3
Suppose -3*q + 23 = 4*u, 12*u - 7*u - 30 = -4*q. Factor 2/7*t**4 + 0*t + 0 + 2/7*t**u - 4/7*t**3.
2*t**2*(t - 1)**2/7
Let i(z) be the first derivative of -z**4/30 - 62*z**3/45 + z**2/15 + 62*z/15 + 538. Determine v, given that i(v) = 0.
-31, -1, 1
Factor 2*p**3 + p + 652*p**4 + 8*p**2 + 6*p + 649*p**4 - p**5 + 2 - 1303*p**4.
-(p - 2)*(p + 1)**4
Let l(a) be the third derivative of -a**7/980 + a**6/28 - 9*a**5/20 + 7*a**4/4 - 22*a**3/3 - 44*a**2. Let x(j) be the first derivative of l(j). Factor x(p).
-6*(p - 7)**2*(p - 1)/7
Factor 0 + 4/9*l**3 + 16/9*l**2 - 2/9*l**4 + 0*l.
-2*l**2*(l - 4)*(l + 2)/9
Let -1/9*a**4 + 8/9*a**2 + 0*a + 0 + 2/9*a**3 = 0. Calculate a.
-2, 0, 4
Let x(f) be the third derivative of f**6/600 + 3*f**5/100 + f**4/8 - 5*f**3/6 + 434*f**2. Factor x(d).
(d - 1)*(d + 5)**2/5
Let b be ((-123)/6 + 20)/(3/(-2)). Determine t, given that -2*t**4 + 3/2*t**3 + 5/6*t**5 + 0*t + 0 - b*t**2 = 0.
0, 2/5, 1
Let k be (2/(-5))/((-342)/285). Determine q, given that -q**2 - q - k - 1/3*q**3 = 0.
-1
Let m = -17 + 14. Let j = m - -6. Factor 3*i**3 - j*i**3 - 3*i**3 - 12*i**3 + 12*i**4 + 3*i**2.
3*i**2*(i - 1)*(4*i - 1)
Let t(b) be the third derivative of b**5/60 - 21*b**4/4 + 1323*b**3/2 + 193*b**2. Suppose t(x) = 0. Calculate x.
63
Suppose 14 = -0*u + 7*u. Factor -o**5 - o**4 + 2*o**2 + u*o**3 - 2*o + 0 + o - 1.
-(o - 1)**2*(o + 1)**3
Let g(f) be the third derivative of f**7/630 + 43*f**6/360 - f**5/2 + 2*f**2 - 327*f. Factor g(i).
i**2*(i - 2)*(i + 45)/3
Factor 6/7*a**4 + 16/7*a**2 + 2*a**3 + 9/7*a + 1/7*a**5 + 2/7.
(a + 1)**4*(a + 2)/7
Let y(v) be the first derivative of 6/7*v**2 + 19 + 2/7*v**3 - 24/7*v - 3/28*v**4. Factor y(c).
-3*(c - 2)**2*(c + 2)/7
Let a(v) = 11*v**2 - 20*v + 20. Let x(s) be the second derivative of -10*s**4 + 110*s**3/3 - 110*s**2 + 8*s. Let g(h) = 65*a(h) + 6*x(h). Solve g(m) = 0 for m.
2
Let s be ((-1)/4)/(1 + -2 - -2)*-2. Factor 1/2*h**4 + h**3 - s*h**2 + 0 - h.
h*(h - 1)*(h + 1)*(h + 2)/2
Let s = -12 - -15. Suppose -s*d + m + 16 = 0, 3*m - 12 = 3*d - 6*d. Factor 7*t**5 + 3*t + 4*t**3 - 10*t**3 - 3*t**5 - t**d.
3*t*(t - 1)**2*(t + 1)**2
Let i(f) be the third derivative of 2*f**7/105 + f**6/15 - 7*f**5/15 + 2*f**4/3 + 180*f**2. Factor i(x).
4*x*(x - 1)**2*(x + 4)
Factor -1/2*o**2 + 24*o + 49/2.
-(o - 49)*(o + 1)/2
Let c = 1761 - 1759. Let -4/7*b - 6/7 + 2/7*b**c = 0. Calculate b.
-1, 3
Let x(m) be the third derivative of -m**7/1785 - m**6/85 + 13*m**5/510 + 8*m**2 + 7*m. Factor x(y).
-2*y**2*(y - 1)*(y + 13)/17
Let v = -7 + 11. Let a(l) = -2*l + 3. Let k be a(0). Factor j**5 + 7*j**2 + 2*j - 7*j**4 + 10*j**v + 2*j**4 + 9*j**k.
j*(j + 1)**3*(j + 2)
Let d be (-2 - 0)/(-1) - 0. Factor 12*g - 8*g**d + 5 - 1 + 0 - 26*g.
