i(p) = -2*p**2 - 20*p + 40. Let a(j) be the first derivative of -j**3/3 - 7*j**2 + 27*j + 204. Let s(f) = 8*a(f) - 5*i(f). Factor s(q).
2*(q - 4)*(q - 2)
Let g be (-10)/770*-15*(-826)/(-177). Factor -17/11*x + g*x**2 - 6/11.
(x - 2)*(10*x + 3)/11
Let x = -670/29 - -361829/15660. Let q(y) be the third derivative of -1/270*y**5 + x*y**6 + 0*y + 0 + 0*y**3 - 1/108*y**4 + 1/945*y**7 - 23*y**2. Factor q(l).
2*l*(l - 1)*(l + 1)**2/9
Let 1467/8*w - 135/4 - 495/4*w**4 + 1341/4*w**3 + 75/8*w**5 - 741/2*w**2 = 0. What is w?
3/5, 1, 10
Determine x so that 225/4*x - 1/2*x**4 - 39/4*x**3 - 63/2 + 37/2*x**2 = 0.
-21, -2, 1/2, 3
Suppose 7*k - 21780 = -61323. Let h be (3/(42/4))/((-1345)/k). Suppose h*o**2 + 0 + 0*o + 3/5*o**4 + 9/5*o**3 = 0. Calculate o.
-2, -1, 0
Let y = -132445 + 1192013/9. Factor -22/9*l + 2*l**2 - 2/9*l**3 - 2/9*l**4 + y.
-2*(l - 1)**3*(l + 4)/9
Let k = 931701/7 - 133059. Determine y, given that -33/7*y**4 + 0 + 0*y - 1/7*y**5 - k*y**3 - 256/7*y**2 = 0.
-16, -1, 0
Let 13064/9*c - 4232/9 - 1250/9*c**4 + 7100/9*c**3 - 4894/3*c**2 = 0. What is c?
1, 46/25
Suppose 20*o + 4*o = 54*o - 90. Let u(n) be the first derivative of -39 + 5/3*n**2 + 0*n + 5/12*n**4 + 5/3*n**o. Factor u(s).
5*s*(s + 1)*(s + 2)/3
Let s(t) = 31*t**3 + 7*t**2 - 12*t + 6. Let u(j) = 5*j**3 + 2*j**2 - 2*j + 1. Let o(i) = s(i) - 6*u(i). Determine d, given that o(d) = 0.
0, 5
Let p(a) be the second derivative of -a**5/110 + 34*a**4/33 + a**3/33 - 68*a**2/11 - 173*a. Suppose p(h) = 0. Calculate h.
-1, 1, 68
Let o(y) = -20*y**2 - 2622*y + 28. Let f(z) = -13*z**2 - 1748*z + 18. Let h(u) = 14*f(u) - 9*o(u). Suppose h(n) = 0. Calculate n.
-437, 0
Let g be (-1)/2 + 11/2. Factor -3*z**2 - 16*z**4 - 19*z**5 + 14*z**3 + z**2 - 13*z**g.
-2*z**2*(z + 1)*(4*z - 1)**2
Suppose -1/5*j**3 + 75*j - 746/5 + 372/5*j**2 = 0. What is j?
-2, 1, 373
Let c be ((-36)/(-306))/(72/1428). Suppose 6*u = 8*u. What is z in u*z**4 - 2*z**2 - c*z**3 + 0 + 0*z + 1/3*z**5 = 0?
-2, -1, 0, 3
Let i(t) be the third derivative of t**7/105 - 7*t**6/60 + 17*t**5/30 - 17*t**4/12 + 2*t**3 - 841*t**2. Factor i(b).
2*(b - 3)*(b - 2)*(b - 1)**2
Find a, given that -2636/3*a + 2102/3*a**2 - 2/3*a**4 - 520/3*a**3 + 352 = 0.
-264, 1, 2
Let j(d) be the second derivative of -d**7/84 + 3*d**6/10 + 3*d**5/40 - 13*d**4/6 - 3*d**3 + 5*d + 255. Determine c, given that j(c) = 0.
-1, 0, 2, 18
Let z(i) be the second derivative of 13*i**5/20 - 5*i**4/2 + 7*i**3/2 - 2*i**2 - 354*i. Find y, given that z(y) = 0.
4/13, 1
Find w, given that -2304 - w**3 + 1082*w**2 + 1125*w**2 - 2283*w**2 - 804*w = 0.
-64, -6
Let n(q) = -q**2 - 79*q - 132. Let x be n(-34). Let c = x + -15368/11. Factor -4/11 - c*k + 8/11*k**2 + 6/11*k**3.
