= 0. What is l?
-5, 0
Let p(d) be the second derivative of -d**8/2856 - d**7/595 + 7*d**2/2 + 45*d. Let w(b) be the first derivative of p(b). Factor w(k).
-2*k**4*(k + 3)/17
Let o(g) be the second derivative of -g**5/10 + 11*g**4/6 + 15*g**3 - 567*g**2 + 198*g. What is l in o(l) = 0?
-7, 9
Let n(d) be the third derivative of 2/15*d**5 - 16/3*d**3 + 0*d + 0 + 2/3*d**4 + 6*d**2 - 1/30*d**6. Solve n(g) = 0 for g.
-2, 2
Let b be 87/493 - (-217)/119. Factor -4/7*m + 0 - 1/7*m**b.
-m*(m + 4)/7
Let m = 3184 + -12731/4. Suppose 3/4*p**3 - 3/2*p**2 - 3/8 - 1/8*p**4 + m*p = 0. Calculate p.
1, 3
Let q(j) be the second derivative of -j**6/480 + j**5/30 - j**4/6 - 45*j**2/2 - 13*j. Let w(f) be the first derivative of q(f). Find a such that w(a) = 0.
0, 4
Let f(m) be the third derivative of 0*m - 1/13*m**3 - 8*m**2 - 1/39*m**4 - 1/390*m**5 + 0. Factor f(l).
-2*(l + 1)*(l + 3)/13
Factor -1728/7 - 3/7*z**2 + 144/7*z.
-3*(z - 24)**2/7
Suppose -5/2*u - 20*u**3 - 11*u**4 - 13*u**2 - 3/2*u**5 + 0 = 0. What is u?
-5, -1, -1/3, 0
Let a(f) be the first derivative of 2*f**6/15 - 24*f**5/25 + 9*f**4/5 - 66. Factor a(y).
4*y**3*(y - 3)**2/5
Let f = -37259389/135612 - 2/33903. Let t = -274 - f. Let -9/4*u**2 + 0*u + 0 + t*u**3 = 0. What is u?
0, 3
Let h(g) be the third derivative of -g**6/320 - g**5/40 + 3*g**4/64 + 9*g**3/8 + 152*g**2. Factor h(c).
-3*(c - 2)*(c + 3)**2/8
Factor -8/13*v**2 - 2/13*v**3 + 0 + 0*v + 10/13*v**4.
2*v**2*(v - 1)*(5*v + 4)/13
Let n(k) be the first derivative of k**6/15 + 4*k**5/25 - k**4/5 - 8*k**3/15 + k**2/5 + 4*k/5 + 35. Solve n(i) = 0.
-2, -1, 1
Factor -152*p - 2/3*p**2 - 8664.
-2*(p + 114)**2/3
Let g(x) be the third derivative of -3/44*x**4 + 0*x - 1/660*x**6 + 0*x**3 + 1/55*x**5 - 25*x**2 + 0. Suppose g(u) = 0. Calculate u.
0, 3
Let c = -41 - -50. Suppose -4*n**2 - 1 - c + 16*n - 10 + 4 = 0. What is n?
2
Let q(t) be the first derivative of t**8/336 - t**7/42 + 5*t**6/72 - t**5/12 + 3*t**3 - 13. Let r(f) be the third derivative of q(f). Factor r(x).
5*x*(x - 2)*(x - 1)**2
Let f = 88 + -142. Let w = f + 272/5. Factor 0 + w*p + 2/5*p**3 - 4/5*p**2.
2*p*(p - 1)**2/5
Factor 6/7*p**3 - 15/7*p**2 + 9/7*p**4 - 12/7*p + 0.
3*p*(p + 1)**2*(3*p - 4)/7
Let s(l) be the third derivative of 0*l + 8*l**2 + 0*l**4 - 1/150*l**5 + 1/120*l**6 + 1/1680*l**8 + 0 + 0*l**3 - 2/525*l**7. Find o such that s(o) = 0.
0, 1, 2
Let c(l) be the third derivative of -l**5/120 + l**4/24 + l**3/4 - 6*l**2 + 2. Factor c(y).
-(y - 3)*(y + 1)/2
Let b = -16 - -19. Suppose 0*j - 6 = -b*j. Factor d**3 + 9*d**j - 2 + 0 - d - 6*d**2 - d**4.
-(d - 2)*(d - 1)*(d + 1)**2
Let y(z) be the third derivative of 1/30*z**4 + 0*z**3 - 1/150*z**5 + 0*z + 0 - 13*z**2. What is j in y(j) = 0?
0, 2
Let a(b) be the third derivative of b**7/630 + 7*b**6/180 - 71*b**5/180 - 35*b**4/3 + 200*b**3 + 94*b**2. Factor a(w).
