second derivative of n(y). Factor q(u).
-4*u**4*(u + 2)/5
Let m(n) = 2*n. Let d be m(2). Find q, given that d*q**2 - 6*q**3 + 0*q**3 - 5*q**2 + 5*q**3 = 0.
-1, 0
Suppose -52*r + 49*r = -12. Suppose -3*m = -s - 12 + 1, r*m - 13 = s. Solve m + 9/2*j**2 + 10*j = 0 for j.
-2, -2/9
Suppose -53/3*h - 73/6*h**2 - 35/6 - 1/3*h**3 = 0. Calculate h.
-35, -1, -1/2
Let q(d) = -d**2 - 25*d + 123. Let i be q(-29). Let l(k) be the third derivative of -4/3*k**3 + 2/15*k**5 - i*k**2 + 0 - 1/2*k**4 + 0*k. Factor l(c).
4*(c - 2)*(2*c + 1)
Let b(x) be the second derivative of 1/18*x**4 + 22*x + 16/3*x**2 + 8/9*x**3 + 0. Find v, given that b(v) = 0.
-4
Let a be (-8)/(-14) + (-136)/(-56). Suppose -h + 16 = a*h. Suppose -4*r**2 + h*r**2 + 48*r**4 + 36*r**5 + 16*r**3 + 0*r**4 = 0. Calculate r.
-2/3, 0
Let r be (-2 - -12) + (-7 - -3). Let 2*t**5 + 166*t**4 - 160*t**4 + t**2 + t**2 + r*t**3 + 0*t**3 = 0. What is t?
-1, 0
Let v(r) be the first derivative of r**5/25 - 4*r**4/5 + 14*r**3/5 - 4*r**2 + 13*r/5 - 12. Factor v(x).
(x - 13)*(x - 1)**3/5
Let k(n) be the first derivative of 2/3*n**3 + 0*n - 2/5*n**5 + 0*n**2 + 0*n**4 - 2. Factor k(l).
-2*l**2*(l - 1)*(l + 1)
Let p(i) be the second derivative of 1/5*i**4 + 0 - 27*i + 3/10*i**2 + 1/2*i**3. Factor p(z).
3*(z + 1)*(4*z + 1)/5
Suppose 45*c = -37*c - 36*c. Factor 1/8*w**3 - 3/8*w - 1/4 + c*w**2.
(w - 2)*(w + 1)**2/8
Let u(j) be the first derivative of -j**5/160 + 3*j**4/32 - 9*j**3/16 - 12*j**2 + 33. Let c(t) be the second derivative of u(t). Find i, given that c(i) = 0.
3
Suppose 4*j - 18 = 10. Factor 0 - f + 2 - 5*f**4 + j*f**3 - 6*f**2 - 5*f**4 + 8*f**4.
-(f - 2)*(f - 1)**2*(2*f + 1)
Let y be (-10)/(-6)*48/480. Let -1/6*h**2 + y + 0*h = 0. What is h?
-1, 1
Suppose -687 = -14*z - 631. Factor 0 + 16/7*v**2 + 0*v + z*v**3 + 12/7*v**4.
4*v**2*(v + 1)*(3*v + 4)/7
Let g(p) be the first derivative of -10/7*p**2 + 4/21*p**3 + 27 - 24/7*p. Find n such that g(n) = 0.
-1, 6
Suppose -4*w**3 + 141*w - 562*w + 161*w + 144 + 128*w + 40*w**2 = 0. Calculate w.
3, 4
Let r(m) = -m**2 - 3*m + 1. Let u be r(-3). Let v be 4 + -2 + (-2)/u. Solve -31*x**2 + v + 2*x**3 + 0 + 29*x**2 = 0.
0, 1
Suppose -3*l = -12 - 78. Suppose l = c + 4*c. What is z in 2*z**2 + z**2 + 2 + 1 + c*z + 0*z**2 = 0?
-1
Let d be 27567/378 + (-4)/(-7). Let q = 297/4 - d. Find n such that -27/4 + 15/4*n**2 - 9/4*n - q*n**3 = 0.
-1, 3
Let m = 15 - 12. Solve -10*z**5 + 14*z**5 - m*z**5 + 2*z**4 = 0.
-2, 0
Suppose -q = -2*q + 2*f + 12, 16 = -q - 5*f. Factor 6*y + 8 + q*y**2 - 13*y - 5*y.
4*(y - 2)*(y - 1)
Let d be (-5 - (-96)/18)/((-2)/(-66)) - 7. Factor -2/3*r**3 + 1/3*r**2 + 0 - 1/3*r**d + 2/3*r.
-r*(r - 1)*(r + 1)*(r + 2)/3
Let f(j) = -20*j**2 + 25*j. Let n(q) = q**3 - 19*q**2 + 22*q. Let k(d) = 4*f(d) - 5*n(d). Suppose k(r) = 0. Calculate r.
