- r*n**3 - n**2 + 0 = 0.
-1, 0, 2
Let a(q) be the third derivative of -q**5/12 - 335*q**4/12 - 22445*q**3/6 - 85*q**2. Factor a(c).
-5*(c + 67)**2
Let n(s) be the third derivative of -5*s**2 + 1/270*s**5 + 0*s + 0*s**3 + 1/54*s**4 + 0. What is m in n(m) = 0?
-2, 0
Let y be 1620/77 - -2 - 4/22. Let u = -215/14 + y. Solve -u*t**2 - 3/2 + 9*t = 0.
1/5, 1
Let u(d) = 6*d - 61. Let g be u(11). Let c(b) be the second derivative of 1/20*b**6 + 1/4*b**3 + 0*b**2 - 4*b + 0 - 1/8*b**4 - 3/40*b**g. Factor c(z).
3*z*(z - 1)**2*(z + 1)/2
Suppose 2*q - 2 = -4*x + 2, 4*q - 8 = 3*x. Determine p so that -1/7*p**3 + 1/7*p**5 + x*p**4 + 0*p + 0 + 0*p**2 = 0.
-1, 0, 1
Suppose 9*p - 4*p = 10. Let b be (4/1)/((-16)/(-12)). Factor b*y + 15*y**2 + 6*y**3 + 11*y - p*y + 3.
3*(y + 1)**2*(2*y + 1)
Let v(z) be the second derivative of -z**6/15 - 9*z**5/110 + 13*z**4/66 + 3*z**3/11 - 2*z**2/11 + 5*z - 1. Find y, given that v(y) = 0.
-1, 2/11, 1
Let p(l) = 4*l**2 - 28*l. Let n(s) = s. Let a(o) = -16*n(o) - p(o). Factor a(m).
-4*m*(m - 3)
Suppose 39*r**2 + 48 - 96*r - 12*r**4 + 39/2*r**3 + 3/2*r**5 = 0. What is r?
-2, 1, 4
Let v(f) = -12*f - 3. Suppose 0 = -g - 5*j + 5, -2*j - 21 = -3*g - 6. Let u(h) = -h**2 - h - 1. Let y(m) = g*u(m) - v(m). Factor y(d).
-(d - 1)*(5*d - 2)
Let a(c) be the first derivative of 2/9*c**3 - 15 - 4/3*c**2 + 8/3*c. Factor a(g).
2*(g - 2)**2/3
Let n = -40098/91 - -5732/13. What is c in 8/7*c + n*c**2 + 8/7 = 0?
-2
Let q(v) be the first derivative of v**4/14 - 40*v**3/21 + 117*v**2/7 - 324*v/7 - 363. Factor q(d).
2*(d - 9)**2*(d - 2)/7
Suppose 4*r - 23 = 25. Factor 18 + 2*f**2 - r*f - 7*f**2 + 7*f**2.
2*(f - 3)**2
Suppose -22/13*j**3 + 16/13 - 4*j - 2/13*j**4 + 2/13*j**5 + 58/13*j**2 = 0. Calculate j.
-4, 1, 2
Let j be 3/12 - (-3)/4 - -1. Factor -3*v**3 + 32*v**4 - 22*v**4 + 0*v**3 - 5*v**5 - j*v**3.
-5*v**3*(v - 1)**2
Let u(m) = 25*m**3 - 65*m**2 + 120*m - 60. Let l be (-306)/(-15) - 14/35. Let t(p) = p**3 - p**2 + 1. Let k(a) = l*t(a) - u(a). Solve k(v) = 0.
1, 4
Let z = 585/4 + -583/4. Factor 3/4*u + z + 1/4*u**2.
(u + 1)*(u + 2)/4
Let g(x) be the third derivative of -x**6/360 + x**5/40 - x**4/12 - x**3 - 8*x**2. Let l(z) be the first derivative of g(z). Factor l(i).
-(i - 2)*(i - 1)
Find p such that 7 + 439*p**2 - 3 + 4*p - 438*p**2 = 0.
-2
Let o(n) be the third derivative of n**6/96 + 7*n**5/240 + n**4/48 + 2*n**2 + 8. Factor o(t).
t*(t + 1)*(5*t + 2)/4
Let i(x) be the third derivative of 0 - 1/8*x**4 - 3/4*x**3 + 1/40*x**5 + 0*x + 6*x**2. Find f such that i(f) = 0.
-1, 3
Let j(q) be the second derivative of -36*q + 0 - 8/5*q**3 + 144/5*q**2 + 1/30*q**4. Suppose j(f) = 0. What is f?
12
Let h(p) be the first derivative of -2*p**3/15 - 3*p**2 + 32*p/5 - 104. Solve h(f) = 0 for f.
-16, 1
Factor d**2 + 5/2*d + 2 + 1/8*d**3.
