t a be q(29). Factor 0*k**3 - 6*k**2 + 3/2*k**a + 0 + 0*k.
3*k**2*(k - 2)*(k + 2)/2
Let v(i) be the first derivative of i**4/4 + i**3/3 - 17*i**2/2 + 15*i - 190. Factor v(w).
(w - 3)*(w - 1)*(w + 5)
Suppose -40 = -i - 3*x + 2*x, -3*i - 5*x + 126 = 0. Suppose i*a = 33*a + 12. Factor 2/7*u**2 + 0 - 2/7*u**a + 2/7*u - 2/7*u**4.
-2*u*(u - 1)*(u + 1)**2/7
Let f(d) be the third derivative of 13/300*d**5 + 17/1050*d**7 - 1/25*d**6 + 10*d**2 + 0*d + 0 + 0*d**3 - 1/60*d**4 - 1/420*d**8. Let f(p) = 0. Calculate p.
0, 1/4, 1, 2
Let i(c) be the third derivative of -1/15*c**5 + 0 + 0*c - 1/30*c**6 + 1/84*c**8 + 0*c**3 - c**2 + 0*c**4 + 2/105*c**7. What is b in i(b) = 0?
-1, 0, 1
Let q be ((-20)/15)/((-52)/351). Let h(z) be the second derivative of -1/100*z**5 + 0 - 7/30*z**3 + 1/12*z**4 + 3/10*z**2 + q*z. Factor h(p).
-(p - 3)*(p - 1)**2/5
Let n(g) be the first derivative of 2/27*g**3 + 0*g + 5 + 1/18*g**4 - 2/9*g**2. Factor n(j).
2*j*(j - 1)*(j + 2)/9
Factor 28*p**2 - 12 - 24*p - 65*p**2 - 9 + 34*p**2.
-3*(p + 1)*(p + 7)
Suppose 12*n = 5*n + 3283. Let f = n + -6059/13. Factor 16/13*v + f*v**2 + 14/13*v**3 - 8/13.
2*(v + 1)*(v + 2)*(7*v - 2)/13
Let m(y) be the second derivative of -13*y + 0 + 1/48*y**4 - 1/40*y**5 + 1/4*y**2 + 5/24*y**3. Factor m(b).
-(b - 2)*(b + 1)*(2*b + 1)/4
Let v = 547/825 + 1/275. Suppose -a - 2*a + 6 = 0. Solve -o**a + 1/3*o**3 + 0 + v*o = 0 for o.
0, 1, 2
Factor 1458 + 147*p**2 + 136*p**2 - 335*p**2 - p**3 - 621*p.
-(p - 2)*(p + 27)**2
Let c(v) = 5*v**2 + 10*v - 27. Let t(s) = -20*s**2 - 40*s + 105. Let d(h) = 15*c(h) + 4*t(h). Factor d(z).
-5*(z - 1)*(z + 3)
Let j be 0 + -17 + -3 + -2. Let o be (-84)/j - 18/(-99). Determine f, given that 0*f - 6*f - o - 2*f - 4*f**2 + 0*f = 0.
-1
Factor 0*u + 6/5*u**4 - 2/5*u**5 + 0 + 0*u**2 - 4/5*u**3.
-2*u**3*(u - 2)*(u - 1)/5
Let n = -10 - 9. Let i(f) = f**2 + 20*f + 23. Let d be i(n). Determine z so that 9 - 4*z - 5 + 4 - d*z**2 = 0.
-2, 1
Let j = 271283/224913 + -6/5767. Let p = -7/13 + j. What is g in 2/3*g + 0 - 2/3*g**4 + 2/3*g**2 - p*g**3 = 0?
-1, 0, 1
Let g(k) be the first derivative of 3*k**5/25 + 69*k**4/10 + 144*k**3 + 1215*k**2 + 2025*k - 80. Find h, given that g(h) = 0.
-15, -1
Let o(y) be the second derivative of y**5/80 - 11*y**4/48 - y**3/2 + 3*y + 83. Suppose o(a) = 0. Calculate a.