(w - 5)**2*(w + 12)**2/3
Let m(u) = -41*u**2 + 1104*u + 7. Let o(t) = -24*t**2 + 552*t + 4. Let a(s) = 4*m(s) - 7*o(s). Factor a(f).
4*f*(f + 138)
Suppose 16*s - 3 = -h + 15*s, -s = -3. Find c such that -2/5*c**2 - 4/5*c + h = 0.
-2, 0
Suppose -11 = -t + 5*y + 6, 19 = 5*t - 3*y. Factor 0*n**2 - 6*n + 3 + 0*n**2 + 3*n**t.
3*(n - 1)**2
Suppose 5 - 7 = 3*k - r, 0 = r + 4. Let v(p) = p**3 - p + 1. Let a(s) = -s**5 - 2*s**4 - 3*s**3 + 2*s - 2. Let d(l) = k*a(l) - 4*v(l). Factor d(w).
2*w**3*(w + 1)**2
Let w(p) = p**3 + p**2 - 3*p - 1. Let d be w(2). Factor -9*h**3 + 1 + 3*h**d + 14*h**2 - 1 - 20*h**2.
3*h**2*(h - 2)*(h + 1)**2
Suppose 5 = 6*u - 1. Find d, given that u - 14*d**2 + 3 + 31*d**2 - 18*d**2 = 0.
-2, 2
Suppose 0 = 4*i + 171 - 179. Let y(h) = -h**2 - 8*h + 12. Let a be y(-9). Factor -10/13*p - 4/13 - 2/13*p**a - 8/13*p**i.
-2*(p + 1)**2*(p + 2)/13
Let s = 558 + -3904/7. Factor -s + 1/7*w + 1/7*w**2.
(w - 1)*(w + 2)/7
Let l(x) be the first derivative of -x**4/2 - 20*x**3/9 - x**2 - 114. Let l(t) = 0. Calculate t.
-3, -1/3, 0
Let c = -15 - -18. Factor -15*v**2 + 5*v**2 + 7*v**2 - c + 6*v.
-3*(v - 1)**2
Let l(m) be the first derivative of 0*m - 1/6*m**4 - 7 + 2/27*m**3 + 2/9*m**2 + 1/27*m**6 - 2/45*m**5. Suppose l(c) = 0. Calculate c.
-1, 0, 1, 2
Let x = 24829/9 + -2757. Find v such that 32/9 + 2/9*v**2 - x*v = 0.
4
Let v(g) be the first derivative of 9*g**4/4 + 50*g**3 - 213*g**2/2 + 54*g + 365. Determine a, given that v(a) = 0.
-18, 1/3, 1
Let -68*p**4 + 73*p**4 - 24*p**2 + 19*p**2 = 0. What is p?
-1, 0, 1
Let p(q) be the third derivative of q**8/840 + 4*q**7/525 - 7*q**5/75 - 17*q**4/60 - 2*q**3/5 + 56*q**2 + 2. Factor p(n).
2*(n - 2)*(n + 1)**3*(n + 3)/5
Factor -6/11*s**4 + 0 + 0*s**2 + 0*s + 12/11*s**3.
-6*s**3*(s - 2)/11
Let r(n) be the third derivative of -n**8/24 + 11*n**7/105 - 8*n**6/105 + 2*n**5/105 + 309*n**2 - n. Solve r(m) = 0 for m.
0, 2/7, 1
Let q(b) be the first derivative of 4*b**3/3 - 2*b**2 - 8*b - 135. Factor q(c).
4*(c - 2)*(c + 1)
Suppose -4*b - 6 = 22. Let r(p) = -p - 4. Let m be r(b). Determine a so that 6*a + 0*a**5 + 0*a + 3*a**4 - 15*a**2 + 9*a**m - 3*a**5 = 0.
-2, 0, 1
Suppose 4*q = 2*q - 6*q. Determine l so that -6/5*l**3 + 2/5*l**5 - 2/5*l**2 + q + 4/5*l + 2/5*l**4 = 0.
-2, -1, 0, 1
Suppose 4*s + 9 = 7*s. Factor 2*a**3 + 3*a**4 + 0*a**3 - 4*a - s*a**2 + 2*a.
a*(a - 1)*(a + 1)*(3*a + 2)
Let g(c) be the third derivative of c**6/1080 + c**5/135 + 390*c**2. Determine b so that g(b) = 0.
-4, 0
Let p(c) be the second derivative of -c**7/70 + 21*c**5/100 + 3*c**4/10 - 110*c. Find h, given that p(h) = 0.
-2, -1, 0, 3
Solve -24*d**2 + 3*d**3 - 8 - 7*d - 26*d + 45 + 17 = 0.
