k. Let f be n(6). Factor -5*h - 6*h**3 - 3*h + f*h - 9*h**2.
-3*h*(h + 1)*(2*h + 1)
Let v(f) be the first derivative of -f**3 - 3/4*f**4 + 8 + 15/2*f**2 - 9*f. Factor v(j).
-3*(j - 1)**2*(j + 3)
Let v(f) be the third derivative of -f**6/840 + f**5/84 - f**4/28 + 43*f**2 - 2. Factor v(r).
-r*(r - 3)*(r - 2)/7
Let l(w) = -w**4 + 52*w**2 - 96*w + 43. Let k(h) = h**4 - h**2 - 1. Let o(m) = -2*k(m) + l(m). Suppose o(q) = 0. What is q?
-5, 1, 3
Let q(i) be the first derivative of -i**4/12 + 5*i**3/9 - 2*i**2/3 - 178. Factor q(l).
-l*(l - 4)*(l - 1)/3
Let n(p) = -p**4 + 2*p**3 - 27*p**2 + 17*p + 4. Let o(v) = 2*v**4 - v. Let h(z) = -n(z) - 5*o(z). Solve h(q) = 0.
-2, -2/9, 1
Let g(r) be the first derivative of -r**5/25 + r**4/20 + 4*r**3/5 + 2*r**2/5 - 16*r/5 - 64. Factor g(y).
-(y - 4)*(y - 1)*(y + 2)**2/5
Factor 44*l**5 + 5*l**2 + 0*l - 34*l**5 + 0*l + 18*l**3 - l**2 + 24*l**4.
2*l**2*(l + 1)**2*(5*l + 2)
Let j be (-759)/(-2691) - (-2)/6. Let 4/13 - 6/13*v**3 - j*v**2 + 10/13*v = 0. Calculate v.
-2, -1/3, 1
Let k(n) be the first derivative of -n**6/21 - 44*n**5/35 - 93*n**4/14 + 240*n**3/7 + 432*n**2/7 + 112. Determine y, given that k(y) = 0.
-12, -1, 0, 3
Let x be (-3)/(-15) - ((-69)/5 + 1). Factor 0*f**2 - 18 + x*f - 5*f - 2*f**2 - 20*f.
-2*(f + 3)**2
Determine n, given that -2 + 2/3*n**2 - 4/3*n = 0.
-1, 3
Solve -12 + 14*d - 3*d**2 - d**2 - d**2 + 3*d**2 = 0 for d.
1, 6
Suppose 4*l - 2 = 90. Suppose 19*k + 8 = l*k. Let 2*n**k + 2*n**5 + 4*n**4 + 3*n**4 - 3*n**2 - 4*n**4 = 0. What is n?
-1, 0, 1/2
Let j(u) be the third derivative of -u**8/110880 + u**7/9240 - 2*u**5/15 + 9*u**2. Let n(w) be the third derivative of j(w). Factor n(x).
-2*x*(x - 3)/11
Solve 24/7*y**2 - 4/7*y**3 - 24/7 + 4/7*y = 0 for y.
-1, 1, 6
Suppose -4*q = 23 - 67. Let m = 14 - q. Suppose 6*d**4 + 4*d**2 - 4*d**4 - 6*d**4 - 6*d**m - 2*d**2 + 2 + 6*d = 0. What is d?
-1, -1/2, 1
Suppose -q + 70 = 6*q. Suppose -q*i = -6*i. Factor 0*p**3 + i*p - 2/15*p**2 + 2/15*p**4 + 0.
2*p**2*(p - 1)*(p + 1)/15
Let m(y) be the first derivative of y**6/2 + 24*y**5/5 + 9*y**4 - 508. Let m(i) = 0. What is i?
-6, -2, 0
Factor 4*t + 0 + 2*t**2 - 5/2*t**4 - 1/2*t**5 - 3*t**3.
-t*(t - 1)*(t + 2)**3/2
Factor -84/5*a + 3/5*a**2 + 156/5.
3*(a - 26)*(a - 2)/5
Let i(k) be the second derivative of -k**5/50 - 2*k**4/15 + 4*k**3/15 + 16*k**2/5 + 62*k. Determine d so that i(d) = 0.
-4, -2, 2
Suppose 40 = 5*u + 10. What is r in -339 + r**3 - u*r**2 + 339 = 0?
0, 6
Let p(m) be the third derivative of 0*m + 17*m**2 + 0*m**4 - 1/9*m**3 + 0 + 1/90*m**5. Factor p(u).
2*(u - 1)*(u + 1)/3
Let z(c) = c**4 - 2*c**3 + 2*c**2 - 2*c - 1. Let l(x) = -x**3 + x**2 + x + 1. Let b be 8/(-16) - (-10)/4. Let f = b + -1. Let a(g) = f*z(g) + l(g). Factor a(v).
v*(v - 1)**3
Let c = -117 - -66. Let s = -49 - c. Let -4/15*o + 2/15*o**s + 0 = 0. Calculate o.
