).
3*j*(j - 1)**2*(j + 1)/2
Let a(m) be the third derivative of m**5/80 - 7*m**4/16 + 45*m**3/8 + 245*m**2 - 2. Factor a(s).
3*(s - 9)*(s - 5)/4
Suppose 4*q - 10 = -2. Suppose -5*x + 3 = -q*x. Factor -4*m**2 + 1 - 4*m**3 + x - m**4 + 2*m**5 + 2*m + 3*m**4.
2*(m - 1)**2*(m + 1)**3
Let f be -6*(-3)/6*1. Factor 6*k**2 + 3*k - 8 + 8 + 3*k**f.
3*k*(k + 1)**2
Suppose -53 = 3*u + g - 65, 5*g - 15 = 0. Let i(o) be the third derivative of 5*o**2 + 0*o - 1/2*o**4 + 0*o**u - 1/15*o**5 + 0. Factor i(s).
-4*s*(s + 3)
Let g(s) be the second derivative of -s**8/84 + 2*s**7/35 - s**6/10 + s**5/15 + 5*s**2 + 5*s. Let m(b) be the first derivative of g(b). Factor m(z).
-4*z**2*(z - 1)**3
Let o(x) be the second derivative of 0*x**2 + 15*x - 1/10*x**5 + 1/3*x**4 + 0 + 0*x**3. Solve o(v) = 0 for v.
0, 2
Suppose -4*j + 110*k = 105*k + 15, 4*j - 9 = -3*k. Let z(t) be the second derivative of j - 1/5*t**3 - 4*t - 1/5*t**2 - 1/15*t**4. Factor z(q).
-2*(q + 1)*(2*q + 1)/5
Let y = 584 + -582. Let k(s) be the second derivative of 3/22*s**4 + 1/11*s**y + 0 - 2/11*s**3 + 12*s. Let k(p) = 0. What is p?
1/3
Let g(k) be the second derivative of 1/2*k**3 - 3/2*k**2 + 1/4*k**4 - 9*k + 0 - 3/20*k**5. Factor g(s).
-3*(s - 1)**2*(s + 1)
Let i(b) be the first derivative of -b**6/1080 - b**5/360 + b**4/36 - 11*b**3 + 1. Let a(f) be the third derivative of i(f). Suppose a(x) = 0. Calculate x.
-2, 1
Let t(n) be the third derivative of n**7/6300 - n**6/2700 - 7*n**3/6 + 17*n**2. Let x(f) be the first derivative of t(f). Suppose x(a) = 0. What is a?
0, 1
Let w(n) be the third derivative of n**6/30 + 14*n**5/15 + 32*n**4/3 + 64*n**3 + 62*n**2. Factor w(v).
4*(v + 4)**2*(v + 6)
Suppose 8/19*s - 2/19*s**2 + 90/19 = 0. Calculate s.
-5, 9
Find j such that -93/2*j + 0 - 3/2*j**2 = 0.
-31, 0
Suppose 12 = 10*z - 8*z. Let d(f) = f**3 - 7*f**2 + 8*f - 9. Let u be d(6). Find x such that -2*x**4 - 9*x**3 + x**4 - u + 4*x**4 + 3*x**3 + z*x = 0.
-1, 1
Let h = -21 - -24. Suppose -h*j + 4 = -j. Let -7*d**3 + 5*d**2 - 2*d**j + 4*d**3 = 0. What is d?
0, 1
Let w(z) be the first derivative of z**5/10 - z**4/6 - 2*z**3/3 - 5*z - 5. Let a(t) be the first derivative of w(t). Factor a(m).
2*m*(m - 2)*(m + 1)
Let i(o) = o**2 + 4*o - 7. Let p be i(-6). Suppose 5*j = p + 10. Solve 3*t**2 - 3*t - j*t + 1 + 2 = 0.
1
Let r(o) be the second derivative of o**7/2520 - o**6/720 - o**5/60 - o**4/2 - 2*o. Let n(v) be the third derivative of r(v). Let n(w) = 0. What is w?
-1, 2
Let g(a) be the first derivative of 0*a - 3/4*a**4 - 11 + 0*a**2 - 3/4*a**5 - 1/4*a**6 - 1/4*a**3. Factor g(d).
-3*d**2*(d + 1)**2*(2*d + 1)/4
Let q = 4118914/46655 - -8/6665. Let y = q + -88. Find l, given that 0 - 8/7*l**3 + 10/7*l**2 - 4/7*l + y*l**4 = 0.
0, 1, 2
Suppose -4*l + 2 = -2*s, -4*l + 3*s = -l. Let d = -183 + 187. Suppose d*j - 2*j**3 - l + 5*j**4 - 7*j**4 - 2*j + 3*j**4 = 0. What is j?