-1, 0, 12
Let m = -1 + -1. Let v(j) = -j**2 - 1. Let n(p) = -11*p + 13*p + 16509 + 13*p - 16505 - 15*p**2. Let u(k) = m*v(k) - n(k). Factor u(i).
(i - 1)*(17*i + 2)
Let x = -114 + 119. Let y(l) be the third derivative of -1/630*l**7 - 1/180*l**x - 1/180*l**6 + 0 + 0*l + 0*l**3 - l**2 + 0*l**4. Find m such that y(m) = 0.
-1, 0
Suppose 0 = -11*d + 9*d + 8. Let 3*y - 64*y**2 + 25*y**3 + 12*y**4 + 13*y - 5*y**3 + 16*y**d = 0. Calculate y.
-2, 0, 2/7, 1
Find a such that -167*a**3 + 30*a + 35*a**2 - 276*a**4 - 58*a**3 + 346*a**4 = 0.
-2/7, 0, 1/2, 3
Suppose 0 = -4*o - 4*m + 12, 3 = 4*o - 9*m + 4*m. Factor -x**3 - 3*x**4 + 47*x**2 + 3*x - 44*x**2 - o*x**3.
-3*x*(x - 1)*(x + 1)**2
Determine o so that 3/4*o**2 + 768 - 48*o = 0.
32
Let o = 14 - -20. Factor -25*q**5 - 4*q + 2*q + 55*q**2 + 51*q**4 - 105*q**3 - 8*q + o*q**4.
-5*q*(q - 1)**3*(5*q - 2)
Factor 24 - 442*m**3 + 20*m**2 + 46*m + 220*m**3 + 220*m**3.
-2*(m - 12)*(m + 1)**2
Solve 4/3 + 1/3*d - 1/6*d**2 = 0.
-2, 4
Let x(b) = 131*b + 262. Let r be x(-2). Let r + 2/9*i**4 - 2/9*i**2 + 4/9*i**3 - 4/9*i = 0. What is i?
-2, -1, 0, 1
Let u be ((-38)/76)/((-7)/28). Solve 0*g - 2/3*g**2 + 0 - u*g**3 + 8/3*g**4 = 0 for g.
-1/4, 0, 1
Let y(z) be the first derivative of -16*z**3/15 - 17*z**2/5 - 4*z/5 - 546. Factor y(x).
-2*(x + 2)*(8*x + 1)/5
Let s = -171 + 90. Let k be (-1 - 0)*s/54. Find f such that -3 + k*f**2 + 3/2*f = 0.
-2, 1
Let z(q) be the second derivative of -q**5/170 - 13*q**4/51 + 9*q**3/17 - 14*q + 4. Solve z(y) = 0.
-27, 0, 1
Let r(g) be the third derivative of -g**7/945 + g**6/135 + 7*g**5/270 - 5*g**4/54 + 298*g**2. Determine m so that r(m) = 0.
-2, 0, 1, 5
Let 9/4 + 9/4*k - 5/6*k**3 + 7/12*k**4 - 3/2*k**2 - 1/12*k**5 = 0. What is k?
-1, 3
Let d(r) = -r**5 - 5*r**4 - 7*r**3 + r**2 + 12*r + 4. Let u(q) = 2*q**5 + 10*q**4 + 14*q**3 - 2*q**2 - 25*q - 8. Let c(t) = 9*d(t) + 4*u(t). Factor c(w).
-(w - 1)*(w + 1)**2*(w + 2)**2
Let -16*w**5 - 31*w - 112*w**3 - w + 200 - 88*w**2 - 204 - 68*w**4 = 0. Calculate w.
-1, -1/4
Let k(m) be the first derivative of 4/55*m**5 + 0*m + 0*m**4 + 0*m**2 + 1/33*m**6 + 3 + 0*m**3. Determine p, given that k(p) = 0.
-2, 0
Let f(h) = -h + 13. Let d be f(11). Factor 2*r**d + 1 + 3*r + 8 + 7*r - 1.