2*(k - 1)*(k + 2)*(3*k + 1)/11
Let r(c) be the first derivative of 5*c**3/3 + 85*c**2 + 840*c - 624. Factor r(h).
5*(h + 6)*(h + 28)
Solve -16*i**4 - 14928*i - 8220*i**3 + 2720 + 23624*i**2 - 40*i**4 - 31*i**4 - 13*i**4 = 0.
-85, 2/5, 2
Let b(c) be the first derivative of 5*c**4/4 + 325*c**3 - 1480*c**2 + 1980*c + 978. Solve b(n) = 0.
-198, 1, 2
Let w = -6 - -6. Let p(b) = b**2 + 88*b - 1426. Let x be p(-102). Solve w*f - 3/2*f**x + 0 = 0 for f.
0
Let f(r) = -17*r**3 + 108*r**2 - 508*r + 22. Let y(v) = -9*v**3 + 54*v**2 - 255*v + 12. Let u(n) = 6*f(n) - 11*y(n). Factor u(w).
-3*w*(w - 9)**2
Suppose 0 = 6*y + 127 - 43. Let t be 21/y + 0 + (2 - 0). Factor -2 + t*i**2 + 0*i.
(i - 2)*(i + 2)/2
Let y be (-9 - (-4 - -1))*(17/(-8) + 2). Let d(i) be the first derivative of -1/5*i**5 + 0*i + y*i**4 + 0*i**2 - 1 - 2/3*i**3. Factor d(m).
-m**2*(m - 2)*(m - 1)
Suppose 44*g + 33189 + 44779 = 0. Let t = 1775 + g. Find h such that 4/3*h**4 - 26/3*h**t + 20*h**2 - 56/3*h + 16/3 = 0.
1/2, 2
Let i be -3*26/(-90) + 2/15. Let l(c) be the first derivative of 0*c + i + 1/4*c**3 + 0*c**2. Factor l(m).
3*m**2/4
Let v be (18/(-30))/((-2)/20). Let k = 60 + -56. Let -10*y**5 + k*y**3 - v*y + 12*y**5 + 6*y**4 - 2*y**2 - 2 - 2*y**2 = 0. Calculate y.
-1, 1
Let y be -53 - 42/12*2. Let s be -5 + (4 - y/50). Find f such that -7/5*f**2 + 3/5 + f**3 - s*f = 0.
-3/5, 1
Let -2214/5*k**2 - 1494/5*k**3 - 2/5*k**5 + 0*k + 0 - 258/5*k**4 = 0. What is k?
-123, -3, 0
Let s be ((-25)/15)/((-65)/117). Let k(z) be the first derivative of -7/2*z**4 + 8*z - 38/3*z**s + 15 - 8*z**2. Find h such that k(h) = 0.
-2, -1, 2/7
Let d be ((264/(-32) - -6)/(-8 - -11))/(6/(-18)). Factor -5/4*w + 0 - 1/4*w**4 + d*w**2 - 3/4*w**3.
-w*(w - 1)**2*(w + 5)/4
Factor 3/2*o**2 + 135*o - 273/2.
3*(o - 1)*(o + 91)/2
Suppose 360*u + u**2 + 504 - 1983 + 174 + 581 = 0. What is u?
-362, 2
Let r(w) be the first derivative of w**4/4 - 2*w**3/3 - 99*w**2/2 - 1319. Solve r(x) = 0 for x.
-9, 0, 11
Let j = 726 + -738. Let o be (44/55)/(j/(-30)). Find k, given that -3/4*k + 1/8*k**5 + 0 - 3/8*k**3 + 3/8*k**4 - 11/8*k**o = 0.
-3, -1, 0, 2
Let x(h) be the third derivative of -h**6/24 + 2*h**5 - 475*h**4/24 - 2*h**2 + 455. Factor x(b).
-5*b*(b - 19)*(b - 5)
Let v(a) be the first derivative of -79 - a**3 + 33/2*a**2 + 36*a. Let v(m) = 0. Calculate m.
-1, 12
Let o(b) = -8*b**5 - 36*b**4 - 120*b**3 - 132*b**2 + 4*b. Let j(g) = 25*g**5 + 107*g**4 + 358*g**3 + 397*g**2 - 13*g. Let y(p) = 4*j(p) + 13*o(p). Factor y(l).
-4*l**2*(l + 2)*(l + 4)**2
Let n be (144 - 159) + ((-223)/(-14) - 352/(-616)). Factor 1/6*w**2 + 0 + n*w.
w*(w + 9)/6
Let n(j) = 3*j**4 - 33*j**3 - 338*j**2 - 812*j - 656. Let h(k) = 2*k**4 - 22*k**3 - 225*k**2 - 542*k - 437. Let s(r) = 24*h(r) - 15*n(r). Factor s(o).
