/24*p**6 + 25/48*p**4 + 0*p**2 - 1/42*p**7 + 0 - 60*p - 21/40*p**5 - 1/6*p**3. Find z such that a(z) = 0.
0, 1/4, 1, 4
Let 2*j + 25*j**2 + 3*j - 12*j - 156 - j**3 + 9*j + 30*j = 0. Calculate j.
-3, 2, 26
Suppose -45*r - 3 = -113*r - 3. Let k(v) be the second derivative of r*v**2 + 0 + 1/180*v**6 + 0*v**4 + 0*v**3 + 15*v - 1/120*v**5. Factor k(w).
w**3*(w - 1)/6
Solve 528/7*x**2 - 114264/7 - 4/7*x**3 - 15732/7*x = 0.
-6, 69
Factor -6041288/9 - 18130816/9*k - 2/3*k**3 - 20858/9*k**2.
-2*(k + 1738)**2*(3*k + 1)/9
Let z(t) be the second derivative of 21*t**4/8 - 31*t**3/4 + 15*t**2/2 + t - 423. Factor z(i).
3*(i - 1)*(21*i - 10)/2
Let h(r) be the third derivative of 169/480*r**6 + 13/80*r**5 - 2*r**2 + 15*r - 8/3*r**3 + 0 - 3/2*r**4. Suppose h(x) = 0. Calculate x.
-8/13, 1
Suppose -o + 9 = l, 0 = -o + 124*l - 119*l - 15. Let f(u) be the second derivative of 0*u**3 + 0*u**2 + 1/48*u**4 + 3*u + 0 + 1/80*u**o. Solve f(p) = 0.
-1, 0
Factor -1989*q - 14394/7*q**2 - 4563/7 - 243/7*q**4 - 5274/7*q**3 - 3/7*q**5.
-3*(q + 1)**3*(q + 39)**2/7
Let j(s) be the first derivative of -s**6/1980 - s**5/132 - s**4/33 - 196*s**3/3 - 278. Let x(c) be the third derivative of j(c). Factor x(m).
-2*(m + 1)*(m + 4)/11
Let r be ((-5 - 2) + 5)*-1. Solve -6*b**r - 120*b - 8*b**2 - 115 + 9*b**2 - 605 = 0 for b.
-12
Let -1089/4 + 28*z**2 + 1/4*z**4 + 99/2*z - 11/2*z**3 = 0. Calculate z.
-3, 3, 11
Let i be (20 - 24)*((-2*2)/4)/1. Let u be (-59)/(-3) - (-4)/(-6). Factor -u*n**2 - 3*n + 17*n**2 - i*n**2.
-3*n*(2*n + 1)
Let l = 2776 + -2773. Let t(j) be the second derivative of -1/9*j**4 + 0*j**2 + 8*j - 1/30*j**5 + 0 + 0*j**l. Find p such that t(p) = 0.
-2, 0
Solve -428/7*c**2 + 78/7*c**3 - 4/7*c**4 + 324/7 + 414/7*c = 0.
-1/2, 2, 9
Let a(c) be the second derivative of c**4/12 - 11*c**3 - 67*c**2/2 + 59*c. Solve a(y) = 0.
-1, 67
Let w(f) = f**5 + f**3 - 2. Let c(a) = -52*a**4 - 1056*a**3 - 2864*a**2 + 9088*a - 5116. Let q(z) = 2*c(z) + 4*w(z). Let q(v) = 0. Calculate v.
-8, 1, 40
Let g(o) = -10*o**2 - 228*o + 74. Suppose 363*a = 368*a - 20. Let i(h) = -12*h**2 - 229*h + 73. Let s(c) = a*i(c) - 6*g(c). Factor s(n).
4*(n + 38)*(3*n - 1)
Let f = -47077 + 94155/2. Let i be -2 - (-1 - 15/6). Let 3/2*k + 1/2 + f*k**3 + i*k**2 = 0. Calculate k.
-1
Suppose 2*s - 234 = -16*s. Let t be (-29)/116 + s/4. Factor -971 + 971 + 3*p - 3*p**t.
-3*p*(p - 1)*(p + 1)
Solve -29*d + 493*d**2 + 640*d**4 + 324*d**5 - 16*d**3 - 493*d**2 + 29*d = 0 for d.
-2, 0, 2/81
Let r(k) be the third derivative of 1801*k**5/390 - k**4/78 - 6507*k**2. Find h such that r(h) = 0.
0, 2/1801
Factor -250 - 2592/5*a**2 - 720*a.
