+ 5*p**4/18 + 20*p**3/9 + 2*p**2 - 78*p. Determine y so that t(y) = 0.
-2, -1, 2
Let l(p) be the third derivative of 0 + p**2 - 1/8*p**4 + 1/2*p**3 + 0*p + 1/80*p**5. What is r in l(r) = 0?
2
Let s(g) be the first derivative of -5/6*g**6 - 20 + 3*g**5 + 0*g**2 - 5/2*g**4 + 0*g + 0*g**3. Factor s(q).
-5*q**3*(q - 2)*(q - 1)
Let y(a) be the second derivative of a**9/756 + 4*a**8/735 + 11*a**7/1470 + a**6/315 + a**3/3 + 14*a. Let r(z) be the second derivative of y(z). Factor r(g).
4*g**2*(g + 1)**2*(7*g + 2)/7
Factor -8*i**4 + 80*i**2 - 24*i**3 - 23 + 75 - 28 + 4*i**5 - 76*i.
4*(i - 2)*(i - 1)**3*(i + 3)
Let j(n) be the second derivative of -n**6/10 - 9*n**5/5 + 27*n**4/4 - 7*n**3 + 8*n - 5. What is o in j(o) = 0?
-14, 0, 1
Let w be -4 - ((0 - 3) + 3). Let u be 2/8 - 7/w. Find k such that 3*k**4 + 6*k**5 - 2*k**3 + k**4 + 4*k**4 - k**u - 3*k**2 = 0.
-1, 0, 2/3
Factor 2/11 + 232/11*g**2 - 234/11*g.
2*(g - 1)*(116*g - 1)/11
Suppose -3*v + 21 = -3*u, 0 = -3*v + 4*v - 2*u - 8. Factor -3*t**4 - 118*t + 57*t + 55*t + v*t**3 + 3.
-3*(t - 1)**3*(t + 1)
Let o(c) = -70*c**3 + 718*c**2 - 828*c + 187. Let z(f) = -47*f**3 + 479*f**2 - 552*f + 125. Let i(u) = 5*o(u) - 7*z(u). Let i(b) = 0. Calculate b.
2/7, 1, 10
Determine q so that -20/13 + 74/13*q - 14/13*q**2 = 0.
2/7, 5
Let q(t) be the first derivative of t**5/5 - 5*t**4/4 + t**3 + 5*t**2/2 - 4*t + 179. Factor q(w).
(w - 4)*(w - 1)**2*(w + 1)
Let z(f) be the third derivative of 5*f**8/336 + f**7/42 - f**6/8 - f**5/12 + 5*f**4/12 + 3*f**2 + 45. Let z(c) = 0. Calculate c.
-2, -1, 0, 1
Let v(o) be the first derivative of -o**3/4 - 7*o**2/8 + 3*o/2 - 58. Factor v(t).
-(t + 3)*(3*t - 2)/4
Let r(v) = 2*v**2 - 37*v + 18. Let n be r(18). Let w be ((-10)/(-8))/(5/2). Solve -w*o + 5/4*o**2 + n = 0.
0, 2/5
Let u(s) be the first derivative of s**2 - 1/20*s**5 + 0*s + 1/3*s**4 - 2/3*s**3 - 5. Let z(f) be the second derivative of u(f). Suppose z(h) = 0. Calculate h.
2/3, 2
Let w be ((-108)/(-135))/((-34)/5). Let m = 23/51 + w. Factor m*q**2 + 1/3 + 2/3*q.
(q + 1)**2/3
Let b(m) = -3*m - 33. Let r be b(-11). Let l(n) be the third derivative of 0*n + 6*n**2 + 0*n**4 + 1/180*n**5 + 0*n**3 + r. Let l(i) = 0. Calculate i.
0
Let q(f) be the third derivative of 0 + 3/112*f**8 + 0*f**3 + 11/70*f**7 + 15*f**2 + 9/20*f**5 + 1/4*f**4 + 3/8*f**6 + 0*f. Factor q(v).
3*v*(v + 1)**3*(3*v + 2)
Let 3/8*u**4 + 9/8*u**2 + 0 + 15/8*u**3 + 0*u - 3/8*u**5 = 0. What is u?
-1, 0, 3
Let y(m) = m**3 + 6*m**2 + 2*m + 3. Let s be y(-5). Let u = -11 - -18. Solve 19*x**3 + 18*x + 12*x**2 + 3 - u*x**3 - 3*x**2 + s*x**2 = 0 for x.
-1, -1/4
Let y(l) = l**2 + 64*l + 1018. Let n(p) = -p**2 - 64*p - 1017. Let h(g) = -6*n(g) - 7*y(g). Find w, given that h(w) = 0.
