ve of -1/32*k**4 - 1/480*k**6 + 0 + 0*k + 1/24*k**3 + 24*k**2 + 1/80*k**5. Suppose l(x) = 0. What is x?
1
Let u(y) be the first derivative of 1/3*y**3 + 1/24*y**4 + 4/3*y + 10 - 5/4*y**2. Determine k so that u(k) = 0.
-8, 1
Factor 9*k**3 - 32 + 56*k + 34 - 118*k**2 + 51*k**3.
2*(k - 1)**2*(30*k + 1)
Suppose 51*k**2 + 4*k**2 - 52*k**2 + 204*k = 0. What is k?
-68, 0
Let z(h) be the second derivative of -4*h**6/165 - h**5/10 + 13*h**4/22 - 29*h**3/33 + 5*h**2/11 - 31*h + 2. Find b, given that z(b) = 0.
-5, 1/4, 1
Suppose -5*d + 6*d = 0. Suppose -10*g + 3 = -y - 7*g, 2*y = -4*g + 14. Let 12/5*t**y - 9/5*t + d*t**2 + 3/5 = 0. What is t?
-1, 1/2
Factor 53/3*u**2 - 1/3*u**3 - 52/3*u + 0.
-u*(u - 52)*(u - 1)/3
Let d(p) be the third derivative of p**8/672 - 3*p**7/70 + 11*p**6/80 - 2*p**5/15 + 4*p**2 + 19*p. Factor d(w).
w**2*(w - 16)*(w - 1)**2/2
Factor 0*j + 1/5*j**5 - 1/5*j**4 + 0 + 1/5*j**2 - 1/5*j**3.
j**2*(j - 1)**2*(j + 1)/5
Suppose 0 = -274*j - 348*j + 1244. Determine d so that 2 + 1/2*d**5 + 11/2*d**j - 1/2*d**3 - 3/2*d**4 - 6*d = 0.
-2, 1, 2
Suppose -2*j = 0, 0*j - 576 = -4*z + 4*j. Let q be 0 - 15/(1 - 6). Factor 8*r**3 + z*r**2 - 3*r**q - 134*r**2.
5*r**2*(r + 2)
Factor 3*u**2 - 8*u + 7 - 9*u**2 + 10*u**2 - 3.
4*(u - 1)**2
Let i(h) be the third derivative of 5*h**8/336 - 5*h**7/42 + h**6/6 - h**2 - 7*h. What is s in i(s) = 0?
0, 1, 4
Let l be (-6)/10 - 238/(-280). Let r(i) be the first derivative of 3 - l*i**2 - 1/20*i**5 - 1/4*i**4 + 0*i - 5/12*i**3. Suppose r(n) = 0. Calculate n.
-2, -1, 0
Suppose -2 = 4*c - 2*g, -g - 1 = -4*c + 2*g. Let o(p) = 21*p**2 + 90*p + 99. Let l(d) = -3*d**2 - 13*d - 14. Let m(z) = c*o(z) - 15*l(z). Factor m(v).
3*(v + 1)*(v + 4)
Let h(i) be the second derivative of i + 1/2*i**2 + 0 + 1/9*i**3 - 1/36*i**4. Solve h(n) = 0.
-1, 3
Let m(f) = 14*f**2 - 28*f - 52. Let z(s) = 26*s**2 - 55*s - 104. Let h(y) = -11*m(y) + 6*z(y). Suppose h(v) = 0. Calculate v.
-2, 13
Let h = 717 - 714. Factor 0 - 1/2*m**h + 0*m - 4*m**2.
-m**2*(m + 8)/2
Let w be 140/3*(-21)/14. Let q be ((-15)/w)/((-12)/(-14)). What is g in 0 - 1/4*g**4 + 0*g + 1/4*g**2 - 1/4*g**3 + q*g**5 = 0?
-1, 0, 1
Let w(r) = r**3 + 8*r**2 - 4*r + 2. Let t be w(0). Let s be (-2)/(-4) + 106/12. Factor -2/3 - s*z**t + 5*z.
-(4*z - 1)*(7*z - 2)/3
Suppose 187*l = -186*l + 379*l - 18. Find h, given that 2/13*h**4 - 6/13 + 2/13*h**5 - 12/13*h**l + 4/13*h**2 + 10/13*h = 0.
-3, -1, 1
Let o(r) = -r**3 - 5*r**2 + 9*r - 32. Let w be o(-7). Factor -4*p - 1/4*p**3 + 7/4*p**2 + w.
-(p - 3)*(p - 2)**2/4
Let m(k) = 7*k**4 + 15*k**3 + 20*k**2 + 8*k - 4. Let o(q) = -8*q**4 - 15*q**3 - 19*q**2 - 7*q + 5. Let a(y) = -5*m(y) - 4*o(y). Suppose a(c) = 0. What is c?
