- 1/24*x**6 + 0 + 0*x**3. Factor a(p).
p*(p - 2)**2*(p - 1)
Let h(d) be the first derivative of 0*d - 5/16*d**2 - 156 + 1/6*d**3 + 1/32*d**4. Factor h(a).
a*(a - 1)*(a + 5)/8
Let f(o) be the second derivative of -o**5/80 + 65*o**4/16 - 63*o**3 + 374*o**2 + 2*o + 11155. Factor f(m).
-(m - 187)*(m - 4)**2/4
Let x(m) be the third derivative of m**8/16 - 17*m**7/350 - 61*m**6/200 + m**5/4 + 13*m**4/20 - 4*m**3/5 + 733*m**2 - 2. Solve x(j) = 0 for j.
-1, -4/5, 2/7, 1
Let u be (-34)/374 + 910/572. Factor -1/2*b**3 - 3/2*b**2 + u + 1/2*b.
-(b - 1)*(b + 1)*(b + 3)/2
Let r be (2*((-1183)/112 + 10))/((-5)/10). Let m be 1*((3 - 1) + -2). Factor -3/4*d**2 + m - r*d.
-3*d*(d + 3)/4
Let x(p) be the second derivative of -p**6/45 + p**5/15 + 55*p**4/18 + 88*p**3/9 - 48*p**2 - 4426*p. Suppose x(c) = 0. Calculate c.
-4, 1, 9
Let y(j) be the first derivative of -2*j**3/33 - 270*j**2/11 - 36450*j/11 - 2698. Suppose y(s) = 0. What is s?
-135
Suppose -15/4*s**4 + 81/4*s**2 - 9/2*s**5 + 3/2 + 39/4*s + 51/4*s**3 = 0. Calculate s.
-1, -1/2, -1/3, 2
Let z(l) = l**2 + 4*l - 5. Let r be (-5)/(-2)*(4 - (3 + 3)). Let y be z(r). Let -t**2 - 5*t + 2*t + y*t + 2*t = 0. Calculate t.
-1, 0
Let y(z) be the second derivative of z**9/30240 - 11*z**8/53760 + z**7/3360 + 131*z**4/12 + 96*z + 2. Let m(u) be the third derivative of y(u). Factor m(g).
g**2*(g - 2)*(4*g - 3)/8
Let y be (36/(-15) - -3) + (-132)/(-55). Suppose -4*r = 0, -m - r + y = -0*m. Factor -2/5*j + 4/5*j**m + 7/5*j**2 + 0.
j*(j + 2)*(4*j - 1)/5
Suppose 120*m - 63 = 99*m. Suppose 4*a - 62 = 2*q - 50, -m*a = -3*q - 6. Solve -2/7*r + 4/7 - 4/7*r**q + 2/7*r**3 = 0 for r.
-1, 1, 2
Let h be 3 - 3*(-10)/10. Let s(f) be the third derivative of -1/120*f**h + 0*f + 21*f**2 + 0 - 1/30*f**5 + 0*f**3 + 0*f**4. Factor s(g).
-g**2*(g + 2)
Suppose 288*v = -120*v - 295*v. Suppose 2/13*w**5 + 70/13*w**3 + 0*w + 22/13*w**4 + v + 50/13*w**2 = 0. What is w?
-5, -1, 0
Suppose 18*r = -2*r + 620. Let b be 74/8 - (r - 25). Find k such that 3/4*k**2 + b*k - 5/2 = 0.
-5, 2/3
Let s(z) be the first derivative of z**6/3 - 12*z**5/5 - 3*z**4/2 + 40*z**3/3 - 12*z**2 - 4874. Factor s(b).
2*b*(b - 6)*(b - 1)**2*(b + 2)
Let t(n) be the second derivative of -n**7/273 - 2*n**6/195 + n**5/130 + n**4/39 + 125*n. Suppose t(g) = 0. Calculate g.
-2, -1, 0, 1
Let k(i) be the first derivative of i**7/560 - i**6/120 + i**5/80 + 2*i**3 + 3*i**2/2 + 53. Let n(m) be the third derivative of k(m). Solve n(a) = 0.
0, 1
Let f(i) = 23*i**2 + 10*i - 207. Let m(g) = 155*g**2 + 70*g - 1460. Let t(q) = -20*f(q) + 3*m(q). Factor t(c).
5*(c - 6)*(c + 8)
Let o(k) be the second derivative of k**6/360 - k**5/40 + k**4/12 + 2*k**3/3 - k**2 + 68*k. Let y(n) be the second derivative of o(n). Factor y(r).
(r - 2)*(r - 1)
Let w(z) be the first derivative of 1/6*z**3 + 305 + 13*z - 15/4*z**2. Factor w(t).