(d + 2)**2*(d + 4)/8
Suppose 2*t - 15 = u, -3*t + 9 = t + 5*u. Let h = t - 4. Factor -r**3 - 4*r**3 + 5*r**h + 6*r**3 + 8*r + 5 - 1.
(r + 1)*(r + 2)**2
Let w = -31 + 34. Factor j**2 + 18*j + 5*j**3 - w*j**4 + 2*j**2 - 6*j - 17*j**3.
-3*j*(j - 1)*(j + 1)*(j + 4)
Let y(b) = 2*b**4 + 27*b**3 + 57*b**2 + 53*b + 18. Let x(n) = -15*n**4 - 190*n**3 - 400*n**2 - 370*n - 125. Let i(r) = -3*x(r) - 20*y(r). Solve i(s) = 0 for s.
-3, -1
Let u(b) = b**2 - 7. Let y be u(-5). Factor y*t**3 + 8*t**2 - 16*t + 2*t**3 + 24*t**2.
4*t*(t + 2)*(5*t - 2)
Let c = 60193/5 - 24077/2. Determine n so that -1/5*n**3 + 2/5*n**4 + 0 + 9/10*n - 6/5*n**2 + c*n**5 = 0.
-3, 0, 1
Let x be 4/(-480) + (-6)/(-45). Let f(s) be the second derivative of 1/8*s**4 - x*s**3 + 0*s**2 + 0 + 9*s. Factor f(y).
3*y*(2*y - 1)/4
Let i(b) = -6*b + 61. Let p be i(8). Let v(k) be the first derivative of 2/15*k**3 - p - 2/5*k**2 + 0*k. Factor v(r).
2*r*(r - 2)/5
Let r(m) = 4*m**2 - 1. Let y be r(2). Let t = -12 + y. Factor -t*k**4 + 5*k**4 - 6*k + 2*k - 6*k**2 + 0*k.
2*k*(k - 2)*(k + 1)**2
Let b(g) be the second derivative of -g**4/54 - 55*g**3/27 + 56*g**2/9 + 130*g + 3. Determine i so that b(i) = 0.
-56, 1
Let q = -10 + 16. Let w(i) = 7*i**2 + 8*i + 6. Let r = -12 - -7. Let f(s) = 8*s**2 + 8*s + 6. Let v(d) = q*w(d) + r*f(d). Factor v(h).
2*(h + 1)*(h + 3)
Let p(c) be the second derivative of -c**7/6720 + c**6/480 - c**5/120 - 5*c**3/2 + 43*c. Let l(o) be the second derivative of p(o). Factor l(a).
-a*(a - 4)*(a - 2)/8
Suppose -7*s = -2*s - 20. Suppose 5*z = -s*r - 6, -5*r - 16 = -r. Factor -7*h**3 - 3*h**2 + 0*h**z + 4*h**3.
-3*h**2*(h + 1)
Let d(c) be the second derivative of 0 + 0*c**5 + 0*c**3 + 0*c**2 + 2/15*c**6 + 0*c**4 - 1/21*c**7 + 12*c. Suppose d(s) = 0. Calculate s.
0, 2
Suppose -4*j = q - 0 - 6, 4 = q + 2*j. Factor 0*w - q + w**2 - 2 + 4*w - 2*w**2.
-(w - 2)**2
Let h be 4/6 - (-70)/(-15). Let w be 3/h*(-2 - 2). Determine c so that 3 - 26*c - 5*c**w - 13*c**3 - 7 - 48*c**2 = 0.
-2, -1/3
Let c**2 + 66*c + 927 + 911 - 2819 + 914 = 0. Calculate c.
-67, 1
Let i(x) be the second derivative of 31*x + 0 - 1/8*x**4 + 11/16*x**3 + 9/16*x**2. Factor i(z).
-3*(z - 3)*(4*z + 1)/8
Let t(h) be the third derivative of 0*h**3 + 1/300*h**5 - 1/1050*h**7 + 0 + 1/120*h**4 - 1/600*h**6 - 27*h**2 + 0*h. Factor t(w).
-w*(w - 1)*(w + 1)**2/5
Let o = -44 + 106. Suppose 33*g**4 + 45*g**3 + 36*g**4 - 18*g**5 - 257*g**2 + o*g**2 - 54 - 207*g = 0. Calculate g.
-1, -2/3, -1/2, 3
Let h(p) be the second derivative of 10*p**7/63 + 13*p**6/6 + 67*p**5/6 + 25*p**4 + 15*p**3 - 45*p**2/2 + 65*p. Let h(t) = 0. Calculate t.
-3, -1, 1/4
Let m be ((-27)/((-4860)/(-16)))/((-15)/9 - -1). Suppose -2/5*d + 0 - m*d**2 = 0. Calculate d.
