ivative of s(i). Factor y(m).
-m*(m + 2)/6
Suppose 69*m = 76*m - 602. Factor 82*y - 16 + 4*y**2 + m*y - 156*y.
4*(y - 1)*(y + 4)
Let l(y) be the third derivative of y**6/120 + 45*y**5/4 + 50625*y**4/8 + 3796875*y**3/2 + 31*y**2 - 2*y - 30. Factor l(j).
(j + 225)**3
Let f be 1 + 21/(-3) + 6. Suppose 10*c - 5*c = -5*d + 45, f = -3*d + 12. Factor 2/13*t + 0*t**3 + 0 - 2/13*t**c - 4/13*t**2 + 4/13*t**4.
-2*t*(t - 1)**3*(t + 1)/13
Let j(i) = -i**3 - i**2 + 3. Let u be j(-2). Find q, given that -23*q**3 - 20*q**4 + 5*q + 10*q**2 + 14*q**5 - u*q**3 + 6*q**5 + 15*q**3 = 0.
-1/2, 0, 1
Let z(x) be the third derivative of 14*x - 1/60*x**6 - 7/25*x**5 - 14/15*x**3 + 2*x**2 - 17/20*x**4 + 0. Let z(p) = 0. What is p?
-7, -1, -2/5
Let h be -32 - -29 - 1*-5. Factor 14*n - 8*n - 30*n - 3*n**h + 27.
-3*(n - 1)*(n + 9)
Let s(u) be the second derivative of u**6/10 - 3*u**5/10 + u**3 - 3*u**2/2 + 227*u - 8. Factor s(k).
3*(k - 1)**3*(k + 1)
Let u = 182 + -181. Let x(k) = k**3 - k - 1. Let c(i) = -i**3 - 9*i**2 + 25*i + 79. Let t(a) = u*c(a) - 2*x(a). Solve t(g) = 0.
-3, 3
Let v(m) be the first derivative of -2*m**3/21 + 90*m**2/7 - 4050*m/7 + 2375. Factor v(l).
-2*(l - 45)**2/7
Let r(i) be the second derivative of -i**7/168 - 7*i**6/120 + 49*i**5/80 + 343*i**4/48 + 3242*i. Solve r(c) = 0.
-7, 0, 7
Let c be (6/(-28))/((-9)/(-540)*-18). Let o(z) be the first derivative of -12/7*z - 2/21*z**3 + 3 + c*z**2. Suppose o(w) = 0. Calculate w.
2, 3
Let t be ((-1)/4)/((-4)/48). Factor -352*z - 2*z**5 - 146*z**t + 0 + 13 + 8*z**4 + 115 + 344*z**2 + 20*z**4.
-2*(z - 4)**3*(z - 1)**2
Let f(p) be the third derivative of -p**8/141120 - p**7/2352 + p**5/60 - 37*p**4/24 - 38*p**2. Let n(s) be the third derivative of f(s). Solve n(y) = 0 for y.
-15, 0
Suppose -3*f - 3*s - 300 - 171 = 0, -5*f + 2*s - 806 = 0. Let r = f + 482/3. Factor -r + 2/3*g**2 - 4/3*g**3 + 0*g**4 + g + 1/3*g**5.
(g - 1)**3*(g + 1)*(g + 2)/3
Factor 2182*v - 808*v - 526 - 2*v**3 - 1750 - 220*v**2 + 188.
-2*(v - 3)**2*(v + 116)
Suppose 0 = -8*h - 5*h + 312. Factor -87*y + 16*y**2 + h - 4*y**3 + 16*y**2 + 35*y.
-4*(y - 6)*(y - 1)**2
Suppose -12*r + 18*r - 12 = 0. Determine x so that -18*x**2 - 5*x + 5 + 35*x**2 + 5*x**3 - 22*x**r = 0.
-1, 1
Let t(x) be the second derivative of 2/15*x**2 - 43/45*x**3 - 46/45*x**4 + 0 + 117*x - 47/150*x**5. Solve t(h) = 0 for h.
-1, 2/47
Let p(b) be the first derivative of -2*b**3/9 - 143*b**2/3 + 96*b - 9023. Factor p(k).
-2*(k - 1)*(k + 144)/3
Let x(r) = -r**3 + 4*r**2 + 9*r - 8. Let t be x(6). Let y = -23 - t. Factor -5*g**3 + 0*g**y + 3*g**5 + 2*g**5.
5*g**3*(g - 1)*(g + 1)
Suppose -y + 3*g + 2*g + 35 = 0, 3*y - g = 21. Let q(c) be the third derivative of 0 + 1/16*c**4 - 1/80*c**y + 0*c**3 - 1/160*c**6 - 6*c**2 + 0*c. Factor q(n).
