- 1/8*v**3 + 0 - 14*v.
-v*(v - 28)*(v - 4)/8
Let a(y) be the third derivative of y**8/84 + 12*y**7/35 + 3*y**6/2 - 4*y**5/15 - 10*y**4 - 30*y**2 + 6*y. What is b in a(b) = 0?
-15, -2, 0, 1
Factor -56*q + 0 - 5060/3*q**3 + 1846/3*q**2 - 121/6*q**4.
-q*(q + 84)*(11*q - 2)**2/6
Suppose -2*p = -3*x - 260, p - 137 = -0*x + 5*x. Determine s so that 18*s - 20*s**3 - p*s**5 - 15*s**4 + 129*s**5 + 15*s**4 = 0.
-3, -1, 0, 1, 3
Let n(z) = 4*z**3 + 8*z - 23. Let v be n(4). Let w = v + -1309/5. Factor -w - 4/5*x + 2/5*x**2.
2*(x - 4)*(x + 2)/5
Let b(q) be the third derivative of 3*q**6/10 - 8*q**5/3 - 29*q**4/6 + 40*q**3/3 + 17*q**2 + 71*q. Suppose b(w) = 0. Calculate w.
-1, 4/9, 5
Let p(q) = -5*q**4 + 19*q**3 + 3*q**2. Let n(s) = -6*s**4 + 20*s**3 + 2*s**2. Let d(k) = 7*n(k) - 8*p(k). Factor d(o).
-2*o**2*(o + 1)*(o + 5)
Let b be (-2)/3*(21*(-10)/12 - -13). Find h, given that 0*h + 0 + 2/3*h**b - 4*h**2 = 0.
0, 6
Let p be (585/(-60) - -15)*566/6. Let f = p - 495. Solve 5/4*w**2 + f*w**3 + 2*w + 1 = 0 for w.
-2, -1
Let d(o) be the third derivative of -o**5/40 - 575*o**4/48 + 16*o**3 + 5*o**2 - 118*o. Solve d(p) = 0.
-192, 1/3
Let j(p) = p + 3. Suppose -4*t + 1 = 2*x - 5, -4*x + 6 = 5*t. Let n be j(x). Factor 6/7*y + 3/7*y**n + 3/7.
3*(y + 1)**2/7
Let a(b) be the third derivative of -b**7/7560 - 13*b**6/2160 - b**5/12 + 7*b**4/6 - b**3/6 + 74*b**2. Let x(h) be the second derivative of a(h). Factor x(v).
-(v + 3)*(v + 10)/3
Let j = 17497 + -17497. Let w(f) be the first derivative of j*f**2 + 6/7*f**3 - 2/7*f**5 + 3/14*f**4 + 1/21*f**6 + 0*f + 34. Factor w(r).
2*r**2*(r - 3)**2*(r + 1)/7
Let m(j) be the first derivative of 2*j**3/3 + 49*j**2 + 440*j - 12120. Determine h, given that m(h) = 0.
-44, -5
Suppose 89 + 82 = 19*l. Let a be 6/(-25)*l/54*-15. Factor 60 + 12*n + a*n**2.
3*(n + 10)**2/5
Suppose 5*z**5 - 1513*z**2 - 9*z**4 + 180 - 1520*z**2 - 26*z**4 + 3128*z**2 + 55*z**3 - 300*z = 0. What is z?
-2, 1, 2, 3
Let h(d) be the third derivative of 0 + 64*d**2 - 3/4*d**5 - 25/12*d**4 + 5/2*d**3 + 1/6*d**6 + 0*d. Suppose h(z) = 0. What is z?
-1, 1/4, 3
Let s(h) = -h**3 - 14*h**2 - 14*h - 11. Let k be -2 + 22/(-3 - (2 - 3)). Let x be s(k). Factor -7*v**2 + 2*v**2 + 3*v**2 + 81 - 18*v + 3*v**x.
(v - 9)**2
Factor 632/3*j**3 + 82/3 + 490/3*j + 324*j**2 - 16/3*j**4.
-2*(j - 41)*(2*j + 1)**3/3
Factor 15821*m + 3559*m + 5*m**3 + 26829 + 15207 + 1080*m - 650*m**2 + 1524.
5*(m - 66)**2*(m + 2)
Let z(s) be the first derivative of s**6/30 - 2*s**5 - 31*s**4/6 - 183*s**2/2 - 184. Let q(p) be the second derivative of z(p). Solve q(m) = 0 for m.
-1, 0, 31
Let k(a) be the first derivative of -65/3*a**3 - 105/2*a**4 + 210*a**2 - 45 - 180*a - 9*a**5. Factor k(f).
