+ 0*n**4 - 3/5*n**5 + 2*n**3. Factor g(b).
-3*(b - 1)**2*(b + 1)**2
Let g be ((-6)/(-15))/((-9)/(-5)). Suppose -5*d = -3*k + 15, -8*d + 5*d = -3*k + 15. Find c, given that 2/3*c**4 + 2/9*c**3 + d - g*c - 2/3*c**2 = 0.
-1, -1/3, 0, 1
Let a(w) be the first derivative of 0*w**2 + 1/10*w**6 - 3/4*w**4 - 4 + 0*w**5 - w**3 + w. Let i(s) be the first derivative of a(s). Factor i(y).
3*y*(y - 2)*(y + 1)**2
Let f(o) be the second derivative of o**5/20 - 3*o**4/2 + 71*o**3/6 - 39*o**2 - 13*o - 1. Determine m, given that f(m) = 0.
2, 3, 13
Factor 312/19*q**2 + 2/19*q**4 + 60/19*q**3 + 592/19*q + 384/19.
2*(q + 2)**3*(q + 24)/19
Let y(m) be the first derivative of m**3 + 25*m**2/6 - 2*m - 82. Factor y(q).
(q + 3)*(9*q - 2)/3
Let w(r) = -14*r - 24. Let d be w(-5). Let n = 46 - d. Solve -3 + n*q**2 - 3/2*q**3 + 9/2*q = 0.
-2, 1
Let n = 39 - -191. Let n*s**4 + 7*s**3 + 5*s**2 - 215*s**4 - 27*s**3 = 0. What is s?
0, 1/3, 1
Let u(g) = 3*g**2 - 124*g + 244. Let c be u(2). Let n(s) be the second derivative of 7/5*s**5 - 12*s - 19/3*s**4 + 16/3*s**3 + c*s**2 + 0. Solve n(f) = 0.
-2/7, 1, 2
Let j(x) be the second derivative of x**6/120 - x**5/6 + 25*x**4/24 + 3*x**2/2 + 14*x. Let u(q) be the first derivative of j(q). Factor u(f).
f*(f - 5)**2
Let g(j) = 2*j**2 - 4*j. Let k(y) = 22*y**2 + 50*y. Let i(t) = 12*g(t) - k(t). Factor i(q).
2*q*(q - 49)
Factor 111/4 - 3/8*u**2 + 105/8*u.
-3*(u - 37)*(u + 2)/8
Let x = -757 + 759. Let i = -4/133 + 1616/665. Factor 0 - 15*l**3 - i*l - 12*l**x.
-3*l*(5*l + 2)**2/5
Determine t, given that -90/13*t - 42/13*t**2 - 46/13 + 2/13*t**3 = 0.
-1, 23
Let m = 23 - 20. Solve 6*p**2 + 14*p**m - 3*p**2 + 2*p + 6*p**4 + 7*p**2 = 0 for p.
-1, -1/3, 0
Suppose -315*v - 4960 = -1116*v - 439*v. Let x = -13/4 + 69/20. Suppose -x*k**v + 7/10*k + 1/5 - 1/10*k**5 + 1/5*k**3 + 4/5*k**2 = 0. Calculate k.
-1, 2
Let c(s) be the second derivative of -s**7/42 - 77*s**6/120 - 439*s**5/80 - 301*s**4/48 + 2695*s**3/24 + 343*s**2/4 - 7*s + 7. Suppose c(d) = 0. What is d?
-7, -1/4, 2
Suppose -x + 0*x + 13 = 0. Suppose 0 = -2*p - p + 2*b + x, 3*p = -2*b + 17. Factor -4/3*k**4 - 2/3*k**p + 0*k + 0 + 0*k**2 - 2/3*k**3.
-2*k**3*(k + 1)**2/3
Let g(u) = u**3 + 35*u**2 - 44*u - 80. Let o(v) = 25*v**3 + 770*v**2 - 970*v - 1760. Let r(a) = -45*g(a) + 2*o(a). Suppose r(f) = 0. Calculate f.
-1, 4
Let q(d) = -70*d**5 - 85*d**4 + 203*d**3 + 420*d**2 + 261*d + 49. Let w(n) = n**5 + n**4 + n**3 - 1. Let p(z) = q(z) - 5*w(z). Solve p(u) = 0.
-1, -3/5, 2
Let r be 3*(9 + (-723)/81). Factor -2/3*a - 2 - r*a**3 + 10/9*a**2.
-2*(a - 3)**2*(a + 1)/9
Let g be (-3)/(-5)*(60/25 + 5/50). Solve g*m**2 - 3/2*m + 0 = 0 for m.