0, 2
Suppose 5*o + 2 = 3*a + 9, 0 = 5*a - 5. Let t(b) be the first derivative of 0*b**2 + 0*b + 0*b**3 + o + 1/4*b**4. Let t(c) = 0. Calculate c.
0
Suppose 5*r + 15 = 0, -6 = -5*l - 2*r - 2. Let n be (-9)/3 - (-3 - l). Factor -5/8*k + n*k**2 - 1/4 - 9/8*k**3.
-(k - 1)**2*(9*k + 2)/8
Let h(u) be the third derivative of u**6/80 - u**5/10 + 5*u**4/16 - u**3/2 + u**2 + 18. Factor h(c).
3*(c - 2)*(c - 1)**2/2
Factor -36/7*c + 4/7*c**2 - 88/7.
4*(c - 11)*(c + 2)/7
Let o(u) = -24*u + 52. Let w be o(2). Let n(b) be the first derivative of 1/16*b**w + 0*b + 0*b**3 - 3 + 0*b**2. Determine m, given that n(m) = 0.
0
Let y(q) be the second derivative of q**6/15 + q**5/4 + q**4/4 - q**3/6 - q**2/2 - 51*q + 1. Factor y(g).
(g + 1)**3*(2*g - 1)
Let o(c) = 3*c**5 - 7*c**4 + 8*c**3 - 2*c**2. Let d(x) = -x**4 - x**3 + x**2. Let v(w) = -2*d(w) - o(w). Determine g, given that v(g) = 0.
0, 1, 2
Let h(d) be the third derivative of d**9/37800 - d**8/2100 + d**7/350 - 9*d**5/100 - d**4/4 + 12*d**2. Let p(o) be the second derivative of h(o). Factor p(z).
2*(z - 3)**3*(z + 1)/5
Let -54/5 + 78/5*k + 2/5*k**3 - 26/5*k**2 = 0. Calculate k.
1, 3, 9
Suppose -296*n = -291*n - 35. Let y be 44/n - (-156)/(-26). Factor 0*z + 0 + y*z**2 + 2/7*z**4 - 4/7*z**3.
2*z**2*(z - 1)**2/7
Let k(b) = 8*b**2 - 112*b + 100. Let f(c) = -15*c**2 + 223*c - 201. Let n(z) = -4*f(z) - 7*k(z). Factor n(t).
4*(t - 26)*(t - 1)
Let a(n) be the second derivative of n**5/10 - 5*n**4/6 + n**3 + 9*n**2 + 342*n - 2. Factor a(q).
2*(q - 3)**2*(q + 1)
Let 145*c**2 - 79*c**2 - 100*c**2 + 2*c**3 - 74*c - 38 = 0. Calculate c.
-1, 19
Factor 13*k - 13*k + 110*k**4 - 3380*k**2 - 273*k**3 + 13*k**3 - 115*k**4.
-5*k**2*(k + 26)**2
Let v(h) be the first derivative of -25/2*h**2 - 42 - 5/3*h**3 + 30*h. Suppose v(u) = 0. Calculate u.
-6, 1
Let i(l) be the second derivative of 0*l**2 + 0 - 1/150*l**6 + 1/20*l**3 + 16*l + 1/60*l**4 - 1/50*l**5 + 1/420*l**7. Let i(t) = 0. What is t?
-1, 0, 1, 3
Let k be (19/(3591/36))/((-4)/(-28)). Factor -1/9*v**2 - 4 + k*v.
-(v - 6)**2/9
Let k be (-1)/(-2) - 7/14. Suppose k = -4*z - 0*z. Determine y so that -2/5*y + z - 2/5*y**2 = 0.
-1, 0
Let y(t) = 15*t**3 + 115*t**2 + 10*t. Let x(m) = 7*m**3 + 58*m**2 + 4*m. Let z(k) = -5*x(k) + 2*y(k). Factor z(p).
-5*p**2*(p + 12)
Factor -i**5 - 68*i**4 + 189*i**4 - 62*i**4 - 58*i**4.
-i**4*(i - 1)
Let l be (-6)/14*6*(-18)/81. Find i, given that l*i**3 + 8/7*i**2 + 0 + 4/7*i = 0.
-1, 0
Factor -6/13*m + 6/13*m**2 + 2/13 - 2/13*m**3.
-2*(m - 1)**3/13
Let s(l) be the first derivative of -l**6/10 - 3*l**5/10 + l**4/4 + l**3 + 24*l + 7. Let h(c) be the first derivative of s(c). Let h(d) = 0. What is d?