(t - 13)*(t - 2)/2
Factor 6716/17*o**3 - 6050/17 - 18812/17*o**2 + 18370/17*o - 226/17*o**4 + 2/17*o**5.
2*(o - 55)**2*(o - 1)**3/17
Solve -10033*b**4 - 72 + 72 - 604*b**3 + 9929*b**4 + 4*b**5 - 496*b**2 = 0.
-4, -1, 0, 31
Let v be -16 - (-46 - 6696/(-234)). Factor v*j - 2/13*j**3 + 10/13 + 6/13*j**2.
-2*(j - 5)*(j + 1)**2/13
Let d(s) be the first derivative of -9/8*s**4 - 38 + 0*s**5 + 0*s + 0*s**2 + 1/120*s**6 - s**3. Let n(o) be the third derivative of d(o). Factor n(m).
3*(m - 3)*(m + 3)
Let p(q) = 16*q**2 + 929*q - 4490. Let g(f) = 4*f**2 + 232*f - 1112. Let y(s) = 15*g(s) - 4*p(s). Factor y(m).
-4*(m - 5)*(m + 64)
Let j(p) = 105*p**4 - 9216*p**3 + 18414*p**2 - 9204*p + 33. Let x(z) = 16*z**4 - 1418*z**3 + 2833*z**2 - 1416*z + 5. Let u(i) = 5*j(i) - 33*x(i). Factor u(k).
-3*k*(k - 236)*(k - 1)**2
Factor -30*l**2 - 44*l - 133 + 5 - 245*l - 119*l - 142*l**2.
-4*(l + 2)*(43*l + 16)
Let v = -1/83241 - -110989/83241. Factor -v*s**3 + 8/3 + 2/3*s**4 - 2*s**2 + 8/3*s.
2*(s - 2)**2*(s + 1)**2/3
Let t(r) be the third derivative of -r**8/84 + 38*r**7/105 + 2*r**6/3 - 72*r**2. Suppose t(b) = 0. Calculate b.
-1, 0, 20
Let i = -36 + 35. Let z be (-8 + i)*((-32)/(-12))/(-8). Factor 1/3*l**z + 0 - 1/6*l**2 - 1/6*l**4 + 0*l.
-l**2*(l - 1)**2/6
Let n(p) = -5*p**4 - 33*p**3 + 90*p**2 + 2*p + 2. Let s(g) = -5*g**4 - 32*g**3 + 90*g**2 + 3*g + 3. Let o(c) = 3*n(c) - 2*s(c). Factor o(r).
-5*r**2*(r - 2)*(r + 9)
Solve 13*b**5 + 198*b**2 - 24*b**5 - 88*b**4 - 208*b**2 + 15*b**5 + 404*b**3 - 310*b**2 = 0.
0, 1, 5, 16
Let i be (-24)/48 + 503/30 + 1. Let b = -3307/195 + i. Solve -6/13*q + b + 2/13*q**2 = 0.
1, 2
Let d(p) be the third derivative of 0*p**4 + 0*p - 2/105*p**7 - 2/15*p**5 + 1/168*p**8 + 10 + 0*p**3 - 7/60*p**6 - 4*p**2. Let d(g) = 0. Calculate g.
-1, 0, 4
Suppose 7*p - 11*p + 84 = 0. Let r be (-2)/3 + 22757/p. Suppose 11 - 2 - 155*n + r*n**2 - 73*n + 3 = 0. Calculate n.
2/19
Let m(h) = h**3 - 4*h**2 + 2. Let i = 460 + -456. Let s be m(i). Factor 4/5*k - 6/5 + 2/5*k**s.
2*(k - 1)*(k + 3)/5
Let n(w) = -629*w + 3145. Let m be n(5). Let y(t) be the third derivative of m*t - 1/240*t**5 + 0 + 0*t**3 + 2*t**2 + 1/48*t**4. Factor y(c).
-c*(c - 2)/4
Let y = 480777 + -3365435/7. Let y - 2/7*x**2 + 2/7*x = 0. What is x?
-1, 2
Let w(z) = -2507*z + 52647. Let x be w(21). Factor 0 + 12*g**3 + x*g - 3/2*g**5 - 3/2*g**4 + 18*g**2.
-3*g**2*(g - 3)*(g + 2)**2/2
Factor -1224/5 - 2/5*f**2 - 1226/5*f.
-2*(f + 1)*(f + 612)/5
Suppose p = -3*p - v + 73, p - 4*v - 14 = 0. Suppose 2 + p = 5*d. Find b, given that -2*b + 139*b**3 - 287*b**3 + d*b**2 - 4*b**4 + 2*b**5 + 148*b**3 = 0.