0, 1, 2
Suppose -156*m = -158*m. Let q = -11/4 - -13/4. Factor -q*g + m + 1/2*g**2.
g*(g - 1)/2
Factor 12/5 - 6/5*p**3 + 6*p**2 - 2/5*p**4 - 34/5*p.
-2*(p - 1)**3*(p + 6)/5
Suppose -7*n = -2*n - 15. Suppose -2*l + n*u - 6 = 0, -2*l + 2*u - 2 = u. Factor 0*g**2 + l + 0*g + 3/4*g**3 - 3/4*g**4.
-3*g**3*(g - 1)/4
Let a be 2/45*((-4)/(-3))/((-330)/(-2475)). Factor 0 - a*k - 2/9*k**3 + 2/3*k**2.
-2*k*(k - 2)*(k - 1)/9
Let m be (4 + (-28)/7)/(-1). Let n(t) be the third derivative of 1/16*t**4 + 4*t**2 - 1/80*t**6 + m + 0*t**3 + 0*t + 0*t**5. What is g in n(g) = 0?
-1, 0, 1
Let v(a) be the second derivative of -a**5/150 - 76*a**4/45 - 395*a**3/3 - 750*a**2 - 300*a. Factor v(k).
-2*(k + 2)*(k + 75)**2/15
Suppose -2*l + 3*l + 4*t = -125, 476 = -4*l - 4*t. Let h be (5 + l/21)/(50/(-35)). Factor 1/5*d**3 - 4/5*d**2 - h + d.
(d - 2)*(d - 1)**2/5
Let w(r) be the first derivative of 11*r**5/20 + 25*r**4/8 + 17*r**3/3 + 3*r**2 + 247. Factor w(p).
p*(p + 2)**2*(11*p + 6)/4
Let u = 0 + 4. Solve 8*k**2 + 2*k + 6*k - u*k - 2*k**2 + 2*k**3 = 0.
-2, -1, 0
Let k = -957 - -19143/20. Let p(a) be the second derivative of -k*a**4 + 7/10*a**3 - 4*a - 3/5*a**2 + 0. Factor p(j).
-3*(j - 2)*(3*j - 1)/5
Let c(o) be the third derivative of 0*o + 0 + 8*o**2 - 1/15*o**3 + 1/150*o**5 + 0*o**4. Solve c(y) = 0 for y.
-1, 1
Let j(w) be the second derivative of 12/5*w**5 + 0 + 4/3*w**4 + 0*w**3 + 6/5*w**6 + 0*w**2 - 20*w. Factor j(b).
4*b**2*(3*b + 2)**2
Let z(g) = g**2 - 5*g + 6. Let y be z(4). Factor 5*w**4 + 61*w**3 - 9*w - 51*w**3 - 3*w**2 - w - y*w**2.
5*w*(w - 1)*(w + 1)*(w + 2)
Let n = -91 + 93. Factor 3/4*w**3 + 0*w + 3/4*w**4 + 0*w**n + 0.
3*w**3*(w + 1)/4
Let o be -3 - (4 - 51)/(7 - -6). Solve o*v + 0 - 2/13*v**2 = 0 for v.
0, 4
Determine j so that 25921/8*j**3 - 161/4*j**2 + 0 + 1/8*j = 0.
0, 1/161
Let a = 14 - 11. Let h(d) be the third derivative of -1/480*d**6 + 0 + 0*d + 1/96*d**4 + 0*d**5 + 5*d**2 + 0*d**a. Factor h(j).
-j*(j - 1)*(j + 1)/4
Let q be -5 - 0*(-2 + 3). Let y be (-1)/(q - -1)*12. Factor -y*p**2 - 198 + 198.
-3*p**2
Let d(y) be the third derivative of -y**7/1680 + y**6/160 - y**5/40 + 5*y**4/8 + 2*y**2. Let w(v) be the second derivative of d(v). Suppose w(k) = 0. What is k?
1, 2
What is v in -33*v + 64 + 50*v + 47*v - 2*v**2 + 14*v**2 = 0?
-4, -4/3
Let t = -26 - -30. Factor -9*w - 2*w**4 + 21*w**3 + 6*w**2 + 8*w**4 - 5*w**4 + 5*w**t.
3*w*(w + 1)*(w + 3)*(2*w - 1)
Factor 38*a**2 - 116/3*a - 12*a**3 + 13 - 1/3*a**4.
-(a - 1)**3*(a + 39)/3
Let h(n) be the third derivative of -3*n**7/70 - n**6/4 + 2*n**5/5 + 89*n**2. Factor h(o).
