be the first derivative of r(p). Suppose f(u) = 0. What is u?
-3, -1, 0, 1
Let i be (-48*1)/((-15)/2). Let o = -2918 + 2920. Find j, given that -16/5*j - 2/5*j**o - i = 0.
-4
Factor 2/9*w + 10/9*w**3 - 4/9 + 16/9*w**2.
2*(w + 1)**2*(5*w - 2)/9
Let l be 3 + 101/(-84) - (-22)/77. Let y(n) be the third derivative of -2*n**2 + 0 - 5/24*n**4 + 0*n - l*n**3 - 1/120*n**5. Factor y(a).
-(a + 5)**2/2
Let u be (3 - 43)/(1430/(-44)). Suppose u*s - 2/13*s**2 - 14/13 = 0. What is s?
1, 7
Let h = -6 + 8. Let m = -321 + 322. Factor 4*w**4 - 3*w**h + w**2 - 2*w**4 - w**4 + m.
(w - 1)**2*(w + 1)**2
Let l be 20/(-12)*(-15)/50. Factor -3/4*y**3 - 1/4*y**4 + 1/4*y**5 - l*y + 0 + 5/4*y**2.
y*(y - 1)**3*(y + 2)/4
Let d(a) be the first derivative of 10*a**6/3 - 11*a**5 + 25*a**4/4 + 10*a**3/3 - 63. Determine s, given that d(s) = 0.
-1/4, 0, 1, 2
Let t(a) be the first derivative of -a**8/1176 + 2*a**7/735 - a**6/420 - 55*a**2/2 - 24. Let z(h) be the second derivative of t(h). Suppose z(s) = 0. What is s?
0, 1
Suppose -w + n + 4 = -0, n = -2*w + 5. Determine c, given that 8*c - w*c**2 - 6*c + 4*c**3 - 3*c = 0.
-1/4, 0, 1
Let g(h) be the first derivative of 196*h**5/5 - 105*h**4 + 96*h**3 - 32*h**2 - 60. Factor g(c).
4*c*(c - 1)*(7*c - 4)**2
Suppose -5*m = -4*k + 3*k - 132, -39 = -2*m + 5*k. Suppose -b - m + 27 = 0. Factor 0 + 2/5*c**2 + b*c + 2/5*c**4 - 4/5*c**3.
2*c**2*(c - 1)**2/5
Determine y so that 3/7*y**3 + 12/7 + 18/7*y**2 + 27/7*y = 0.
-4, -1
Suppose -20 = -10*q + 5*q. Suppose -3*w + 2 = 2*f - 14, 0 = 4*w - f - 3. What is s in -48*s**3 + 11*s**w + 3*s**q + 25*s**2 - 3*s**2 - 6*s + 18*s**4 = 0?
0, 2/7, 1
Let n(j) be the third derivative of 20*j**2 + 1/48*j**6 + 0*j + 0*j**3 + 0 + 0*j**4 - 5/24*j**5. Factor n(s).
5*s**2*(s - 5)/2
Let o(j) be the first derivative of j**4/4 - 73*j**3/3 + 684*j**2 - 1296*j - 104. Factor o(x).
(x - 36)**2*(x - 1)
Suppose 92*l - 71998 + 71170 = 0. Suppose -l*b**4 + 1/2*b**5 - 126*b**2 + 109/2*b**3 + 0 + 98*b = 0. What is b?
0, 2, 7
Let k(h) be the first derivative of -5*h**4/12 + 25*h**3/6 - 15*h**2 - 38*h - 1. Let c(v) be the first derivative of k(v). Factor c(a).
-5*(a - 3)*(a - 2)
Let b(z) be the second derivative of 9*z**5/50 - 29*z**4/10 + 17*z**3/5 + 27*z**2/5 - 6*z - 4. Factor b(h).
6*(h - 9)*(h - 1)*(3*h + 1)/5
Let l(q) = 2*q**4 - 2*q**3 - 10*q**2 - 6*q + 4. Let r(m) = 10*m**4 - 10*m**3 - 50*m**2 - 30*m + 22. Let v(o) = -22*l(o) + 4*r(o). Solve v(g) = 0.
-1, 0, 3
Let i = -48057 - -48060. Factor 12/11 - 2/11*g**i - 12/11*g**2 + 2/11*g.
-2*(g - 1)*(g + 1)*(g + 6)/11
Let v(k) be the third derivative of k**7/63 + 13*k**6/180 - k**5/15 - 5*k**4/9 + 8*k**3/9 + 42*k**2. Let v(g) = 0. What is g?
-2, 2/5, 1
Let j(b) = 274*b + 1644. Let i be j(-6). Factor 4/3*c**2 + i*c + 2/9*c**3 + 0.