-2*(36*a + 25)**2/5
Suppose 14 = 18*t - 4. Let v be 2/(-7)*t - (-784)/343. Factor 2 + 1/2*p**v + 5/2*p.
(p + 1)*(p + 4)/2
Let t(d) = d**3 - 13*d**2 + 10*d + 26. Let i be t(12). Suppose 3*p = 3*y + 11 - i, -9 = -4*p + 3*y. Factor p + 2/13*m + 14/13*m**2.
2*m*(7*m + 1)/13
Let k(s) = -19*s**3 - s. Let t = 27 - 28. Let p be k(t). Factor p*i - 35*i - 4*i**2 - 17*i.
-4*i*(i + 8)
Let p be 2/(-10) + (-156)/(-30). What is k in -80 - 50*k - p*k**2 + 5*k**2 - k**2 - 4*k**2 = 0?
-8, -2
Suppose -19*h - 40 = -11*h. Let z be -13 + (5 - h) + 8 + 0. Determine k so that 6/5*k**2 + 0*k + 2/5*k**3 - 2/5*k**z + 0 - 6/5*k**4 = 0.
-3, -1, 0, 1
Let a(w) = 5*w**3 + 7*w**2 - 105*w + 202. Let x be a(-6). Find l such that 2/7*l**2 - x + 26/7*l = 0.
-14, 1
Suppose 5*x + 15 = -w, -9*w - 4*x = -8*w + 11. Find n, given that 355*n**4 - 18*n**5 + 95*n**2 - 5 + 54*n**w + 5 + 10*n + 300*n**3 + 104*n**5 = 0.
-1, -2/7, -1/4, 0
Let n(a) = -a**2 - 4*a - 1. Let t(g) = -4*g**2 - 83*g - 3. Let d(o) = -6*n(o) + 2*t(o). Factor d(x).
-2*x*(x + 71)
Solve 834/7*r - 2/7*r**2 + 3368/7 = 0 for r.
-4, 421
Suppose -12*v - 84 = -33*v. Suppose 0 = -4*h, v*d = 2*d - 4*h. Determine j so that d - 4/5*j + 1/5*j**3 + 0*j**2 = 0.
-2, 0, 2
Let j(f) = -63*f**3 - 606*f**2 - 1861*f - 1801. Let t(i) = -i**3 - 2*i**2 + i + 1. Let u(c) = -j(c) - t(c). Factor u(q).
4*(q + 2)*(4*q + 15)**2
Let x(b) be the third derivative of -b**7/150 - 31*b**6/600 - 3*b**5/25 + b**4/30 + 8*b**3/15 - 3161*b**2. What is n in x(n) = 0?
-2, -1, 4/7
Factor -68*y**2 + 19*y**4 + 80*y**2 - 186*y**3 + 183*y**2 + 207*y - 22*y**4 + 171*y.
-3*y*(y - 2)*(y + 1)*(y + 63)
Let q = 1 + 2. Suppose -4 = -y, 2*m + q*m = -3*y + 782. What is l in -26*l**2 + 2 - 10*l - 196*l**4 + 79*l**4 + m*l**3 - 3*l**4 = 0?
-1/4, 1/5, 1/3, 1
Suppose -1/2*o**4 - 83*o**2 + 132*o + 12*o**3 - 121/2 = 0. Calculate o.
1, 11
Let x be 0 - (-25 + 792/36). Let 0*l**2 + 2/3*l**x - 14/3*l + 4 = 0. Calculate l.
-3, 1, 2
Let r(z) be the third derivative of z**5/90 + 35*z**4/4 - 316*z**3/9 + 871*z**2. Factor r(j).
2*(j - 1)*(j + 316)/3
Let j be ((-25)/6)/5*-1*51/170. Let o(v) be the first derivative of -1/18*v**6 - j*v**4 - 1 + 0*v**2 - 1/9*v**3 - 1/5*v**5 + 0*v. Find r, given that o(r) = 0.
-1, 0
Let q(u) = u**2 + 185*u + 1056. Let l(g) = 4*g**2 + 365*g + 2115. Let o(i) = 2*l(i) - 5*q(i). Factor o(a).
3*(a - 70)*(a + 5)
Let 108475*z - 1779*z**2 + 21*z**3 - 7*z**3 - 11*z**3 + 157910*z - 783225 = 0. Calculate z.
3, 295
Let s(j) be the third derivative of j**6/45 + 31*j**5/18 - 181*j**4/12 + 14*j*