
4*(w - 60)**2*(w + 3)/7
Let b(s) be the second derivative of 3/16*s**4 + 9/20*s**5 + 0*s**2 + 7/40*s**6 + 77*s + 0 - 1/4*s**3. Determine g so that b(g) = 0.
-1, 0, 2/7
Factor -421/3*a**4 + 2391200/3*a + 1/3*a**5 + 19738*a**3 - 2800280/3*a**2 + 5488000.
(a - 140)**3*(a - 3)*(a + 2)/3
Let r(y) = y**3 - 4*y**2 - 68*y + 8. Let l(h) = 3*h**3 + 21*h**2 + 340*h - 40. Let o(u) = 4*l(u) + 22*r(u). Factor o(k).
2*(k - 2)*(k + 2)*(17*k - 2)
Let o(p) be the third derivative of 1/8*p**6 + 0 + 17*p + 0*p**3 + 1/70*p**7 + 7/20*p**5 + 3/8*p**4 - 2*p**2. Factor o(x).
3*x*(x + 1)**2*(x + 3)
Let v = -351 + 354. Suppose -3*n = -2*y + 5*y + 9, -v*y - 4 = 2*n. Factor -1/2*r + 0 - 3/4*r**y.
-r*(3*r + 2)/4
Let p(l) be the first derivative of -l**3/21 + 3*l**2/7 - 5*l/7 + 1353. Suppose p(f) = 0. Calculate f.
1, 5
Let d(p) be the second derivative of -p**4/12 + p**3/3 + 18*p. Let h(o) = 32*o**2 - 89*o - 15. Let g(v) = -2*d(v) - h(v). Factor g(j).
-5*(j - 3)*(6*j + 1)
Let m(n) be the second derivative of -n**4/20 + 1131*n**3/5 - 3837483*n**2/10 - 383*n. Suppose m(z) = 0. Calculate z.
1131
Determine x, given that 2248/5*x + 276/5*x**3 - 96 - 16/5*x**4 - 276*x**2 = 0.
1/4, 3, 4, 10
Suppose 2720 = 15*j - 2650. Let a = -1787/5 + j. Solve a + 0*t + 0*t**3 + 3/5*t**4 - 6/5*t**2 = 0.
-1, 1
Let z be ((-3)/((-45)/(-78)))/(32/(-80)). Determine m, given that -2*m + z*m**2 + 14*m**2 - 6*m - 29*m**2 = 0.
-4, 0
Let m = 47 - 44. Suppose 9 = m*x - 0. Let -4*l**2 + 30*l + 20*l**4 + 34*l**3 - 16 + 14*l**x - 78*l = 0. What is l?
-2, -1, -2/5, 1
Let s = 0 + 4. Let g = 6042 + -12081/2. Solve 1/2*c**s + 0 + 1/2*c + 3/2*c**3 + g*c**2 = 0.
-1, 0
Let p(b) = -4*b**3 + 80*b**2 + 300*b - 382. Let n(i) = -12*i**3 + 238*i**2 + 898*i - 1145. Let s(c) = 2*n(c) - 7*p(c). Factor s(g).
4*(g - 24)*(g - 1)*(g + 4)
Suppose -4*z - 4*a + 184 = 0, 3*a - 24 = 5*z - 294. Let r be -35 - -23 - z/(-4). Factor -1/2*o - 1/4*o**4 + 1/2*o**3 - r + o**2.
-(o - 3)*(o - 1)*(o + 1)**2/4
Solve -108/5 + 20*z**3 - 324/5*z - 36*z**2 = 0 for z.
-3/5, 3
Let b(i) be the second derivative of 5*i**7/42 + 20*i**6 + 3599*i**5/4 - 50*i**4 - 3000*i**3 + 195*i. Suppose b(z) = 0. What is z?
-60, -1, 0, 1
Let o(g) = -4*g**2 + 192*g - 1072. Let p(w) = 4*w**2 - 190*w + 1076. Let a(t) = -5*o(t) - 4*p(t). Factor a(q).
4*(q - 44)*(q - 6)
Let l(f) be the second derivative of 1/3*f**4 - 2*f + 7 - 16/3*f**3 + 0*f**2. Factor l(q).
4*q*(q - 8)
Let w(n) be the second derivative of -n**5/50 - n**4/10 + 46*n**3/15 + 48*n**2/5 - 451*n. What is f in w(f) = 0?
-8, -1, 6
Let z = -182 - -187. Factor 21*w - 30*w**2 + 4*w**4 - 19*w + 26*w**2 - 2*w**z.
-2*w*(w - 1)**3*(w + 1)
Let x(t) be the second derivative of t**7/7560 + t**6/2160 - 13*t**4/3 + t**3/6 - t + 20. Let n(k) be the third derivative of x(k). Let n(v) = 0. What is v?