-2*(g + 2)*(4*g - 1)
Suppose -42 - 68*x - 18*x**5 + 46*x**5 - 170*x**2 + 34 + 43*x**4 - 95*x**3 = 0. Calculate x.
-2, -1, -2/7, -1/4, 2
Let y(a) = -2*a**4 - 4*a**3 + 6*a**2 - 10*a + 4. Let u(z) be the third derivative of z**6/120 + 15*z**2. Let x(k) = -6*u(k) - y(k). Solve x(j) = 0 for j.
-2, 1
Factor 0*q + 0 + 1/2*q**3 + 0*q**2 + 1/8*q**4.
q**3*(q + 4)/8
Let p(h) = 3*h**3 + 45*h**2 + 205*h + 147. Let y(r) = -r**3 - 15*r**2 - 69*r - 49. Let f(w) = -3*p(w) - 8*y(w). Factor f(b).
-(b + 1)*(b + 7)**2
Let d(z) = -z**3 + 28*z**2 + 57*z + 92. Let t be d(30). Let -100/7 - 4/7*k**t + 40/7*k = 0. What is k?
5
Let g(r) be the second derivative of 0*r**2 - 2/21*r**7 - 2/3*r**3 + 20*r - 6/5*r**5 + 0 - 8/15*r**6 - 4/3*r**4. Factor g(u).
-4*u*(u + 1)**4
Let h(j) be the first derivative of -5/3*j**3 - 15/2*j**2 - 10*j - 15. Factor h(g).
-5*(g + 1)*(g + 2)
Let s(n) be the first derivative of 7*n**6/12 - 23*n**5/5 + 27*n**4/2 - 59*n**3/3 + 61*n**2/4 - 6*n + 12. Let s(q) = 0. Calculate q.
4/7, 1, 3
Let p(n) = 25*n**3 + 10*n**2 - 20*n - 15. Let y(v) = -v**4 + v**3 - v**2 + 1. Let d(r) = p(r) - 5*y(r). Factor d(i).
5*(i - 1)*(i + 1)*(i + 2)**2
Let d be (396/(-84) + 5)/(5/7). Let 2/5*z + 0 - 2/5*z**2 + d*z**4 - 2/5*z**3 = 0. Calculate z.
-1, 0, 1
Let i = 16 - 9. Factor -i*c**2 - 6*c**2 - c**3 - 2*c**3 + 19*c**2.
-3*c**2*(c - 2)
Solve -19*b**2 - 18*b**2 + 42 + 40*b**2 - 8*b - 25*b - 12*b = 0.
1, 14
Suppose -5*r + 1975 = 680. Suppose -r = 4*d - 11*d. Suppose 12*c**2 - 14*c**4 - 11*c**3 - 12*c**4 + d*c**3 + 34*c**4 - 6*c**5 = 0. Calculate c.
-1, -2/3, 0, 3
Let j = -3614/9 + 402. Let r be ((-4)/(-45))/(-6 + (-32)/(-5)). Let -2/9*o - r*o**5 - 2/9 - 2/9*o**4 + j*o**3 + 4/9*o**2 = 0. Calculate o.
-1, 1
Let h(f) be the third derivative of -f**6/600 + 7*f**5/100 - 7*f**4/15 + 6*f**3/5 - f**2 + 37. Factor h(g).
-(g - 18)*(g - 2)*(g - 1)/5
Let d(y) be the third derivative of 0*y**3 + 0*y - 25*y**2 + 2/35*y**7 - 4/15*y**6 + 0 + 1/3*y**4 + 1/5*y**5. Factor d(w).
4*w*(w - 2)*(w - 1)*(3*w + 1)
Suppose 2*w + 2*k + 2 = 0, 0 = 2*w + 3*k - 0 + 1. Let t be 3 + (-12)/(-3) + w. Factor 2*x**2 + 3*x - x**5 + 6*x**4 - 8*x**2 - 2*x**t.
-3*x*(x - 1)**3*(x + 1)
Let o(p) be the second derivative of -p**4/3 - 128*p**3/3 - 2048*p**2 - 211*p. Suppose o(v) = 0. Calculate v.
-32
Let 1/8*r**2 + 1/8*r - 5/2 = 0. Calculate r.
-5, 4
Let l = 322 + -129. Let r = l - 96. Factor r*v**3 + 23*v**2 - 6*v - 85*v**3 - 2*v**2.
3*v*(v + 2)*(4*v - 1)
Let p(j) = j**3 - 6*j**2 + j - 4. Let l be p(6). Find b such that -6*b + b - 4*b + 3*b**l + 0*b = 0.
0, 3
Let d(w) = w**5 - w**3 + w**2 - 1. Let i = 53 - 54. Let u(s) = -s**5 + 9*s**4 - 2*s**3 - 10*s**2 - 2. Let o(f) = i*u(f) + 2*d(f). Factor o(p).