-5*(f + 3)**2*(3*f - 2)**2
Suppose -2624*k**3 - 51*k**4 - 7745 + 6*k**4 + 2032*k + 2829*k**2 + 81*k**5 + 875*k**2 + 7985 = 0. Calculate k.
-6, -2/9, 2, 5
Let q(g) be the second derivative of g**5/20 - 37*g**4/12 - 77*g**3/6 - 39*g**2/2 + 3*g + 194. Solve q(u) = 0.
-1, 39
Let w(i) = 2*i + 15. Let d be w(0). Find m, given that 12 + d*m - 19*m - 4*m**2 - 9*m + 15*m = 0.
-3/2, 2
Let f(g) be the second derivative of -g**9/15120 - 9*g**8/2240 + g**7/90 + g**4/3 + 19*g**3/3 - 294*g. Let s(q) be the third derivative of f(q). Factor s(r).
-r**2*(r - 1)*(r + 28)
Suppose -1 = p - k, -4*p - 5*k + 2 = -3*k. Suppose 13*q - 114192 + 29016 = p. Factor -2*j**4 + 6552*j**2 + 2*j**5 - 4*j**3 - q*j**2.
2*j**3*(j - 2)*(j + 1)
Find f, given that 386*f**4 + 3/5*f**5 + 0 - 208012/5*f**2 + 309763/5*f**3 - 103684/5*f = 0.
-322, -1/3, 0, 1
Let h(t) = -6*t**2 - 4273*t - 25420. Let z be h(-6). Factor 15*f + 27/2*f**z + 25/6.
(9*f + 5)**2/6
Let q be 3450/18975 + (-40812)/(-110). Factor 0 + 4752/5*w**3 + 256/5*w + 1458/5*w**5 + q*w**2 + 972*w**4.
2*w*(w + 2)*(9*w + 4)**3/5
Let m(x) be the third derivative of x**10/45360 - x**9/22680 - x**8/5040 - 9*x**4/4 - x**3/3 + 39*x**2. Let q(k) be the second derivative of m(k). Factor q(r).
2*r**3*(r - 2)*(r + 1)/3
Let s(v) be the third derivative of v**5/330 + 9*v**4/44 - 6*v**3 - v**2 + 8*v + 21. Factor s(d).
2*(d - 6)*(d + 33)/11
Let x(a) be the second derivative of -a**6/20 + 9*a**5/20 + a**4/2 - 27*a**3/2 + 135*a**2/4 - 1940*a. What is o in x(o) = 0?
-3, 1, 3, 5
Let f(b) = 9*b**2 + 60*b + 357. Let o(m) = -492 + 1143 + 421 + 26*m**2 + 181*m. Suppose 9*i - 85 = 4*i. Let r(k) = i*f(k) - 6*o(k). Factor r(s).
-3*(s + 11)**2
Suppose 3187*t - 3182*t = -3*z + 35, -5*t + 35 = -5*z. Factor 0*o + 0 + 0*o**3 + 1/2*o**4 + z*o**2 + 1/2*o**5.
o**4*(o + 1)/2
Determine n, given that 104/11*n**2 - 18/11*n**3 + 0*n - 2/11*n**4 + 0 = 0.
-13, 0, 4
Suppose -2*j - 1 = -7. Let a be 7*j - ((-2 - -5) + -6). Factor 7 - a*u + 2 + 24 + 2*u**2 + 39.
2*(u - 6)**2
Factor 305 + 2*w**2 + 19 + 6 - 116*w.
2*(w - 55)*(w - 3)
Let d(o) be the second derivative of -7*o**3/6 - 12*o**2 - 9*o. Let b be d(-4). Factor -16*i**3 + 11*i**2 - 17*i**2 - 14*i**2 - b*i**4 - 8*i.
-4*i*(i + 1)**2*(i + 2)
Let f be (12/(-114) - (-814)/(-209))/(-22). Let v(y) be the second derivative of f*y**2 + 0 + 30*y - 4/33*y**4 - 5/11*y**3. Factor v(d).
-2*(d + 2)*(8*d - 1)/11
Solve -66*l**4 - 3/2*l**5 - 44217 + 87567/2*l - 774*l**3 + 1275*l**2 = 0.
-17, 1, 6
Let g be (-12)/(-9) + (1 - -4 - 11) + 7. Let w(d) be the first derivative of 11 - g*d**2 + 16/9*d**3 + 4/3*d - 1/2*d**4. Factor w(r).
-2*(r - 1)**2*(3*r - 2)/3
Let u = -146 + 132. Let g be (48/u)/6*(-14)/4. Factor -1/4*w - 1/8*w**g + 1/8*w**4 + 0 + 1/4*w**3.
w*(w - 1)*(w + 1)*(w + 2)/8
Let v = -126 - -131. Suppose 0*p + 4*q = -2*p, v*q - 3 = -4*p. Let 371*u - 78*u**p + 280*u + 2*u**3 - 220*u - 4394 + 583*u = 0. What is u?