-1, 0
Let y(k) = -3*k + 38. Let x be y(5). Factor x*o - 24*o**2 + 10*o + 2*o**3 + 3*o + 2*o**3.
4*o*(o - 3)**2
Let w(n) be the first derivative of -8/7*n + 212 - 62/21*n**3 - 5/21*n**6 + 2/5*n**5 + 20/7*n**2 + 13/14*n**4. Solve w(b) = 0 for b.
-2, 2/5, 1
Let q(d) = 4*d**5 - 34*d**4 - 102*d**3 + 460*d**2 - 514*d + 182. Let i(z) = z**5 - z**4 - 3*z**3 + 1. Let c(p) = 2*i(p) - q(p). Factor c(y).
-2*(y - 18)*(y - 1)**3*(y + 5)
Suppose -3*z - 2 = m, 2*m + 2310 - 2306 = 0. Let j(y) be the third derivative of 5/3*y**3 + z*y + 0 - 25/24*y**4 + 1/4*y**5 + 3*y**2. Solve j(k) = 0.
2/3, 1
Suppose -470 + 455 = -3*h. Factor -50 - 3*n + 17*n + 4*n**2 + 0*n**2 - h*n**2 + n.
-(n - 10)*(n - 5)
Let b = -7/80 + 421/240. Let q(a) be the first derivative of 0*a - 5/2*a**2 - b*a**3 - 13. Factor q(x).
-5*x*(x + 1)
Suppose 0*g = -5*g + 3*u + 19049, 4*u = 2*g - 7628. Factor 34 - 55 - 58 - 3809*a**2 - 80*a + g*a**2.
-(a + 1)*(a + 79)
Let y = -318176/715 - -28931/65. Factor 0 + 0*t - y*t**4 + 3/11*t**2 + 2/11*t**3.
-t**2*(t - 3)*(t + 1)/11
Let n(o) be the third derivative of -3/140*o**7 + 0*o - 8/15*o**5 - 1/5*o**6 + 70*o**2 + 2 + 0*o**3 + 0*o**4 - 1/1344*o**8. Solve n(x) = 0.
-8, -2, 0
Let j = -431 - -614. Let p = 988 + -985. Let s**4 - 3*s**4 + 6*s**4 + j*s + 6*s**p - 185*s = 0. Calculate s.
-1, 0, 1/2
Let u = -8821 + 8825. Factor 34/3*j**2 + u*j + 0 + 10*j**3 + 2*j**4 - 2/3*j**5.
-2*j*(j - 6)*(j + 1)**3/3
Suppose 0 = -4*y + 4*s + 12, -2*y + 6 - 18 = 4*s. Suppose -d + 35 - 32 = y. Let 0 + 55*a**d + 80*a - 3 + 23 + 10*a**4 + 105*a**2 = 0. What is a?
-2, -1, -1/2
Let n(x) = -x**3 + 19*x**2 + 21*x - 18. Let y be n(20). Determine s so that -111*s**2 + 53*s**y + 55*s**2 + 12*s**3 - 6*s + 9*s**4 = 0.
-1, 0, 2/3
Let g(c) = 36 + 49*c + 8*c**2 - 20*c + 31*c + 16*c**2. Let v(k) = k**3 - 23*k**2 - 61*k - 37. Let d(r) = 5*g(r) + 4*v(r). Factor d(o).
4*(o + 1)*(o + 2)*(o + 4)
Let r(k) be the third derivative of 3/40*k**5 + 0 + 29/64*k**4 + 9/8*k**3 + k**2 + 14*k + 1/320*k**6. Let r(l) = 0. Calculate l.
-9, -2, -1
Let r(q) = 5*q**4 + 25*q**3 + 28*q**2 - 61*q - 3. Let b(m) = 4*m**4 + 24*m**3 + 32*m**2 - 62*m - 2. Let x(l) = -3*b(l) + 2*r(l). Let x(s) = 0. Calculate s.
-8, -4, 0, 1
Let -43 - 379*x**3 - 120 + 492*x**4 - 15*x**5 - 306*x**2 - 30*x**5 + 1618*x**3 - 149 - 1068*x = 0. What is x?
-2, -2/3, -2/5, 1, 13
Factor 9*v - 470234*v**2 - 35*v**4 + 15*v**3 + 40*v**4 - 24*v + 470229*v**2.
5*v*(v - 1)*(v + 1)*(v + 3)
Let i(p) = -26*p**4 + 118*p**3 + 106*p**2 - 22*p + 8. Let s(d) = 27*d**4 - 119*d**3 - 105*d**2 + 23*d - 9. Let l(u) = -9*i(u) - 8*s(u). Factor l(b).