-32
Let b(p) = -7*p**3 + p**2 + 3*p + 5. Let y(a) = -8*a**3 + 4*a + 4. Suppose -4*o + 4 = 24. Let x(g) = o*y(g) + 4*b(g). Suppose x(i) = 0. What is i?
-1, 0, 2/3
Let l be (-2)/(-10)*((-1)/4 - -4). What is x in l*x - 1/2 - 1/4*x**2 = 0?
1, 2
Let j = 66 - 196/3. Let g(c) be the first derivative of 4*c - 2 - j*c**3 + c**2. Find k, given that g(k) = 0.
-1, 2
Factor -2*r**2 + 151*r - 28 - r**2 + 0*r**2 - 223*r - 41.
-3*(r + 1)*(r + 23)
Let i(g) be the first derivative of -g**6/120 + g**5/40 - 5*g**3 + 14. Let a(r) be the third derivative of i(r). Factor a(m).
-3*m*(m - 1)
Let h(w) be the first derivative of 5*w**6/2 - 24*w**5/5 - 9*w**4 + 34*w**3 - 75*w**2/2 + 18*w - 70. Factor h(n).
3*(n - 1)**3*(n + 2)*(5*n - 3)
Let d(i) be the third derivative of -i**6/420 - i**5/42 + 2*i**4/21 - 13*i**3/6 + 3*i**2. Let w(z) be the first derivative of d(z). Factor w(j).
-2*(j + 4)*(3*j - 2)/7
Let b(k) = -2*k**3 - 2*k**2 - 2*k - 6. Let v(u) = u**2 + u + 1. Let n be (1 - -1)/(1/2). Let c(s) = n*v(s) + b(s). Solve c(l) = 0 for l.
-1, 1
Let j(o) = 8*o**2 + 40*o + 48. Let r(b) = -9*b**2 - 42*b - 45. Let k(w) = 5*j(w) + 4*r(w). Suppose k(a) = 0. Calculate a.
-5, -3
Let y be 198/110 + (-48)/30. Factor -y*v**4 + v + 1/5*v**2 + 0 - v**3.
-v*(v - 1)*(v + 1)*(v + 5)/5
Let f(o) be the first derivative of -o**6/25 + 4*o**5/25 - o**4/5 + o**2/5 - 41*o - 44. Let q(c) be the first derivative of f(c). Factor q(r).
-2*(r - 1)**3*(3*r + 1)/5
Let z be ((-64)/(-16))/((-196)/(-21)). Suppose 0 - 3/7*c + 6/7*c**2 - z*c**3 = 0. What is c?
0, 1
Let o(p) be the second derivative of -7/48*p**3 + 0 + 3/32*p**4 + 19*p + 1/8*p**2 + 1/240*p**6 - 1/32*p**5. What is g in o(g) = 0?
1, 2
Let a be 5/(-120)*20*-6*3/30. Find o, given that a*o + 1/6*o**2 + 0 = 0.
-3, 0
Factor 3 - 1/2*y**2 - 5/2*y.
-(y - 1)*(y + 6)/2
Let s be (11 - (9130/(-75))/(-11))*-10. Suppose 50/3*f - 20/3*f**2 + s*f**3 + 0 = 0. What is f?
0, 5
Let x(c) be the third derivative of c**6/120 - c**5/20 + c**4/8 - c**3/6 + 34*c**2 + 1. Factor x(h).
(h - 1)**3
Let q = 119 + -119. Factor 6*s + 8*s**2 - 5 + 1 - 10*s**2 + q*s**2.
-2*(s - 2)*(s - 1)
Let b(s) = 4*s**4 - 8*s**3 - 6*s. Let c(w) = 3*w - 74. Let l be c(25). Let v(y) = y**4 - y**3 + 3*y + 2*y - 6*y. Let x(t) = l*b(t) - 6*v(t). Solve x(j) = 0.
-1, 0
Let u(l) be the second derivative of l**7/630 + 7*l**4/6 - 14*l. Let j(v) be the third derivative of u(v). Factor j(a).
4*a**2
Let u(g) be the first derivative of -g**6/15 + 14*g**5/25 - 11*g**4/10 + 2*g**3/3 - 45. Factor u(o).
-2*o**2*(o - 5)*(o - 1)**2/5
Let q(m) be the third derivative of -m**7/1260 - m**6/180 - m**5/60 - m**4/36 - 3*m**3 - 36*m**2. Let s(h) be the first derivative of q(h). Factor s(p).
-2*(p + 1)**3/3
Suppose -10*i - 7 = -7. Suppose 0 = 9*k - 16 - 11. Factor 2/7*v**4 + 6/7*v**k + i + 4/7*v**2 + 0*v.