-3*o**2*(o + 4)*(3*o - 2)
Let l be (-5)/((-10)/3)*(-2)/(-42). Let o(a) be the second derivative of -6*a + 9/2*a**3 + 3/5*a**6 + 21/10*a**5 + 0 + 4*a**4 + 3*a**2 + l*a**7. Factor o(m).
3*(m + 1)**4*(m + 2)
Let n = -659 - -8571/13. Let g = 6/65 + n. Factor g*c + 0 - 1/5*c**2.
-c*(c - 2)/5
Let g be ((1*4)/(-2))/(40/70). Let n = 25/6 + g. Factor 0*m + 2/3*m**3 + 0 - n*m**5 - 2/3*m**4 + 2/3*m**2.
-2*m**2*(m - 1)*(m + 1)**2/3
Let m(q) be the third derivative of 3*q**6/80 - q**5/20 - 19*q**4/16 - 3*q**3/2 + 78*q**2 - 2*q. Determine h so that m(h) = 0.
-2, -1/3, 3
Let c(i) be the third derivative of i**7/420 + 13*i**6/240 + 11*i**5/40 + 31*i**4/48 + 5*i**3/6 + 2*i**2 + 31*i. Suppose c(q) = 0. What is q?
-10, -1
Let s(z) be the second derivative of -9*z**5/4 - 685*z**4/12 - 220*z**3 - 130*z**2 - 866*z. Solve s(r) = 0.
-13, -2, -2/9
Let c(m) = -23*m**4 + 27*m**3 - 94*m**2 + 139*m - 69. Let s(k) = -2*k**4 + k**3 - 2*k**2 + k + 1. Let r(o) = 2*c(o) - 22*s(o). Factor r(x).
-2*(x - 10)*(x - 2)**3
Let x be (-8)/28*2 + (-40)/(-70). Suppose -4*w + 6 = -q, 2*q - 4 = -3*w + 3*q. What is c in -1/3*c**5 + 0 + 2/3*c**4 - 2/3*c**w + x*c + 1/3*c**3 = 0?
-1, 0, 1, 2
Let t(u) be the third derivative of u**5/300 + 41*u**4/60 - 83*u**3/30 + 441*u**2. Factor t(k).
(k - 1)*(k + 83)/5
Let f(c) be the first derivative of 0*c**2 - 1/15*c**5 - 2/9*c**3 + 0*c + 6 - 1/4*c**4. Factor f(a).
-a**2*(a + 1)*(a + 2)/3
Let n = 50 - -1. What is k in -12 - 28*k**3 - n*k**2 - 52*k - 10*k**2 - 7*k**2 = 0?
-1, -3/7
Suppose 194*x - 1/2*x**2 - 18818 = 0. What is x?
194
Let f be -4 + ((-27)/4)/((-72)/48). Let m(w) be the first derivative of -4*w**2 + 4*w + 2*w**3 + 3 - f*w**4 + 1/20*w**5. Factor m(h).
(h - 2)**4/4
Let o = 85 + -73. Factor -2*q**2 - 24*q**4 + 3*q**5 + 3*q**3 - o*q + 36*q**4 - 28*q**2 + 24.
3*(q - 1)**2*(q + 2)**3
Let y(w) be the second derivative of w**6/50 - w**4/20 + 2*w + 2. Factor y(g).
3*g**2*(g - 1)*(g + 1)/5
Let v(z) be the first derivative of 0*z**3 - 1/168*z**4 - 1/420*z**5 + 2*z**2 + 8 + 0*z. Let o(u) be the second derivative of v(u). Factor o(q).
-q*(q + 1)/7
Let f(t) be the first derivative of -t**8/840 + t**7/210 - 2*t**3/3 - 11. Let i(h) be the third derivative of f(h). Factor i(y).
-2*y**3*(y - 2)
Let i = 4006/11 + -364. Factor -2*z - 8/11 - 18/11*z**2 - i*z**3 + 2/11*z**4.
2*(z - 4)*(z + 1)**3/11
Let q(a) be the second derivative of 0*a**2 - 20*a + 0*a**3 + 0 + 1/10*a**6 + 1/98*a**7 + 33/140*a**5 + 5/28*a**4. Factor q(v).
3*v**2*(v + 1)**2*(v + 5)/7
Let q(w) = -13*w**2 + 5. Let n(k) = -72*k**2 + 28. Let r be 1 + 66 - 3/(-1). Let a be ((-28)/(-10))/(7/r). Let s(d) = a*q(d) - 5*n(d). Let s(b) = 0. What is b?
0
Let z(f) = 73*f**2 + 369*f - 43. Let x(h) = -147*h**2 - 739*h + 85. Let b(k) = 3*x(k) + 5*z(k). Determine g, given that b(g) = 0.
-5, 2/19
Let v be (-1 - 2)*(-700)/(-840)*16/(-10). Suppose 1/2*t**3 - v*t + 0 - t**2 = 0. Calculate