2*b*(b - 7)*(b + 1)*(9*b - 1)
Let x(h) be the first derivative of -2*h**5/25 - 71*h**4/5 - 3166*h**3/5 + 20732*h**2/5 - 42632*h/5 + 1010. Determine s so that x(s) = 0.
-73, 2
Let z(y) be the first derivative of y**5/10 + 23*y**4/24 + 29*y**3/9 + 4*y**2 - 2153. Factor z(b).
b*(b + 2)*(b + 3)*(3*b + 8)/6
Let n = 245954 + -1229742/5. Determine a so that 44/5*a**2 + 4/5*a**4 + 0 + n*a**3 + 4*a = 0.
-5, -1, 0
Let n = -803 - -806. Factor 2*a + 81 - 21*a - 8*a + 51*a**n - 9*a**2 - 48*a**3.
3*(a - 3)**2*(a + 3)
Let a(q) be the first derivative of 4*q**3/3 - 46*q**2 + 240*q - 609. Determine v so that a(v) = 0.
3, 20
Let t(c) be the first derivative of c**3/5 + 27*c**2 - 552*c/5 + 513. Let t(a) = 0. Calculate a.
-92, 2
Suppose -117*o**4 + 367*o**4 - 1056*o + 3*o**3 - 153*o**2 - 896 - 5*o**2 - 111*o**4 - 138*o**4 = 0. Calculate o.
-8, -1, 14
Let g(b) be the second derivative of 2 + 0*b**2 - 25/18*b**4 - 19/12*b**5 + 0*b**3 - 16/45*b**6 - 1/42*b**7 - 5*b. Factor g(n).
-n**2*(n + 5)**2*(3*n + 2)/3
Let f(p) be the first derivative of -p**6/72 + 17*p**5/24 - 25*p**4/4 + 35*p**3/3 + 3. Let a(l) be the third derivative of f(l). What is q in a(q) = 0?
2, 15
Factor -44/9*q**3 - 12*q**2 - 100/9*q - 4/9*q**4 - 32/9.
-4*(q + 1)**3*(q + 8)/9
Let o(c) be the first derivative of 67 + 2523/14*c**2 - 29/7*c**3 - 24389/7*c + 1/28*c**4. Suppose o(b) = 0. What is b?
29
Let a(y) = y**5 + y**4 + y + 1. Let o(q) = -3*q**5 + 15*q**3 - 32*q**2 + 14*q - 2. Suppose -19*k - 43 - 14 = 0. Let n(v) = k*o(v) - 6*a(v). Factor n(d).
3*d*(d - 4)*(d - 1)**2*(d + 4)
Let h(u) be the third derivative of 2/15*u**5 + 0*u**3 - u + 1/540*u**6 + 3*u**4 + 0 + 15*u**2. Factor h(i).
2*i*(i + 18)**2/9
Let p(g) be the second derivative of 2*g**7/189 + 82*g**6/135 + 79*g**5/9 - 605*g**4/27 - 1064*g**3/9 + 392*g**2 + g - 643. Determine q so that p(q) = 0.
-21, -2, 1, 2
Let t(l) be the third derivative of l**5/30 + 7*l**4/24 + 11*l**3/6 - 4*l**2. Let q be t(-4). Let 27*f + 28*f + 5 - 20*f + 20*f**2 - q = 0. What is f?
-2, 1/4
Let s be 10*-1*3*(-3)/9. Let z(f) be the second derivative of 25/6*f**3 + 0 + s*f**2 + 5/12*f**4 + 9*f. Determine x, given that z(x) = 0.
-4, -1
Let z(g) be the third derivative of -75*g**8/56 - 79*g**7/7 - 979*g**6/60 + 365*g**5/6 + 44*g**4 + 12*g**3 + g**2 + 163. Let z(r) = 0. Calculate r.
-3, -2/15, 1
Let u = -3913/11 + 31791/77. Suppose -u - 8*i**2 - 260/7*i - 4/7*i**3 = 0. Calculate i.
-5, -4
Suppose -q + 2 = q + 2*o, 0 = 5*q - 4*o + 13. Let c be 3 - (1 - 2) - q - -1. Let 3*g**2 - 37*g - 7 + 49*g - 5 - c*g**2 = 0. What is g?
2
Let w(o) be the first derivative of 8*o**6/21 - 2*o**5/5 - o**4/14 + 1436. Factor w(b).
2*b**3*(b - 1)*(8*b + 1)/7
Suppose -171*h = -163*h. Suppose h = -207*y + 203*y + 8. Factor -y*f**3 - 1/3*f**5 + 0 - 1/3*f + 4/3*f**4 + 4/3*f**2.
-f*(f - 1)**4/3
Let p(b) = 3*b**2 - 22*b - 13. Let r be p(8). Factor -4*u**2 - 12*u**4 + 13*u