-1, 0, 1
Factor -1008*y**2 - 283*y**3 + 17*y - 2706*y + 203*y**3 - 353*y - y**4 - 669*y**2.
-y*(y + 2)*(y + 39)**2
Suppose -s = 5*p - 321, 0 = -p + 5*p - 5*s - 251. Let y be (p - 64) + 2/11. Find c, given that -6/11*c**2 - 2/11*c**3 + y*c**4 + 4/11 + 2/11*c = 0.
-1, 1, 2
Let p(s) be the first derivative of -s**5 - 15*s**4/2 + 205*s**3/3 + 15*s**2 - 200*s + 1961. Suppose p(y) = 0. Calculate y.
-10, -1, 1, 4
Let a be 4063/478*12/68. Factor 1/2*t**3 - a*t + t**2 + 0.
t*(t - 1)*(t + 3)/2
Let u be (-204)/952*(-175)/15. Factor u*v**2 + 1/6*v**3 + 8*v - 32/3.
(v - 1)*(v + 8)**2/6
Solve -534/7*i - 2/7*i**3 - 14*i**2 - 774/7 = 0 for i.
-43, -3
Determine p so that 11471*p**2 + 10626*p**2 + 16*p - 22803*p**2 = 0.
0, 8/353
Let t(f) = f**3 + 7*f**2 - 1. Let q(v) = 5*v**3 - 190*v**2 + 120*v - 7. Let b(p) = 5*q(p) - 35*t(p). Factor b(u).
-5*u*(u + 120)*(2*u - 1)
Let u(y) be the second derivative of -y**5/5 + 23*y**4/4 - 257*y**3/6 + 30*y**2 + 2*y - 569. Factor u(p).
-(p - 12)*(p - 5)*(4*p - 1)
Let -93/7*z**2 + 183/7*z - 90/7 - 3/7*z**3 + 3/7*z**4 = 0. Calculate z.
-6, 1, 5
Let a(b) be the second derivative of -293*b**4/12 - 97*b**3/2 + b**2 - 12*b + 1. Find h such that a(h) = 0.
-1, 2/293
Let w = -64523 - -322651/5. Factor 0 + 3/5*z**2 + w*z.
3*z*(z + 12)/5
Let h be (-4)/1*(4/5 + (-155)/100). Factor 24/13*a**h + 0 + 20/13*a**2 + 2/13*a**5 + 6/13*a + 12/13*a**4.
2*a*(a + 1)**3*(a + 3)/13
Suppose -5*l + 17 - 7 = -4*r, -2*l + r = -4. Factor 56*u**2 - 105*u**l + 53*u**2 - 4*u**3.
-4*u**2*(u - 1)
Let s(z) be the second derivative of 1/480*z**6 + 0*z**2 + 1/20*z**5 + 1/2*z**4 - 12*z + 11/3*z**3 + 0. Let h(m) be the second derivative of s(m). Factor h(n).
3*(n + 4)**2/4
Suppose -5*z + 3*z + 26 = 4*x, 0 = 3*z - 5*x + 16. Factor 126*j**2 + 256 - 186*j**2 + 192*j + 9*j**z - 5*j**3.
4*(j - 8)**2*(j + 1)
Let b = 6202 + -6200. Let h(c) be the first derivative of 2/13*c - 8 + 2/13*c**b + 2/39*c**3. Find n, given that h(n) = 0.
-1
Suppose 3*p - 76*q + 79*q - 213 = 0, -142 = -2*p + 4*q. Suppose -3*r - p + 77 = 0. Factor -5*v**r + 0*v - 5/2*v**3 + 0.
-5*v**2*(v + 2)/2
Let i be (19/(-2660)*-50)/(5*(-4)/(-140)). Let i*c**4 - 80*c + 105/2 + 5*c**2 + 20*c**3 = 0. What is c?
-7, -3, 1
Let q be 2*135195/(-63) + (-2)/21. Let o = -81520/19 - q. Determine y so that 2/19*y**3 + 98/19*y - o*y**2 + 0 = 0.
0, 7
Let f(t) = -172*t**2 - 52972*t + 1232. Let x be f(-308). Determine i, given that x - 9/10*i**4 + 0*i**2 + 1/5*i**3 + 0*i = 0.
0, 2/9
Let o(l) be the third derivative of -l**5/60 + 171*l**4/4 - 1025*l**3/6 - 3*l**2 + 1392. Factor o(f).
-(f - 1025)*(f - 1)
Let k(x) be the second derivative of -x**5/16 - x**4/12 + 9*x**3/8 - 9*x**2/4 + 632*x. Factor k(m).
-(m - 1)*(m + 3)*(5*m - 6)/4
Let l(u) be the second derivative of -u**6/285 - 23*u**5/95 + 50*u**4/19 - 616*u**3/57 + 416