0, 1
Let f(j) = j**2 + j. Let g be f(1). Suppose 3*s - g - 7 = 0. Determine a, given that -15*a**3 - 3*a**2 - 3*a**5 + 6*a**s - 9*a**4 + 0*a**3 = 0.
-1, 0
Let u(d) be the second derivative of d**5/10 + 7*d**4/6 + 2*d + 3. Suppose u(o) = 0. What is o?
-7, 0
Let r(w) = 7*w**2 - 78*w + 503. Let c(m) = 3*m - 14. Let h be c(6). Let u(p) = 6*p**2 - 78*p + 504. Let o(j) = h*u(j) - 3*r(j). Suppose o(x) = 0. What is x?
13
Let l be (-28)/770*(21 - 1). Let h = l - -68/33. Let -2/3*n**2 + 0*n - h*n**4 + 5/3*n**3 + 1/3*n**5 + 0 = 0. What is n?
0, 1, 2
Let b(d) be the second derivative of -d**5/160 + d**3/16 + 15*d**2/2 - 7*d. Let k(h) be the first derivative of b(h). Suppose k(i) = 0. What is i?
-1, 1
Let o(m) be the second derivative of -m**7/168 - 17*m**6/120 - 7*m**5/5 - 22*m**4/3 - 64*m**3/3 - 32*m**2 - 34*m. Factor o(c).
-(c + 1)*(c + 4)**4/4
Let p(t) be the third derivative of -t**8/3360 - t**7/420 - 13*t**4/12 - 18*t**2. Let v(r) be the second derivative of p(r). Factor v(l).
-2*l**2*(l + 3)
Let f(a) = -a**2 + 7*a + 11. Let b be f(8). Suppose 91*s**2 + 11211 + 104*s**2 + 2504*s - 226 + 5*s**b + 31*s = 0. What is s?
-13
Suppose 4*h = 46 - 18. Suppose -5*a = -22 + h. Determine b so that 108*b - 186*b**2 + 114*b**2 + 20*b**a + 0*b**4 - 54 - 2*b**4 = 0.
1, 3
Let k(c) be the third derivative of 33*c**2 + 0 + 1/112*c**8 - 1/10*c**6 + 1/10*c**5 + 0*c**3 - 1/35*c**7 + 0*c + 3/8*c**4. Determine i so that k(i) = 0.
-1, 0, 1, 3
Suppose 411*q = 403*q + 24. Let p(y) be the third derivative of -5/84*y**4 + 0 + 2/21*y**3 + 2/105*y**5 + q*y**2 - 1/420*y**6 + 0*y. Factor p(g).
-2*(g - 2)*(g - 1)**2/7
Let y(v) be the second derivative of 0 - 7/195*v**6 - 9/65*v**5 - 1/273*v**7 - 7*v - 1/3*v**3 - 3/13*v**2 - 11/39*v**4. Factor y(n).
-2*(n + 1)**4*(n + 3)/13
Let h(n) be the first derivative of n**6/60 - n**5/15 + n**4/12 - 3*n**2 - 2. Let g(p) be the second derivative of h(p). Determine f so that g(f) = 0.
0, 1
Let 9/4*c**2 + 3/8*c**3 + 3*c + 0 = 0. What is c?
-4, -2, 0
Let o(z) be the first derivative of z**4/22 + 4*z**3/33 - 15*z**2/11 + 68. Suppose o(n) = 0. Calculate n.
-5, 0, 3
Let s be -4*(-7)/(168/18) - -1. Factor 0 + 5/3*i**3 + 5/3*i**2 - 5/3*i - 5/3*i**s.
-5*i*(i - 1)**2*(i + 1)/3
Suppose 0*k + 20 = -2*k. Let m be (-38)/k - 2/(-10). Factor 2*x - 4 - 5*x - 1 - 3*x**2 + m - x**3.
-(x + 1)**3
Let g(o) be the first derivative of -29/6*o**3 - 3/8*o**4 - 18 - 65/4*o**2 + 25/2*o. Factor g(w).
-(w + 5)**2*(3*w - 1)/2
Let v = -7107/2 - -3555. Let y = 18 + -15. Find a, given that -v*a - 3/4*a**2 + 0 + 3/4*a**y = 0.
-1, 0, 2
Let h(k) be the third derivative of k**5/70 + 11*k**4/42 - 16*k**3/21 - 6*k**2 + k. Factor h(p).
2*(p + 8)*(3*p - 2)/7
Factor 299 + 120*k + 59 + 542 + 6*k**2 - 2*k**2.
4*(k + 15)**2
Let h = 79 + 77. Let q = 159 - h. Factor 0*o + 0 - 1/6*o**q + 0*o**2.