-2, -1, 0, 1
Let b(i) = 8*i**4 + 750*i**3 + 17479*i**2 - 4413*i + 5. Let p(m) = 4*m**4 + 375*m**3 + 8739*m**2 - 2206*m + 3. Let u(d) = 3*b(d) - 5*p(d). Factor u(z).
z*(z + 47)**2*(4*z - 1)
Let j(f) be the third derivative of f**6/540 - f**5/135 - 5*f**4/27 - 8*f**3/9 - 156*f**2. Factor j(s).
2*(s - 6)*(s + 2)**2/9
Factor 19/4*t**3 - 21/4*t**2 - 19/4*t + 1/4*t**4 + 5.
(t - 1)**2*(t + 1)*(t + 20)/4
Let m(k) be the first derivative of -k**6/2 + 12*k**5/5 - 3*k**4/4 - 14*k**3 + 30*k**2 - 24*k - 55. Determine p, given that m(p) = 0.
-2, 1, 2
Let d(s) = -s**2 - 112*s + 710. Let v be d(6). Factor 0*n**v + 0*n - 4/5*n**4 + 0 + 4/5*n**5 + 0*n**3.
4*n**4*(n - 1)/5
Factor -9*o**4 + 8*o**4 + 34*o**4 - 96*o**2 + 90*o**3 + 3*o**5 - 200*o - 280*o.
3*o*(o - 2)*(o + 4)**2*(o + 5)
Let w(s) = -2*s**3 + 145*s**2 + 2*s - 145. Let b(h) = h**3 - 72*h**2 - h + 72. Let l(z) = 5*b(z) + 3*w(z). Factor l(c).
-(c - 75)*(c - 1)*(c + 1)
Let a(u) = 0*u**3 - u + 2*u**3 - 180 + 181 - u**3. Let c(m) = -2*m**4 + 8*m**3 + 2*m**2 - 8*m + 6. Let l(i) = 12*a(i) - 2*c(i). Find b such that l(b) = 0.
-1, 0, 1
Let y(m) be the second derivative of -3*m**4/5 - 106*m**3/15 + 12*m**2/5 + 70*m - 2. Factor y(z).
-4*(z + 6)*(9*z - 1)/5
Let r(f) be the first derivative of -f**6/300 - f**5/30 - 2*f**4/15 - 4*f**3/15 + 33*f**2/2 + 21. Let b(j) be the second derivative of r(j). Factor b(u).
-2*(u + 1)*(u + 2)**2/5
Let z(p) be the second derivative of -1/14*p**7 + 1/2*p**4 - 3/2*p**2 - 1/10*p**6 - 1/2*p**3 + 0 - 2*p + 3/10*p**5. Solve z(l) = 0.
-1, 1
Let k(g) be the second derivative of 1/80*g**5 + 0 - 1/4*g**2 - 10*g - 1/12*g**4 + 5/24*g**3. Find m, given that k(m) = 0.
1, 2
Let s = 211018/61551 - -2/8793. Factor 4/7*a**2 + 36/7 - s*a.
4*(a - 3)**2/7
Let t = 27307312/31343 + -396/2411. Let u = 872 - t. Factor 0*f + 2/13*f**4 + 18/13*f**2 - u*f**3 + 0.
2*f**2*(f - 3)**2/13
Factor -33655 - 795*i**2 + 33655 + 20*i**4 - 160*i - 615*i**3.
5*i*(i - 32)*(i + 1)*(4*i + 1)
Determine n so that -14/3*n**2 + 4*n + 16/3 - 2/3*n**4 - 4*n**3 = 0.
-4, -2, -1, 1
Let v be (-2)/(-3) + (-37)/(-3). Suppose -7*c + 4*c = -39. Factor -45 + d**2 - c*d**2 + v - 48*d - 12*d**2 - 4*d**3.
-4*(d + 2)**3
Suppose 117*d + 0 = 116*d + 3. Suppose -1/4*r**d - 9/4*r**2 - 27/4*r - 27/4 = 0. What is r?
-3
Let 44*z**3 + 48*z + 28*z + 48 + 148*z - 212*z**2 = 0. Calculate z.
-2/11, 2, 3
Suppose 33*z - 282 = -108*z. Factor -12/11 + 2/11*b**z + 10/11*b.
2*(b - 1)*(b + 6)/11
Suppose 10 = 3*o - d + 4, d - 9 = -2*o. Find i, given that 2/3*i**4 + 1/2*i + 8/3*i**o + 13/6*i**2 + 0 = 0.
-3, -1/2, 0
Suppose 810*z**2 - 8100*z - 36*z**3 + 30375 + 3/5*z**4 = 0. Calculate z.
15
Let s(i) be the third derivative of 0 - 19*i**2 + 0*i**6 - 1/3528*i**8 + 0*i**4 + 2/2205*i**7 + 0*i**5 + 0*i**3 + 0*i. Facto