-3*n*(n - 1)*(n + 2)/4
Let f(w) be the first derivative of 3*w**5/40 + w**4 + 13*w**3/4 + 9*w**2/2 + 70*w - 55. Let z(j) be the first derivative of f(j). Factor z(h).
3*(h + 1)**2*(h + 6)/2
Let s be ((-14)/55)/((-1456)/31200) - 12/(-22). Suppose -2/3*o**3 + s*o - 6 + 2/3*o**2 = 0. What is o?
-3, 1, 3
Let k(w) be the first derivative of -w**6/15 - 296*w**5/25 - 432*w**4/5 - 3424*w**3/15 - 1136*w**2/5 - 13756. Factor k(s).
-2*s*(s + 2)**3*(s + 142)/5
Let g = -319103/560 + 115/112. Let x = 569 + g. Determine q, given that -1/5*q**3 + 0 + 1/5*q + x*q**2 - 1/5*q**4 = 0.
-1, 0, 1
Suppose k - 20 = -16. What is h in -10*h**2 + 6*h**2 + k*h**4 + 6*h**5 + 2*h - 3*h**3 - 5*h**3 + 0*h = 0?
-1, 0, 1/3, 1
Let i be (1333/465 - 3)/(2/(-60)). Suppose -4*c + 6 = -2. Solve -8*o**c - 6/7*o + 4/7 + 114/7*o**3 - 8*o**i = 0 for o.
-1/4, 2/7, 1
Suppose k + 5*m - 17 = 0, -3*k - 1 + 16 = 3*m. What is w in 3 - 10*w**2 + k*w**4 - 5 + 8 + 2 = 0?
-2, -1, 1, 2
Let m(u) be the third derivative of -u**5/80 - 545*u**4/32 - 68*u**3 + 19*u**2 + 25*u. Factor m(h).
-3*(h + 1)*(h + 544)/4
Let j(y) be the third derivative of -y**6/72 - y**5/9 - 5*y**4/24 + 10*y**2 + 17. Find p, given that j(p) = 0.
-3, -1, 0
Suppose 2*p + 28*p - 25*p - 240 = 0. Let o(i) be the first derivative of 0*i**2 + 9*i**3 - 9/2*i**4 + 3/5*i**5 + 0*i + p. Factor o(b).
3*b**2*(b - 3)**2
Let u(k) = 100*k**4 - 1530*k**3 - 4860*k**2 - 4895*k - 1665. Let y(x) = -11*x**4 + 170*x**3 + 540*x**2 + 544*x + 185. Let r(l) = -6*u(l) - 55*y(l). Factor r(d).
5*(d - 37)*(d + 1)**3
Let m = 751350 - 3005235/4. Suppose -5/4*v**2 + m - 10*v = 0. Calculate v.
-11, 3
Let n be 31*-1 - (-122138)/3530. Factor 18/5*r - n*r**3 + 12/5*r**2 + 3/5*r**4 - 3.
3*(r - 5)*(r - 1)**2*(r + 1)/5
Let d(w) = 4*w**2 - 6*w + 21. Let o(b) = -5*b**2 + 5*b - 22. Let x = 271 + -275. Let u(l) = x*d(l) - 3*o(l). Factor u(s).
-(s - 6)*(s - 3)
Let b(g) be the first derivative of -g**6/10 - 27*g**5/25 - 33*g**4/10 - 6*g**3/5 + 69*g**2/10 + 9*g - 1244. Let b(q) = 0. Calculate q.
-5, -3, -1, 1
Factor -381 + 22*r**2 - 398*r**2 + 960*r + 64*r**3 + 182 - 4*r**4 - 701.
-4*(r - 5)**2*(r - 3)**2
Let f be 13/(130/24) + (-98)/245. Let r(i) be the first derivative of -1/9*i**3 - 4/3*i + 2/3*i**f + 18. Factor r(p).
-(p - 2)**2/3
Let q = -411632 + 411636. Suppose 3*c + 3/4*c**3 - 4*c**2 + 1/4*c**q + 0 = 0. What is c?
-6, 0, 1, 2
Let n(w) = w**3 - 2*w**2 + 2. Let i be n(2). Suppose -48*x + 34*x + 126 = 0. Determine r, given that x*r**i - 14*r**2 - 127 + 2*r**2 - 60*r - 173 = 0.
-10
Let i(f) be the first derivative of -68/5*f**5 + 0*f**2 + 33 - f**4 - 28/3*f**6 + 8/3*f**3 + 0*f. Let i(z) = 0. What is z?
-1, -1/2, 0, 2/7
Let i(o) = 83*o - 73. Let u be i(1). Let p be (-236)/(-295) - 8/u. Factor 0*r**3 + p + 0*r**2 + 0*r - 1/4*r**4.