-2, 1, 9
Solve 2*u**3 + 42*u + 272 + 9*u - 5*u**3 + 21*u**2 - 245 = 0 for u.
-1, 9
Let o be ((-3)/6)/(2 - 18/8). Let k(a) be the third derivative of 0*a**5 + 1/1155*a**7 + a**o + 0*a + 1/66*a**4 + 0 - 1/33*a**3 - 1/330*a**6. Factor k(z).
2*(z - 1)**3*(z + 1)/11
Let a(u) = -u**3 - 7*u**2 + 1. Let o(m) = 3*m**3 - 404*m**2 - 62208*m - 2985988. Let z(h) = -4*a(h) - o(h). Factor z(v).
(v + 144)**3
Let g(u) = 2*u + 1. Let d(k) = -k**2 - 10*k - 6. Let q(h) = -d(h) - 6*g(h). Factor q(w).
w*(w - 2)
Let q be (5/6 + 0)/(8100/45360). Factor -49/3 - q*b - 1/3*b**2.
-(b + 7)**2/3
Suppose 26 = y - 4. Let q = 75 - 55. Let 45*n + q + 42*n**2 + 18 - y + 3*n - 98*n**3 = 0. What is n?
-2/7, 1
Solve 6/11*r**3 + 2160/11*r - 234/11*r**2 + 2400/11 = 0.
-1, 20
What is c in -32/5*c**2 - 2/5*c**3 - 6*c + 0 = 0?
-15, -1, 0
Let q(b) = 23*b**2 + 50*b + 110. Let v(x) = -8*x**2 - 16*x - 36. Let l(n) = -6*q(n) - 17*v(n). Factor l(p).
-2*(p + 2)*(p + 12)
Let b = 5006/27963 + 1/2151. Let j = b - -2/13. Suppose j*h**2 + 0 + h = 0. Calculate h.
-3, 0
Let s(d) be the second derivative of -5/147*d**7 - 4/7*d**4 + 0 + 1/3*d**3 + 6/35*d**6 + 6/7*d**2 + 4*d - 1/35*d**5. Determine u, given that s(u) = 0.
-1, -2/5, 1, 3
Let c(f) be the first derivative of -f**5/45 + 11*f**4/18 + 47*f**3/27 + 4*f**2/3 - 32. Suppose c(h) = 0. Calculate h.
-1, 0, 24
Suppose -5*h = -25, 3*c + 0*h + 29 = 4*h. Let a be c*7/(84/(-16)). Solve 6 + 2*y**2 - 4 - a + 0*y**2 = 0.
-1, 1
Determine l so that 10*l**2 + 5/3*l**3 + 0*l + 0 = 0.
-6, 0
Let w(a) be the first derivative of 11 - 3/10*a**2 + 1/15*a**3 + 2/5*a. Suppose w(k) = 0. What is k?
1, 2
Determine p, given that -16/3*p - 1/3*p**2 + 19 = 0.
-19, 3
Let g(m) be the third derivative of 0*m + 0*m**3 + 5*m**2 - 1/336*m**8 + 0*m**4 + 0 + 1/120*m**6 - 1/105*m**7 + 1/30*m**5. Factor g(q).
-q**2*(q - 1)*(q + 1)*(q + 2)
Let p = 1/9 - -7/18. Suppose 41*w - 47 = 35. Factor -p - 1/4*l + 1/4*l**w.
(l - 2)*(l + 1)/4
Suppose -406*p - 5*y = -401*p - 20, 0 = -5*p + 3*y + 4. Solve -2/3*o**p + 0 + 2/3*o + 2/3*o**4 - 2/3*o**3 = 0 for o.
-1, 0, 1
Let x be ((1 + -2)/25)/((-71)/355). Let q(l) be the first derivative of 14/45*l**3 + 2/75*l**5 + 1/6*l**4 + 0*l + x*l**2 - 11. Factor q(k).
2*k*(k + 1)**2*(k + 3)/15
Let k(v) = 9*v**4 + 5*v**3 - 19*v**2 - 21*v - 10. Let c(h) = h**4 - h**2 + h. Let n = 102 - 101. Let q(j) = n*k(j) - 4*c(j). Determine p, given that q(p) = 0.
-1, 2
Suppose 4*j - 3*u - 33 = -6*u, -4*j + 3*u = -63. Factor 5*w**2 + 28 + 5*w**3 - 16 - j - 10*w.
5*w*(w - 1)*(w + 2)
Let p(t) be the second derivative of t**8/10080 - t**6/270 + 7*t**4/6 - 24*t. Let z(s) be the third derivative of p(s). Factor z(w).
2*w*(w - 2)*(w + 2)/3
Let c(f) = -f + 1. Let x be ((-1)/(-3))/((-3)/9). Let h(p) = -p**3 - 4*p**2 - 9*p + 5. Le