-1, 1
Suppose 0 = 29*q - 22*q - 28. Suppose 3 = -q*u + w + 12, -5*u = -w - 12. What is z in 0 + 8/9*z**5 - 10/9*z**2 - 2/9*z - 2/3*z**u + 10/9*z**4 = 0?
-1, -1/4, 0, 1
Let q be (99/(-1188))/(2/(-6)). Let p(j) be the second derivative of -6*j + 1/10*j**6 + 3/20*j**5 - q*j**4 + 0 + 0*j**3 + 0*j**2 - 1/14*j**7. Factor p(s).
-3*s**2*(s - 1)**2*(s + 1)
Suppose 0 + 1/5*g**3 - 9/5*g - 9/5*g**2 + 1/5*g**4 = 0. Calculate g.
-3, -1, 0, 3
Let z(o) be the second derivative of -2*o**6/75 + 13*o**5/25 + 3*o**4 + 94*o**3/15 + 32*o**2/5 - 18*o + 5. Solve z(i) = 0 for i.
-1, 16
Suppose -2*g + 50 = 2*o, -4*o + 5*g + 19 + 90 = 0. Suppose o*c - 25*c - 4 = 0. Factor 0 - 1/5*t**5 - 9/5*t**3 + t**c + 7/5*t**2 - 2/5*t.
-t*(t - 2)*(t - 1)**3/5
Let i(z) = -3*z**2 - 74*z + 182. Let p(x) = 6*x**2 + 143*x - 365. Let g(d) = -5*i(d) - 2*p(d). Factor g(c).
3*(c - 2)*(c + 30)
Let 6*d + 2/3*d**2 + 28/3 = 0. What is d?
-7, -2
Let c(y) be the third derivative of y**7/1680 - y**5/240 + 4*y**3/3 + 13*y**2. Let p(s) be the first derivative of c(s). Determine d, given that p(d) = 0.
-1, 0, 1
Let z(h) be the second derivative of 4*h**7/399 + 5*h**6/57 + 3*h**5/95 - 204*h. Solve z(w) = 0.
-6, -1/4, 0
Suppose 0 = -3*n + b - 7, -3*n = 4*b + 17 - 0. Let w be n/(-12)*4*0. Factor -60*v - 36 - 3*v**3 + 0*v**3 - 28*v**2 - v**3 + w*v**3.
-4*(v + 1)*(v + 3)**2
Suppose v = -4*o - 19, 4*v - o + 3 = -5. Let y be 0 - v/((-18)/(-28)). Factor y*s**3 - 4 + 58/3*s - 20*s**2.
2*(s - 3)*(s - 1)*(7*s - 2)/3
What is r in -296/3*r**2 + 32/3 - 66*r**4 - 566/3*r**3 + 104/3*r = 0?
-2, -1, -2/9, 4/11
Let h(p) be the second derivative of p**6/600 - p**5/150 - p**4/30 + 4*p**3/15 - 6*p**2 - 7*p. Let c(w) be the first derivative of h(w). Factor c(g).
(g - 2)**2*(g + 2)/5
Let s = -5785 - -5788. Factor 0*p + 0 - p**2 + 1/2*p**4 + 1/2*p**s.
p**2*(p - 1)*(p + 2)/2
Let u be (-10)/45 + (-87)/(-27). Solve i**3 - 2*i**2 + i**u + 4*i - 2*i**2 - 2*i**2 = 0.
0, 1, 2
Factor -4*r**2 - 23938 + 23938 + r**3.
r**2*(r - 4)
Let p(o) be the first derivative of o**6/24 + o**5/20 - 3*o**4/8 - o**3/3 + o**2 - 332. Factor p(g).
g*(g - 2)*(g - 1)*(g + 2)**2/4
Let x = -155 - -159. Suppose 5*i - 4*r + 4 = 0, 0*r + x*r = 4. Find f, given that i*f + 0 - 2/9*f**2 + 2/9*f**4 + 0*f**3 = 0.
-1, 0, 1
Let i(h) be the third derivative of -h**6/40 - 3*h**5/20 + 2*h**3 - 98*h**2. Factor i(j).
-3*(j - 1)*(j + 2)**2
Let n(s) be the first derivative of 0*s**3 + 0*s**2 + 0*s**4 + 0*s + 10 - 3/5*s**5. Solve n(k) = 0 for k.
0
Let v(i) be the third derivative of i**6/360 - i**5/60 + i**4/24 + 23*i**3/6 + 14*i**2. Let o(m) be the first derivative of v(m). Suppose o(b) = 0. Calculate b.
1
Find o, given that 2/11*o**2 - 20/11 - 6/11*o = 0.