2*c**2*(c + 6)/9
Let k be (2/(-11) - (-10)/55)/(7/7). Factor k*s - 2/15*s**2 + 0 - 4/15*s**3 - 2/15*s**4.
-2*s**2*(s + 1)**2/15
Let q(x) be the first derivative of 32/3*x**3 + 11 + 4/3*x**6 - 12*x + 18*x**4 + 44/5*x**5 - 8*x**2. Find b such that q(b) = 0.
-3, -1, 1/2
Factor 0*y - 6 + 3/8*y**2.
3*(y - 4)*(y + 4)/8
Solve -4/3*t**5 + 224/9*t**3 - 640/9*t**2 - 512/9*t + 0 + 40/9*t**4 = 0.
-4, -2/3, 0, 4
Let o = -387 + 387. Let z(g) be the third derivative of -1/60*g**5 + 1/120*g**6 + 0*g - 6*g**2 + 0 + o*g**3 - 1/12*g**4. Suppose z(r) = 0. What is r?
-1, 0, 2
Suppose 5*k + s + 3 = 43, 2*k - 28 = 2*s. Let c be -6 - (-22)/k*3. Factor 0*p - 1/3*p**2 + c.
-(p - 2)*(p + 2)/3
Let u be (-3 + (-24)/(-9))/(3/(-54)). What is d in -16*d**2 - 20*d**5 + u - 1 - 16*d**3 + 52*d**4 - 5 = 0?
-2/5, 0, 1, 2
Let j(c) be the second derivative of -c**4/66 + 20*c**3/33 - 100*c**2/11 - 186*c. Determine h, given that j(h) = 0.
10
Let s(a) be the first derivative of -3/10*a**4 - 4/5*a**2 + 3 + 0*a - 16/15*a**3. Factor s(c).
-2*c*(c + 2)*(3*c + 2)/5
Suppose v + 5*d = -25, 3*v - 3*d - 15 = -2*v. Let w(u) be the third derivative of 1/40*u**6 + 0*u**3 + 0 + v*u + 0*u**4 - 4*u**2 - 1/10*u**5. Factor w(n).
3*n**2*(n - 2)
Let p(b) be the third derivative of b**8/840 - b**6/150 + b**4/60 - 8*b**2. Suppose p(u) = 0. Calculate u.
-1, 0, 1
Let y(v) be the third derivative of v**8/2352 + v**7/147 + 17*v**6/420 + 13*v**5/105 + 37*v**4/168 + 5*v**3/21 - 86*v**2. Solve y(i) = 0 for i.
-5, -2, -1
Let p(f) = -10*f**3 + f**2 - f + 1. Let t be p(1). Let q = t + 11. Factor -13*m**2 + 14*m**q + 4 - 2 - 3*m.
(m - 2)*(m - 1)
Let g(b) be the first derivative of -2*b**3/9 + 4*b**2/3 - 8*b/3 - 144. Factor g(k).
-2*(k - 2)**2/3
Let b(s) be the third derivative of s**6/60 + 23*s**5/15 + 89*s**4/12 + 44*s**3/3 - 48*s**2. Factor b(w).
2*(w + 1)**2*(w + 44)
Let t(c) be the third derivative of 1/120*c**7 - 1/48*c**6 + 0*c - 1/1344*c**8 + 9/32*c**4 + 0 - 3/40*c**5 + 9/8*c**3 + 5*c**2. What is w in t(w) = 0?
-1, 3
Let h(w) be the first derivative of 2*w**3/45 - 152*w**2/15 + 11552*w/15 - 242. Factor h(m).
2*(m - 76)**2/15
Let d(w) = 2*w**2 + 178*w + 336. Let q(g) = 5*g**2 + 355*g + 670. Let z(n) = 5*d(n) - 3*q(n). Find h, given that z(h) = 0.
-33, -2
Let k = 8 - 7. Let l = 3 - k. Suppose -5*y + 4*y**2 - y - y**l + 7 - 4 = 0. What is y?
1
Let t(d) be the first derivative of 2*d**3/15 + 71*d**2/5 - 144*d/5 - 384. Factor t(q).
2*(q - 1)*(q + 72)/5
Let x(b) be the first derivative of 12 - 33/14*b**4 - 1/2*b**6 - 18/7*b - 24/7*b**3 + 87/14*b**2 + 18/7*b**5. Solve x(a) = 0.
-1, 2/7, 1, 3
Let q = -114 - -97. Let r(s) = -5*s**2 - 5*s - 6. Let p(x) = 10 + 14*x + 13 - 6 + 14*x**2. Let f(w) = q*r(w) - 6*p(w). Solve f(a) = 0.
-1, 0
Let a be (-4 - -5)/((-18)/(-8) + -2). Let j be (172/15)/a - (-27)/81. Suppose -2/5*y**2 - 32/5 + j*y = 0. Calculate y.