-o**3/6
Let a(p) = p**2 + 12*p + 24. Let f be a(-10). Let x(u) be the third derivative of -1/60*u**5 + 0*u + u**2 + 0 + 0*u**f + 0*u**3. Determine g so that x(g) = 0.
0
Let a(m) be the first derivative of -m**4/10 + 2*m**3/15 + 2*m**2/5 - 47. Factor a(g).
-2*g*(g - 2)*(g + 1)/5
Let x be 13/(-26)*(1 + 0 + -1). Suppose 0 = -x*g + 2*g - 7*g. Factor 0 - 1/2*i**3 + 0*i + 1/2*i**5 + g*i**2 + 0*i**4.
i**3*(i - 1)*(i + 1)/2
Let m(d) = 9*d - 2. Let q be m(2). Factor 3 + 33*b**2 + 1 - q*b - 21*b**2.
4*(b - 1)*(3*b - 1)
Let l(r) be the second derivative of r**6/40 + 3*r**5/80 - 3*r**4/16 - 5*r**3/8 - 3*r**2/4 - 116*r. What is i in l(i) = 0?
-1, 2
Determine b, given that 0 + 6/11*b**2 + 4/11*b + 0*b**3 - 2/11*b**4 = 0.
-1, 0, 2
Let p(y) = -4*y - 75. Let r be p(-20). Suppose -r*c - 4*f + 6 = -0*f, -5*f - 5 = 0. What is o in 8/5 - 4*o - 7/5*o**3 + 1/5*o**4 + 18/5*o**c = 0?
1, 2
Let b(a) be the third derivative of -a**9/60480 + a**8/10080 - a**7/5040 - a**5/6 - 2*a**2. Let g(t) be the third derivative of b(t). Find p such that g(p) = 0.
0, 1
Let h(a) = -a**4 - 80*a**3 + 110*a**2 + 69*a - 142. Let b(o) = 16*o**3 - 22*o**2 - 14*o + 28. Let m(c) = 11*b(c) + 2*h(c). What is y in m(y) = 0?
-1, 1, 2, 6
Suppose 0 = 35*g - 82*g + 94. Let n = 779 - 2317/3. Suppose -n*w**g - 28/3*w - 4/3*w**3 - 4 = 0. Calculate w.
-3, -1
Let w(n) be the first derivative of -5*n**6/2 - 24*n**5/5 + 27*n**4/4 + 8*n**3 - 6*n**2 + 70. Suppose w(t) = 0. Calculate t.
-2, -1, 0, 2/5, 1
Let c be 1/2*(-6)/12*0. Let q(o) be the first derivative of -1/4*o**3 + c*o - 3/32*o**4 + 11 + 0*o**2. Factor q(v).
-3*v**2*(v + 2)/8
Let q(f) be the second derivative of 0*f**2 + 4*f + 0 - 1/180*f**6 + 1/140*f**5 + 0*f**4 + 5/6*f**3. Let w(c) be the second derivative of q(c). Factor w(x).
-2*x*(7*x - 3)/7
Factor 2*h**2 - 22669 + 350*h - 3*h**2 - 7956.
-(h - 175)**2
Let c(x) be the first derivative of 2*x**3/33 - 7*x**2/11 - 16*x/11 + 156. Factor c(r).
2*(r - 8)*(r + 1)/11
Let w(l) be the first derivative of -5/4*l**4 - 13/15*l**5 + 9 - 7/9*l**3 - 1/6*l**2 - 2/9*l**6 + 0*l. Suppose w(b) = 0. What is b?
-1, -1/4, 0
Let r = 15 + -20. Let y be -1 + ((-30)/r)/1. Solve -y - 48*p**2 - 51*p + 81*p + 20*p**3 + 3*p**2 = 0 for p.
1/4, 1
Let b(n) be the first derivative of -n**3/12 + 3*n**2/4 + 7*n/4 - 489. Factor b(t).
-(t - 7)*(t + 1)/4
Suppose 19 = 4*z - 45. Let i be 1 + 1 - (-16 + z). Factor -8 - 18*y + y**4 - 12*y + 18*y + 3*y**3 - 2*y**i.
(y - 2)*(y + 1)*(y + 2)**2
Let b(k) be the second derivative of -k**5/80 - 11*k**4/48 + k**3/2 + k + 17. Factor b(f).
-f*(f - 1)*(f + 12)/4
Let d(p) be the second derivative of -p**4/9 + 302*p**3/9 - 643*p. Solve d(w) = 0 for w.
0, 151
Let j(h) be the first derivative of -5*h + 3 - 1/18*h**3 + 1/36*h**4 + 0*h**2. Let k(l) be the first derivative of j(l). Facto