-2, 5
Factor -22 + 32*h - 2*h**2 - 13 + 2*h**3 - 6*h**3 + 22*h**2 - 13.
-4*(h - 6)*(h - 1)*(h + 2)
Let h(r) = -7*r + 57. Let j be h(9). Let p be (-7)/((-189)/j) - 96/(-27). Determine w so that -p*w + 8/3*w**2 + 4/3 - 2/3*w**3 = 0.
1, 2
Let c(i) = 15*i + 2. Let p be c(2). Suppose -36*a = -p*a. Determine s, given that -1/3*s**4 + 2/3*s + a*s**3 + s**2 + 0 = 0.
-1, 0, 2
Let j(u) = 2*u + 36. Let y be j(-17). Suppose -y*n + 11 - 5 = 0. Factor 0 + 0*a**n - 4/11*a**4 - 2/11*a**5 + 2/11*a + 4/11*a**2.
-2*a*(a - 1)*(a + 1)**3/11
Let b(h) be the second derivative of 1/45*h**4 + 0 + 0*h**3 + 1/150*h**5 - 14*h + 0*h**2. What is k in b(k) = 0?
-2, 0
Let y(l) = 5*l**5 + 17*l**4 - 26*l**3 + 5*l**2 + 21*l. Let u(m) = -m**5 - 3*m**4 + 5*m**3 - m**2 - 4*m. Let s(d) = -22*u(d) - 4*y(d). Factor s(v).
2*v*(v - 2)*(v - 1)*(v + 1)**2
Let u = -248 - -252. Let d(b) be the second derivative of -1/12*b**u + 0 - 1/40*b**5 + 3*b + 0*b**3 + 0*b**2 + 1/60*b**6. Factor d(j).
j**2*(j - 2)*(j + 1)/2
Let -1124*m**2 - 13*m**4 + 4*m**4 + 87*m**3 + 153*m + 935*m**2 - 42 = 0. What is m?
2/3, 1, 7
Factor 208*i**3 + 2*i**4 - 176*i**3 + 2*i**4.
4*i**3*(i + 8)
Let y be ((-4)/(-5) - 0)*(-45)/(-18). Factor -19*r + 36*r - 5*r**y - 17*r - 50*r**3 - 125*r**4.
-5*r**2*(5*r + 1)**2
Let c(f) = f**3 + 30*f**2 - 8*f. Let d(g) = 2*g**3 + 30*g**2 - 6*g. Let o(q) = 3*c(q) - 4*d(q). Find k such that o(k) = 0.
-6, 0
Let b(c) be the first derivative of 2*c**5/35 - 2*c**3/7 - 2*c**2/7 + 80. Factor b(x).
2*x*(x - 2)*(x + 1)**2/7
Factor -53*t**4 + 81*t**2 + 104*t**4 - 48*t**4 - 36*t**3.
3*t**2*(t - 9)*(t - 3)
Suppose 8*v = -72 - 96. Let y(h) = -h**2 - 26*h - 103. Let b be y(v). Factor i + 1/5 + 4/5*i**b.
(i + 1)*(4*i + 1)/5
Let w be -371 + 356 + (-191)/(-9). Factor -28/9*m**2 - 68/3*m - w.
-4*(m + 7)*(7*m + 2)/9
Suppose -3 = -4*q + 13. Suppose -5*o = -3*l - 4 - 12, -2*l - 14 = -4*o. Solve 2*f**3 - 2*f - q*f**2 + 0*f**3 + l*f**2 + 2 - f**2 = 0 for f.
-1, 1
Let s(f) be the first derivative of -f**5/10 + 5*f**4/8 - 2*f**3/3 + 28. Determine p so that s(p) = 0.
0, 1, 4
Let d(y) be the first derivative of -2*y**5/55 - 98*y**4/11 - 19208*y**3/33 - 490. Find p such that d(p) = 0.
-98, 0
Let j(c) be the second derivative of 0 + 0*c**2 - 29*c - 5/42*c**7 - 9/2*c**5 + 25/3*c**4 + 7/6*c**6 - 20/3*c**3. Factor j(o).
-5*o*(o - 2)**3*(o - 1)
Let j = -79720 + 877604/11. Let b = j + -62. Find s such that 0*s - b*s**2 + 2/11 = 0.
-1, 1
Determine p so that -1389/4*p**2 - 117/4*p**3 - 3/4*p**4 - 4743/4*p - 867 = 0.
-17, -4, -1
Let y(o) be the third derivative of o**6/240 + o**5/75 + o**4/240 - o**3/30 + 4*o**2. Factor y(w).
(w + 1)**2*(5*w - 2)/10
Factor 88/5*z**4 - 56/5*z**3 + 0*z - 6/5*z**5 + 0 + 0*z**2.
-2*z