-r**4/4
Let n = -110 - -141. Let p be n/(-62) + (-1)/(-2). Let -4/7*a**2 + 64/7*a**5 + 36/7*a**3 + 0 - 96/7*a**4 + p*a = 0. Calculate a.
0, 1/4, 1
Let a(x) be the first derivative of x**4 + 112*x**3/3 + 956. Factor a(u).
4*u**2*(u + 28)
Let u(o) be the first derivative of -7*o**6/60 - o**5/6 + o**4/6 - 56*o**2 + o + 22. Let d(y) be the second derivative of u(y). Factor d(v).
-2*v*(v + 1)*(7*v - 2)
Let k = 3383 + -3381. Let g(h) be the first derivative of 4/5*h**5 - 6 + 2/3*h**3 + 5/2*h**4 - 2*h**k + 0*h. What is x in g(x) = 0?
-2, -1, 0, 1/2
Let t(f) = -8*f**2 - 20*f + 18. Let c(w) = -7*w + 49. Let p be c(8). Let a(k) = -10*k**2 - 20*k + 17. Let m(d) = p*t(d) + 6*a(d). What is o in m(o) = 0?
2, 3
Determine p, given that -139*p**3 + 260*p**3 - 164*p - 125*p**3 + 80 + 88*p**2 = 0.
1, 20
Suppose -757*a + 1411 = -103. Factor -2/3*m**a + 2/3*m**4 - 2*m**3 + 2*m + 0.
2*m*(m - 3)*(m - 1)*(m + 1)/3
Suppose 7*s - 9*s - 8 = 0, -4*g + 54252 = -4*s. Factor -y**4 + 0*y**4 + y**5 - g*y + 13559*y + y**2 - y**3.
y**2*(y - 1)**2*(y + 1)
Let w(p) = 7*p**2 + 2*p. Let h(i) = 66*i**2 - 1035*i + 1050. Let b(x) = -h(x) + 9*w(x). Factor b(v).
-3*(v - 350)*(v - 1)
Let t = 485 - 483. Suppose -2981*i**3 - 48*i**4 - 4*i**4 + 2813*i**3 - 172*i**t - 58*i + 2*i**5 = 0. Calculate i.
-1, 0, 29
Let c(u) = 1693*u**2 + 5083*u + 40. Let z(b) = 846*b**2 + 2541*b + 21. Let k(m) = -3*c(m) + 7*z(m). Find w, given that k(w) = 0.
-3, -3/281
Let n be -2 - ((5 - 3) + 490/(-70)). Find u, given that n*u**3 + 6*u**2 + 24/7*u + 0 + 3/7*u**4 = 0.
-4, -2, -1, 0
Determine u so that 4127*u**2 - 38 - 232 - 4135*u**2 + 1082*u = 0.
1/4, 135
Let s be -2*(1 + -8) - 455216/34636. Factor s*y**2 + y + 0 - 1/7*y**3.
-y*(y - 7)*(y + 1)/7
Let f(u) be the third derivative of 1/45*u**5 - 34 + 1/36*u**4 - 4*u**2 + 11/1260*u**7 - 1/40*u**6 + 0*u - 1/12*u**3 - 1/1008*u**8. Let f(o) = 0. What is o?
-1/2, 1, 3
Let m = -61463 - -553177/9. Suppose -2/9*u**3 - 4/9 - m*u - 8/9*u**2 = 0. Calculate u.
-2, -1
Let k(t) be the first derivative of 36/5*t**2 - 172/15*t**3 + 12/25*t**5 + 22/5*t**4 + 0*t + 89. Solve k(n) = 0 for n.
-9, 0, 2/3, 1
Let r be 12*(-4 + (-15 - -7)). Let y = r - -147. Factor -2/3*o**2 + 0 - 2/3*o**y + 0*o.
-2*o**2*(o + 1)/3
Let p = -698 + 700. Factor 2 - 14*q**3 + 4 - 6 + 4*q**p.
-2*q**2*(7*q - 2)
Suppose 48 + 1/6*l**3 - 40/3*l - 17/3*l**2 = 0. What is l?
-4, 2, 36
Suppose -8*y - 7*y + 60 = 0. Factor 2790*q**4 - 5579*q**4 + 240*q**2 + 2784*q**y + 165 + 30*q**3 + 370*q.
-5*(q - 11)*(q + 1)**2*(q + 3)
Let 57 + 50 + 52*l + 62 - 4*l**2 - 217 = 0. What is l?
1, 12
Suppose -530 + 225 + 215 = 40*y - 170. Factor -52/3 - 28/3*n - 1/3*n**y.
-(n + 2)*(n + 26)/3
Let d(a) be the third derivative of -a**6/24 - 127*a**5/60 - 2