2*v**2*(v + 1)*(v + 2)/7
Let d = -7147 - -35741/5. Suppose 2*b - 5 + 1 = 0. Factor d*x + 0 - 2/5*x**b.
-2*x*(x - 3)/5
Let w be (168/(-49))/(1/(-7)). Factor 13*a - w + 20*a - 2*a**3 - 17*a + 2*a**2.
-2*(a - 2)**2*(a + 3)
Let h(f) be the third derivative of -f**6/240 + f**5/24 + 7*f**4/24 + 91*f**2. Factor h(c).
-c*(c - 7)*(c + 2)/2
Let j(n) = -n**2 + 4*n - 2. Let z = -137 - -139. Let t be j(z). Factor -1/6*k**t - 8/3 + 4/3*k.
-(k - 4)**2/6
Find b, given that 2/7*b**2 + 90/7 - 36/7*b = 0.
3, 15
Let -d**3 + 320 - 344 + 67*d**2 - 14*d - 58*d**2 = 0. What is d?
-1, 4, 6
Let j(v) be the third derivative of 0*v**3 + 0*v + 1/490*v**7 + 0 + 0*v**5 + 0*v**4 - 18*v**2 - 1/140*v**6 + 1/784*v**8. Let j(c) = 0. Calculate c.
-2, 0, 1
Let t(z) be the first derivative of -2*z**5/35 - 2*z**4/7 + 2*z**3/21 + 4*z**2/7 + 7. Factor t(u).
-2*u*(u - 1)*(u + 1)*(u + 4)/7
Let r(a) be the second derivative of -9*a - 1/60*a**6 + 0*a**4 - 1/12*a**5 + 0 + 1/4*a**2 + 5/18*a**3. Suppose r(f) = 0. Calculate f.
-3, -1, -1/3, 1
Let c be 1 - (3/3 + -2). Factor -3*a**2 - 5*a**3 + c*a**3 + 6*a + 6*a**2.
-3*a*(a - 2)*(a + 1)
Let t(h) = 4*h**2 + 200*h + 2487. Let x(y) = -y**2 - 50*y - 622. Let v(s) = -6*t(s) - 26*x(s). Factor v(i).
2*(i + 25)**2
Let x(d) be the first derivative of -7*d**6/12 + d**5/5 + 7*d**4/8 - d**3/3 - 20. Find t such that x(t) = 0.
-1, 0, 2/7, 1
Suppose -370/23*a**3 - 978/23*a**4 + 0 + 26/23*a**2 + 18/23*a - 360/23*a**5 = 0. Calculate a.
-9/4, -1/3, 0, 1/5
Let w(u) = -3*u**2 - 28*u - 17. Let i(q) = -12*q**2 - 111*q - 69. Let z(c) = 4*i(c) - 15*w(c). Suppose z(t) = 0. Calculate t.
-7, -1
Let f(b) be the first derivative of b**5/70 - b**4/14 + 2*b**3/21 + 26*b - 22. Let m(w) be the first derivative of f(w). Factor m(u).
2*u*(u - 2)*(u - 1)/7
Let y be -6 - (8 + 17/(-2))*(13 + -1). Determine l, given that 0 + 8/7*l**4 + y*l**2 + 2/7*l**3 + 0*l = 0.
-1/4, 0
Find d such that 1/5*d**2 - 83/5*d + 0 = 0.
0, 83
Let k(f) be the third derivative of -f**5/240 + 7*f**4/16 - 41*f**3/24 - 5*f**2 + 22. Find c, given that k(c) = 0.
1, 41
Suppose 21/4*u**5 + 99*u**2 - 99/4*u**4 + 0 + 30*u - 57/2*u**3 = 0. Calculate u.
-2, -2/7, 0, 2, 5
Determine z, given that 20/11*z**2 - 2/11*z**3 - 144/11 - 24/11*z = 0.
-2, 6
Let k(m) = 6 + m**2 + m**2 - 11*m**4 + m - 1 + 8*m**3 + 0*m. Let s(y) = 6*y**4 - 4*y**3 - y**2 - y - 3. Let o(n) = 3*k(n) + 5*s(n). Factor o(l).
-l*(l - 1)**2*(3*l + 2)
Let n be 2*66/(-77)*4/24*-3. Factor 2/7*u**2 + 4/7 - n*u.
2*(u - 2)*(u - 1)/7
Let b(g) be the first derivative of -2*g**3 - 94*g**2 - 62*g - 580. Solve b(l) = 0.
-31, -1/3
Let f(j) = -j**3 - 11*j**2 + 12*j + 1. Let i be f(-12). Let u be ((-6)/12)/(i/(-4)). Factor -6*l**3 + 6*l**2 + 4*l**u + 32*l + l**3 - 40 - 12*l.
-5*(l - 2)**2*(l + 