-3, 0
Let x(v) be the third derivative of -v**7/42 - 17*v**6/24 + v**5/12 + 85*v**4/24 + 174*v**2. Solve x(o) = 0.
-17, -1, 0, 1
Let x(o) = 3*o**4 + 3*o**3 + 3*o**2 + 3*o - 3. Let z(r) = r**2 + r - 1. Let v be 4 + 45/(-5) + 2. Let w(n) = v*z(n) + x(n). Suppose w(g) = 0. Calculate g.
-1, 0
Let q(a) = -a + 0*a**3 - 26*a**2 - 4*a**3 - 3*a**3 - 13 + 5*a**3. Let d be q(-13). Let 2/9*h**3 + d + 2/9*h + 4/9*h**2 = 0. What is h?
-1, 0
Suppose 9*a - a - 40 = 0. Let c(z) be the second derivative of 8/3*z**3 + 9*z + 1/10*z**a + 4*z**2 + 0 + 5/6*z**4. Let c(d) = 0. Calculate d.
-2, -1
Let r = -661 - -471. Let h = r + 192. Factor 2/13*k**3 - 2/13*k - 2/13*k**4 + 2/13*k**h + 0.
-2*k*(k - 1)**2*(k + 1)/13
Let x be (-29)/30 + 5 + (-42)/9. Let v = 1/30 - x. Find h such that 0*h - 2/3*h**2 + v = 0.
-1, 1
Let c(l) be the second derivative of -3*l**5/8 + 65*l**4/24 - 65*l**3/12 + 15*l**2/4 + 24*l - 2. Suppose c(q) = 0. Calculate q.
1/3, 1, 3
Let f(d) be the third derivative of d**5/20 - 19*d**4/20 + 21*d**3/10 - 21*d**2 + d. Factor f(i).
3*(i - 7)*(5*i - 3)/5
Let w(o) be the third derivative of -o**6/24 - o**5/2 + 5*o**4/24 + 5*o**3 + 10*o**2 - 29*o. Determine r so that w(r) = 0.
-6, -1, 1
Let f(j) = 3*j**2 - j + 1. Let p be f(1). Suppose 0 = 4*d + 12, -u + 3 = -4*u - 4*d. Determine k so that -6*k**2 - 5*k - 3*k**p + u*k + 5*k + 6 = 0.
-2, -1, 1
Let p(c) be the third derivative of 0*c + 0 + 1/24*c**4 + 1/630*c**7 + 1/180*c**5 - 1/9*c**3 - 58*c**2 - 1/120*c**6. Let p(f) = 0. What is f?
-1, 1, 2
Let a(t) = -t**2 + 2*t + 2. Let n(x) = 1 + 4 + 8*x - 2*x**2 - 2*x**2 + 4. Let p(k) = 9*a(k) - 2*n(k). Let p(u) = 0. What is u?
0, 2
Let w(m) be the first derivative of -m**4/6 - 14*m**3/27 + 8*m/9 + 103. Suppose w(z) = 0. Calculate z.
-2, -1, 2/3
Let b(t) = -t**3 - 5*t**2 + 7*t + 8. Let j be b(-6). Determine m so that 3*m**3 - 6*m + 5*m + 4 - 8*m + j = 0.
-2, 1
Let j(o) be the second derivative of 0 + 46/15*o**3 + 27/70*o**7 + 43*o + 553/100*o**5 - 12/5*o**6 - 179/30*o**4 - 4/5*o**2. Determine f, given that j(f) = 0.
2/9, 1, 2
Let h be ((3810/(-9))/10)/((-14)/(-6)). Let w = -18 - h. Factor 1/7*u**3 - 1/7*u**5 + w*u**2 + 0*u + 0 - 1/7*u**4.
-u**2*(u - 1)*(u + 1)**2/7
Suppose 4*c - 1 = -r, 2*c + 5*r - 79 + 110 = 0. Factor 4/3*d**c + 20/9 + 4/9*d**3 - 4*d.
4*(d - 1)**2*(d + 5)/9
Let j be -3 - (-1 + (-1 - 3)). Determine t so that -2 - 11*t - 3*t**j - t - 10 + 3 = 0.
-3, -1
Let q(y) = -57*y**2 - 53*y - 25. Let g(m) = 29*m**2 + 26*m + 13. Let l be 3/30*-2*-5. Let b = -8 + l. Let w(s) = b*g(s) - 4*q(s). Factor w(z).
(5*z + 3)**2
Let m = -24 + 30. Let x = 2 + m. Factor 5*t**5 + 0*t + 2*t**5 - 9*t**5 - 2*t + 8*t**4 - 12*t**3 + x*t**2.
-2*t*(t - 1)**4
Let u(c) be the first derivative of 0*c + 20/21*c**3 - 12/7*c**2 - 4