13
Let i(u) be the second derivative of -2 + 4*u - 1/20*u**4 + 0*u**2 + 1/10*u**3. Determine m, given that i(m) = 0.
0, 1
Let z = -17985 - -17985. Let q = -55 + 57. Factor z*m + 2/9 - 2/9*m**q.
-2*(m - 1)*(m + 1)/9
Suppose 4*k + 22*k - 78 = 0. What is h in -8 + 6*h + 22*h**2 + 20*h**2 + 30*h - 36*h**k + 28*h**4 - 62*h**2 = 0?
-1, 2/7, 1
Let p(r) = 11*r**4 - 26*r**2 - 32*r - 1. Let w(v) = 4*v**4 + 31*v**2 + 3*v**2 - 43*v**2 - 11*v. Let t(y) = 3*p(y) - 8*w(y). What is a in t(a) = 0?
-1, 3
Let o(l) be the first derivative of -154 - 60*l - 4/3*l**3 + 16*l**2. Determine s, given that o(s) = 0.
3, 5
Factor -2922 - 4*p**2 + 3*p**2 - 121*p + 3044.
-(p - 1)*(p + 122)
What is q in 17 + 598*q**3 - 35 + 21*q**2 - 3*q**4 - 601*q**3 + 3*q = 0?
-3, -1, 1, 2
Factor 13*b**2 - 8*b**3 + 10*b**3 - 11*b**2 + 0*b - 4*b.
2*b*(b - 1)*(b + 2)
Let q(s) be the first derivative of -34*s**2 - 132*s**3 - 847/4*s**4 - 1331/20*s**5 + 50 - 4*s. Find o, given that q(o) = 0.
-2, -2/11
Let h(b) = -31*b - 153. Let v be h(-5). Suppose 3 = z, 0 = -9*k + 5*k - v*z + 22. Determine y so that 0 + 0*y - 2/3*y**2 - 1/3*y**3 + 1/3*y**k = 0.
-1, 0, 2
Let r(y) be the third derivative of 0*y - 1/40*y**6 + 182*y**2 + 0*y**3 + 0 - 39/8*y**4 - 4/5*y**5. Suppose r(c) = 0. Calculate c.
-13, -3, 0
Let w(n) be the second derivative of n**5/70 - 94*n**4/21 - 379*n**3/21 - 190*n**2/7 - 1588*n. Suppose w(d) = 0. Calculate d.
-1, 190
Let x(h) be the first derivative of -4*h**3/3 + 4*h**2 - 4*h - 141. Let n(w) = 3*w**2 - 9*w + 6. Let y(l) = 3*n(l) + 2*x(l). Suppose y(c) = 0. Calculate c.
1, 10
Suppose -u + 2 + 9 = 0. Factor -u*r + 31*r + 45920*r**2 - 45919*r**2 + 100.
(r + 10)**2
Let h(m) be the first derivative of 2*m**5/35 - 13*m**4/7 - 22*m**3/7 + 162*m**2/7 - 8788. Factor h(p).
2*p*(p - 27)*(p - 2)*(p + 3)/7
Let l(p) be the first derivative of 2*p**5/5 - 7*p**4 - 178*p**3/3 - 114*p**2 + 111. Find d such that l(d) = 0.
-3, -2, 0, 19
Let b(w) = 95*w**3 + 401*w**2 - 457*w + 41. Let p(a) = 104*a**3 + 402*a**2 - 452*a + 42. Let f(o) = -6*b(o) + 5*p(o). Determine k, given that f(k) = 0.
-9, 2/25, 1
Suppose -d = 3*q - 21, 28*d - 28 = 29*d - 4*q. Let f(x) be the third derivative of 0 + 24*x**2 + 0*x + 1/24*x**5 - 5/16*x**4 + d*x**3. Factor f(s).
5*s*(s - 3)/2
Let d(p) be the third derivative of -1/12*p**4 + 1/60*p**6 + 0*p + 4*p**2 - 1/2*p**3 + 1/15*p**5 - 3 - 1/210*p**7. Suppose d(f) = 0. Calculate f.
-1, 1, 3
Let x = -293 - -295. Factor -3*c**2 + 350*c + 0*c**2 - c**2 + c**x - 2*c**2 - 6125.
-5*(c - 35)**2
Let k(c) be the third derivative of c**8/6720 - c**7/672 + c**6/180 - c**5/120 - 2*c**3 - 50*c**2. Let f(g) be the first derivative of k(g). Factor f(y).