-2, -1, 0
Let v be (-396)/(6 - 24) - 19. Factor 0*s**2 - 2/3*s**4 + 0 + s**v - 1/3*s.
-s*(s - 1)**2*(2*s + 1)/3
Let k = 35 + -33. Factor c**2 - 2*c**k + 183*c - 1 - 181*c.
-(c - 1)**2
Let g(b) be the first derivative of -b**5/25 + b**4/20 + b**3/5 - b**2/10 - 2*b/5 + 252. Factor g(t).
-(t - 2)*(t - 1)*(t + 1)**2/5
Let q(k) be the second derivative of -5*k**4/3 - 4*k**3/3 + k. Let y(i) = i**2 - 9*i + 16*i**2 - 47*i**2 - 3*i. Let w(g) = -7*q(g) + 5*y(g). Factor w(v).
-2*v*(5*v + 2)
Suppose 57 - 6 = 17*g. Let m(h) be the first derivative of -3*h**g - 3 + 2*h - 7/2*h**2. Factor m(o).
-(o + 1)*(9*o - 2)
Determine x so that 288 + 288*x**4 + 623*x**2 - 993*x**2 + 2346*x**2 - 1488*x - 1116*x**3 - 28*x**5 = 0.
2/7, 2, 3
Let o(y) be the second derivative of -9*y**5/28 + 19*y**4/28 - 2*y**3/7 + 481*y. Factor o(t).
-3*t*(t - 1)*(15*t - 4)/7
Let p = 22 - 1. Let c = 23 - p. Factor -y**5 - 6*y**2 + y**3 + c*y**4 + 8*y**2 - 4*y**2.
-y**2*(y - 2)*(y - 1)*(y + 1)
Let m be (-1)/(-5) - ((-964)/105 - -9). Let g(z) be the first derivative of -m*z**3 - 3/7*z**2 - 4 + 2/7*z. Solve g(k) = 0 for k.
-1, 1/4
Let g be (-2)/14*16*(5984/(-320) - -18). Determine x, given that g - 6/5*x**2 + 0*x - 2/5*x**3 = 0.
-2, 1
Find o such that -3750/13*o - 150/13*o**2 - 31250/13 - 2/13*o**3 = 0.
-25
Let q(p) be the first derivative of p**3 - 156*p**2 + 359. Factor q(y).
3*y*(y - 104)
Let o = -258 - -261. Let s(t) be the second derivative of 2/21*t**o + 3/35*t**6 + 0 + 0*t**2 - 8/35*t**5 - 4*t + 5/42*t**4. What is w in s(w) = 0?
-2/9, 0, 1
Let d(q) = -5*q + 1 + 75*q**2 - 76*q**2 - 3. Let v be d(-3). What is t in -4*t**4 - 3*t - 3*t**2 + 15*t**3 + t**4 - 2*t**4 - 4*t**v = 0?
-1/3, 0, 1
Let j be -6 - ((-506)/55*1)/((-6)/(-4)). Factor 0 - 2/5*r - j*r**3 + 8/15*r**2.
-2*r*(r - 3)*(r - 1)/15
Let u(q) be the first derivative of q**3 + 87*q**2/2 - 101. Let u(s) = 0. What is s?
-29, 0
Suppose -7*l - 60 = -10*l. Factor -5*w**4 - 30*w**2 - 2 + l*w**3 - 5 + 14*w + 2 + 6*w.
-5*(w - 1)**4
Let r = -267/4 + 3487/52. Let v be -4*(-3)/(-6) - -2*1. Factor -2/13*x**4 - 2/13*x**5 + 0 + r*x**3 + 0*x + v*x**2.
-2*x**3*(x - 1)*(x + 2)/13
Factor 2*p + 2/15*p**4 - 58/15*p**2 + 0 + 26/15*p**3.
2*p*(p - 1)**2*(p + 15)/15
Let a(o) = 2*o**2 - 26*o + 27. Let y be a(12). Let f(n) be the first derivative of -4 - 2*n - 2/3*n**y + 2*n**2. What is t in f(t) = 0?
1
Let n(m) = -19*m + 307. Let i be n(16). What is v in -4/7*v - 2/7*v**i - 6/7*v**2 + 0 = 0?
-2, -1, 0
Let c(b) be the second derivative of 0*b**2 - 1/18*b**4 - 1/20*b**5 + 1/18*b**3 + 0 - 9*b. Factor c(q).
-q*(q + 1)*(3*q - 1)/3
Let n(w) be the third derivative of w**6/60 - 7*w**5/10 - 35*w**4/6 - 16*w**3 + 754*w**2. Find j such that n(j) = 0.
-2, -1, 24
Let p(g) = -3*g. Let l be p(-1). Suppose -z = z + t - 10, -5*t = l*z - 15. Determine o so that -o**2 - 11*o**4 - 2 - o**z + o**3 + 12*o**4 + 2 = 0.