3*(o - 18)*(o + 2)**2*(o + 3)
Let f(m) be the second derivative of m**4/27 - 28*m**3/27 - 784*m**2/9 - 3365*m. Let f(p) = 0. What is p?
-14, 28
Let b(a) be the second derivative of a**4/6 + 97*a**3/3 + 546*a**2 - 3809*a. Solve b(y) = 0.
-91, -6
Let f = 13847 + -13845. Let r(q) be the third derivative of -6*q**f - 1/48*q**4 + 0*q + 1/18*q**3 + 1/720*q**6 + 0 + 0*q**5. Let r(o) = 0. What is o?
-2, 1
Find t, given that -535*t + 1504*t**2 + 2607*t + 688 - 620*t**2 + 10*t**3 = 0.
-86, -2, -2/5
Let a be (-75)/((-3375)/72) - 172/120. Factor a*o**3 - o**2 + 0 + 0*o.
o**2*(o - 6)/6
Suppose -67*b = 124*b - 239 - 143. Let g(p) be the first derivative of 11 + p**3 + 3/2*p**b - 6*p. What is k in g(k) = 0?
-2, 1
Factor 1/4*o**5 + 83/2*o**4 + 94864 + 73612*o + 7825/4*o**3 + 19651*o**2.
(o + 4)**3*(o + 77)**2/4
Let i be (13 - 18)*((0 - (-4 - 3)) + -13). Factor -3/2*y**2 + i*y + 66.
-3*(y - 22)*(y + 2)/2
Factor 5/3*d**2 + 2420/3*d - 2435.
5*(d - 3)*(d + 487)/3
Let a(c) be the second derivative of 0 - 104/21*c**3 - 9*c - 5/14*c**5 + 145/42*c**4 + 20/7*c**2. Suppose a(b) = 0. What is b?
2/5, 5
Let x = 9949/85775 + -27/235. Let u = x + 2188/1825. Solve -u*h**2 + 9/5*h + 9/5*h**4 - 3/5 - 6/5*h**3 - 3/5*h**5 = 0.
-1, 1
Find c, given that 4180*c + 2*c**2 + 3*c**2 + 235713 + 408505 + 229402 = 0.
-418
Let o(c) be the second derivative of -5*c**5/4 + 415*c**4/12 - 115*c**3/3 - 80*c**2 + 20*c + 39. Determine n so that o(n) = 0.
-2/5, 1, 16
Let q(w) be the first derivative of w**3/12 - 935*w**2/4 + 874225*w/4 - 767. Factor q(i).
(i - 935)**2/4
Let i(b) = 8743*b**2 - 2656*b + 54. Let k(z) = -1747*z**2 + 531*z - 11. Let j(w) = -3*i(w) - 14*k(w). Suppose j(g) = 0. What is g?
4/253, 2/7
Let a(p) be the first derivative of -p**4/8 + 15*p**3 - 567*p**2 + 5292*p - 715. Factor a(j).
-(j - 42)**2*(j - 6)/2
Let d be (-15)/((-420)/(-16)) - 25/(-7). Suppose d*s = -s + 8. Let -2/3*b - 2*b**s + 2 + 2/3*b**3 = 0. What is b?
-1, 1, 3
Let l(f) be the first derivative of f**3/3 - 366*f**2 - 1468*f + 3797. Solve l(s) = 0 for s.
-2, 734
Suppose -2*c + 48 = -300*v + 308*v, -2*c + v - 6 = 0. Factor 4/3*x**3 - 8/3*x**2 + c*x - 1/6*x**4 + 0.
-x**2*(x - 4)**2/6
Let t(z) = z**4 - z**3 - z**2 + 2*z + 1. Let b(g) = -3*g**4 - 33*g**3 + 209*g**2 - 266*g - 1. Let s(m) = -2*b(m) - 2*t(m). Let s(u) = 0. Calculate u.
-22, 0, 2, 3
Suppose -49*i = -47*i + 3*m - 19, 0 = -5*m + 25. Let -32/11*s - 34/11 + 2/11*s**i = 0. Calculate s.
-1, 17
Let n(t) be the second derivative of -t**7/1050 + t**6/225 + t**5/30 - t**4/5 + 30*t**3 + 4*t + 10. Let p(o) be the second derivative of n(o). Factor p(f).
-4*(f - 3)*(f - 1)*(f + 2)/5
Let v be ((-3)/(-2))/(12/4). Let b = 44003 - 88005/2. Factor -v*x**2 - x + 0 + b*x**3.
x*(x - 2)*(x + 1)/2
Let l(k) be the third derivative of 7/660*k**6 - 3 + k**2 + 1/66*k**5