4
Let v(h) = 44*h**4 - 324*h**3 + 248*h**2 + 644*h - 28. Let f(u) = -8*u**4 + 59*u**3 - 45*u**2 - 117*u + 5. Let b(s) = -28*f(s) - 5*v(s). Factor b(r).
4*r*(r - 7)*(r - 2)*(r + 1)
Let q(p) = 8*p**4 + 12*p**3 - 4*p. Let r(a) = -3*a**3 - 2*a - 1. Let d be r(-1). Let z(m) = -m**4 + m. Let t(x) = d*z(x) + q(x). Suppose t(v) = 0. Calculate v.
-3, 0
Solve 4*s**3 - 30/7*s + 2/7*s**5 - 50/7 + 68/7*s**2 - 18/7*s**4 = 0 for s.
-1, 1, 5
Let i(s) be the third derivative of -s**5/30 - s**4/3 - 4*s**3/3 + 203*s**2. Find z, given that i(z) = 0.
-2
Let z(n) be the first derivative of n**5 + 5*n**4/2 - 5*n**3 - 10*n**2 + 20*n - 247. Let z(s) = 0. Calculate s.
-2, 1
Let h(t) be the third derivative of 24*t**2 + 35/24*t**4 + 1/24*t**6 + 0 - 5/2*t**3 + 0*t - 5/12*t**5. Factor h(c).
5*(c - 3)*(c - 1)**2
Let 0*g**3 + 229*g**4 - 14*g**3 - 6*g - 30*g**2 - 12*g - 231*g**4 = 0. What is g?
-3, -1, 0
Let f = 8 + -6. Let o be (6/9)/(f/6). Find r such that 3*r - r**2 + 5*r**2 + 9*r + o - 3*r = 0.
-2, -1/4
Suppose 0 = -2*k - k. Let s be 3*(15/(-35) + 43/84). Factor -1/4*d**2 + k + 0*d + s*d**3.
d**2*(d - 1)/4
Let g = 60856/5 + -12170. Factor 0 + 8/5*a + g*a**2 - 2/5*a**3.
-2*a*(a - 4)*(a + 1)/5
Let x(g) = g**3 + g**2 + g - 1. Let p(z) = -3*z**3 - 11*z**2 + 2*z + 6. Let q(w) = p(w) + 4*x(w). Let b be q(6). Factor -8*f**b + 12*f + 3 - 2 - 5.
-4*(f - 1)*(2*f - 1)
Let x(l) = l**2 + 2*l. Let d(v) = -3*v**2 - 30*v + 15. Let t(m) = d(m) + 6*x(m). Factor t(a).
3*(a - 5)*(a - 1)
Let u(w) = -7*w - 11 + 22*w + 2*w**3 - 8*w - 3*w - w**2. Let y(d) = d**3 - d**2 - 1. Let l(z) = -2*u(z) + 6*y(z). Factor l(p).
2*(p - 2)**2*(p + 2)
Let t(k) = -20*k - 300. Let v be t(-15). Let w(q) be the third derivative of 3/10*q**3 + 0*q - 1/10*q**4 + 12*q**2 + 1/100*q**5 + v. Let w(l) = 0. Calculate l.
1, 3
Factor 0*v - 2/13*v**5 + 0 - 18/13*v**4 - 40/13*v**2 - 48/13*v**3.
-2*v**2*(v + 2)**2*(v + 5)/13
Let s(a) be the second derivative of a**5/5 + 8*a**4/9 + 14*a**3/9 + 4*a**2/3 + 97*a. Solve s(l) = 0.
-1, -2/3
Let r(t) = -169*t - 5067. Let f be r(-30). Solve 0*k**f + 0*k + 2/11*k**2 - 2/11*k**4 + 0 = 0 for k.
-1, 0, 1
Let g(c) be the third derivative of c**8/1344 + c**7/420 - c**6/120 - c**5/120 + c**4/32 - 14*c**2 - 1. Factor g(o).
o*(o - 1)**2*(o + 1)*(o + 3)/4
Let b(p) be the first derivative of 6/7*p**2 - 3/28*p**4 - 1/7*p**3 - 25 + 12/7*p. Let b(d) = 0. Calculate d.
-2, -1, 2
Let 18/5*k**2 + 0 - 6/5*k**4 - 3*k**3 + 0*k + 3/5*k**5 = 0. Calculate k.
-2, 0, 1, 3
Suppose 873*w = 878*w. Factor 3*i**3 + w + 3/4*i**2 + 7/4*i**4 - 1/2*i.
i*(i + 1)**2*(7*i - 2)/4
Let j(l) = l**2 - 2*l - 1. Let o(d) = 10*d**2 + 62*d - 78*d + 10 - 18. Let n(a) =