-1, 0, 1
Let p(k) = k**2 - 1. Let r(i) be the second derivative of -i**4/4 + i**3 + 2*i**2 - 6*i. Let j(s) = 12*p(s) + 3*r(s). Let j(a) = 0. Calculate a.
-6, 0
Let a(o) be the third derivative of o**8/40320 + o**7/5040 - o**6/480 + 11*o**5/60 - 8*o**2. Let k(r) be the third derivative of a(r). Factor k(x).
(x - 1)*(x + 3)/2
Factor -1/4*k**2 - 4*k - 16.
-(k + 8)**2/4
Let a(t) = -t**2 + 1. Let v(l) = -8*l**2 - 12*l - 11. Let b(f) = 1. Let y(h) = 4*b(h) + v(h). Suppose 12 - 2 = 2*p. Let w(c) = p*a(c) - y(c). Factor w(j).
3*(j + 2)**2
Let p(u) = -2*u**2 - 2*u**2 + 4*u**2 + u**2. Let g(f) = 6*f**2 - 1. Let k(h) = 3*g(h) - 15*p(h). Determine x so that k(x) = 0.
-1, 1
Let u be (-12)/(-7) + (-4)/(-14). Let y = -88 + 90. Suppose 2*g**5 - 2*g**4 - y*g**3 + u*g**2 - 22 + 22 = 0. Calculate g.
-1, 0, 1
Solve 4/3*u**4 + 2692/3*u**2 + 768 - 1600*u - 200/3*u**3 = 0.
1, 24
Let l be (-2)/4*-2*3. What is n in 3*n + 6*n**2 - 5*n**3 + n**l + 7*n**3 = 0?
-1, 0
Let l(t) be the second derivative of -t**6/6 - 3*t**5/2 - 65*t**4/12 - 10*t**3 - 10*t**2 + 29*t - 3. Factor l(y).
-5*(y + 1)**2*(y + 2)**2
Factor g**2 + 1/5*g**3 - 12/5 - 8/5*g.
(g - 2)*(g + 1)*(g + 6)/5
Let h(l) be the first derivative of -9/2*l**2 - l**3 + 27 - 6*l. Factor h(m).
-3*(m + 1)*(m + 2)
Let b(l) be the second derivative of l**7/840 - l**6/240 - 3*l**5/20 + l**4/6 + l**2 - 25*l. Let s(q) be the third derivative of b(q). Factor s(p).
3*(p - 3)*(p + 2)
Let f(m) be the third derivative of 2*m**7/35 + 39*m**6/10 + 1441*m**5/20 - 195*m**4 + 200*m**3 + m**2 + 225. What is x in f(x) = 0?
-20, 1/2
Let p(z) be the third derivative of 0*z**5 - 5/6*z**4 - 1/42*z**7 + 1/8*z**6 + 0 - 12*z**2 + 0*z**3 + 0*z. Suppose p(b) = 0. Calculate b.
-1, 0, 2
Let -67/8*q + 1/8*q**5 + 1/8*q**4 - 15/4*q**3 + 37/4*q**2 + 21/8 = 0. What is q?
-7, 1, 3
Find t such that -8*t**2 - 1183*t**5 + 8*t**4 + 594*t**5 - 2*t + 595*t**5 - 4*t**3 = 0.
-1, -1/3, 0, 1
Suppose 5*w + 20 = 7*w. Let q = w - 7. Let 4*h**4 + 17*h**q - 2 - 2*h**4 + 4*h - 21*h**3 = 0. Calculate h.
-1, 1
Let s(h) be the first derivative of h**6/27 + 2*h**5/45 - h**4/6 - 2*h**3/27 + 2*h**2/9 - 54. Find n such that s(n) = 0.
-2, -1, 0, 1
Let g(q) = 3*q**5 - 29*q**4 + 7*q**3 + 12*q**2 + 14*q. Let f(r) = 2*r**5 - 15*r**4 + 4*r**3 + 6*r**2 + 6*r. Let m(t) = 7*f(t) - 3*g(t). Factor m(i).
i**2*(i - 3)*(i - 1)*(5*i + 2)
Let w be 5/15*(1 + -1). Let y = w + 1. Factor z**2 - 5/2*z + y.
(z - 2)*(2*z - 1)/2
Let r be (98/105)/((-63)/(-27)). Factor 0 + r*h**3 + 2/5*h**4 + 0*h + 0*h**2.
2*h**3*(h + 1)/5
Let t(n) be the third derivative of n**6/1080 - 7*n**5/270 + 19*n**4/72 - 4*n**3/3 + 3*n**2 + 5*n. Factor t(m).
(m - 8)*(m - 3)**2/9
Let c = -140 - -77. Let r = c + 65. What is w in 2/11*