3*p**2*(p - 2)**2*(p + 1)
Let y(p) be the second derivative of p**8/1120 - 11*p**7/840 + 13*p**6/240 - p**5/10 - 7*p**4/4 - 11*p. Let a(i) be the third derivative of y(i). Factor a(u).
3*(u - 4)*(u - 1)*(2*u - 1)
Let y(f) be the second derivative of 0 + 1/30*f**4 + 1/100*f**5 - 3/5*f**2 + 23*f - 1/6*f**3. Find g, given that y(g) = 0.
-3, -1, 2
Let d be (2 + (2 - -179))*121/76692. Let s = d + -1/332. What is g in 9/7*g**2 + 1/7*g**4 + g + s + 5/7*g**3 = 0?
-2, -1
Let j = 38 - 6. Determine h so that -74 + 35 - 2*h**2 + j*h - 104 + 15 = 0.
8
Suppose -30*o = -25*o. Let m(z) be the third derivative of 2*z**3 + o*z**4 + 0*z**6 + 0*z + 4*z**2 + 0 - 1/4*z**5 + 1/70*z**7. Solve m(b) = 0.
-2, -1, 1, 2
Suppose 5*k - 72 + 47 = 3*c, 2*k + 11 = -3*c. Let v(b) be the first derivative of 8 - 3/2*b**4 + 2*b**3 + 2/5*b**5 + 0*b - b**k. Factor v(d).
2*d*(d - 1)**3
Factor 44*s**2 + 4*s**4 - 7*s + 5*s**4 - 3*s**3 - 8*s**3 - 17*s - s**5 - 19*s**3.
-s*(s - 3)*(s - 2)**3
Let l(i) be the third derivative of -i**9/60480 + i**7/5040 + 13*i**5/60 - 22*i**2. Let a(f) be the third derivative of l(f). Determine k so that a(k) = 0.
-1, 0, 1
Let g = 2/21209 + 190865/169672. Factor 1/2 + 21/8*l**2 - 2*l - g*l**3.
-(l - 1)*(3*l - 2)**2/8
Let j(w) = -w**2 + 12*w + 38. Let m be j(14). Determine v, given that -m*v**3 - 5*v**4 - 165*v**2 - 6*v**3 - 34*v**3 - 200*v - 80 = 0.
-4, -1
Let 37/4*r + 0 + 1/4*r**2 = 0. Calculate r.
-37, 0
Let s(f) be the second derivative of f**7/28 - 39*f**5/40 - 3*f**4/2 + 25*f - 2. Solve s(b) = 0.
-3, -1, 0, 4
Suppose 34*y - 1554 = 20*y. Let b = -109 + y. Suppose -2/5*g + 4/5 - 2/5*g**b = 0. What is g?
-2, 1
Let i(c) be the second derivative of 2*c**6/15 - 17*c**5/5 - c**4 + 106*c**3/3 - 68*c**2 + 25*c. Find a, given that i(a) = 0.
-2, 1, 17
Let j(z) be the third derivative of -z**4/24 - 2*z**3/3 - 3*z**2. Let y be j(-8). Find o, given that -6*o**3 + y*o**3 - o**3 = 0.
0
Let a(r) = -r**2 - 4*r. Let q = 3 + -6. Let z be a(q). Suppose 2*t**2 - 2*t - z*t**2 + 3*t + 2 + 0 = 0. Calculate t.
-1, 2
Let b(d) be the first derivative of 2*d**3/15 - 4*d**2/5 - 2*d + 80. Factor b(w).
2*(w - 5)*(w + 1)/5
Suppose 49*t = 46*t - 3. Let z(o) = o**4 - o. Let d(v) = 11*v**4 + 10*v**3 + 5*v**2 - 6*v. Let j(q) = t*d(q) + 6*z(q). Factor j(c).
-5*c**2*(c + 1)**2
Let m(a) be the first derivative of -a**4 - 40*a**3/3 - 32*a**2 - 43. Factor m(p).
-4*p*(p + 2)*(p + 8)
Suppose -3*z + 5*d - 40 = 0, -2*z - 2*z + 4*d - 40 = 0. Let v(j) = -3*j - 11. Let x be v(z). Let -u**4 - u**2 - 3*u - u**4 + 3*u**3 + u**x + 2 = 0. Calculate u.
-1, 1, 2
Let r = 169/630 - -2/63. Let y(i) be the second derivative of 0 + 1/21*i**7 + 0*i**2 - 4*i + 1/15*i**6 - r*i**5 + 2/3*i**3 - 1/6*i**4. What is f in y(f) = 0?
-2, -1, 0, 1
Factor 3/4*u**3 + 117/4*u - 135/4 - 33/4*u**2.
3*(u - 5)*(u - 3)**2/4
Let a(z) be the first derivative of -1/11*z**3