2*(r + 1)*(r + 4)
Factor -6/13*j**3 + 4/13*j**4 + 0*j - 4/13*j**2 + 0.
2*j**2*(j - 2)*(2*j + 1)/13
Let q(g) be the first derivative of 3*g**4/8 - 11*g**3/6 + 2*g**2 + 2*g - 518. Suppose q(d) = 0. Calculate d.
-1/3, 2
Suppose 5*v + 10 = 0, -2*v - 111 = p - 109. Factor -12/7*a + 0*a**p - 3/7*a**4 + 0 + 9/7*a**3.
-3*a*(a - 2)**2*(a + 1)/7
Let q = 565/2 + -281. Suppose -q - 1/2*d**2 - 2*d = 0. What is d?
-3, -1
Let j(m) be the first derivative of -1/66*m**4 - 2*m + 0*m**2 + 2/33*m**3 - 1/110*m**5 - 12. Let t(u) be the first derivative of j(u). Solve t(b) = 0.
-2, 0, 1
Let v(d) be the third derivative of 3*d**5/10 + 61*d**4/12 - 14*d**3/3 + 30*d**2. Factor v(y).
2*(y + 7)*(9*y - 2)
Let k be 179/35 - -1 - 348/(-1218). Factor -6/5*c + 0 - k*c**3 - 8/5*c**4 - 26/5*c**2.
-2*c*(c + 3)*(2*c + 1)**2/5
Let a = -67 - -70. Let r(m) be the third derivative of 5*m**2 + 0*m**a + 0*m - 1/40*m**6 - 1/10*m**5 + 0 - 1/8*m**4. What is w in r(w) = 0?
-1, 0
Let y(d) be the third derivative of d**11/831600 - d**10/378000 + 4*d**5/15 - 6*d**2. Let k(q) be the third derivative of y(q). Factor k(i).
2*i**4*(i - 1)/5
Let j = -23 + 28. Suppose 25*n = j*n - 3*n. Factor -6/7*x + n + 2/7*x**2.
2*x*(x - 3)/7
Let n(f) = -f**4 - 1. Let o(q) = 5*q**4 - 15*q**3 - 84*q**2 - 208*q - 186. Let x(a) = 6*n(a) + o(a). Determine y so that x(y) = 0.
-4, -3
Let n(s) be the first derivative of 5*s**9/2592 + s**8/420 + s**7/1260 - 35*s**3/3 - 1. Let b(i) be the third derivative of n(i). Factor b(c).
c**3*(5*c + 2)*(7*c + 2)/6
Suppose 2*l - 48 = -4*s, -5*l + 0 = 3*s - 36. Suppose -m + 5*m = s. Determine b, given that -3/4*b**2 - 1/2*b - 1/4*b**m + 0 = 0.
-2, -1, 0
Suppose 4*m - 56 = -236. Let b = 47 + m. Factor 1/3*y**b - 1/6 + 1/6*y.
(y + 1)*(2*y - 1)/6
Let i = -27748/3 + 9251. Solve 0 - 4/3*p**3 - i*p**2 - 1/3*p = 0 for p.
-1, -1/4, 0
Let q(z) be the third derivative of -1/9*z**4 - 4*z**2 + 2/9*z**3 + 0 + 0*z + 1/45*z**5. Solve q(p) = 0.
1
Let p(s) be the first derivative of -s**6/3780 - s**5/315 + 5*s**4/252 - 3*s**3 - 6. Let u(z) be the third derivative of p(z). Suppose u(l) = 0. What is l?
-5, 1
Let 5472 + 20*x**4 + 7404 + 405*x**3 + 47530*x - 1548 + 46065*x**2 + 677 - 2345*x**3 = 0. What is x?
-1/2, 49
Suppose -5*c + 5*n = 70, 5*c = -5*n + 2*n - 38. Let l be (28/c)/(-7)*2/4. Factor -h**3 - l + 1/5*h + 2/5*h**4 + 3/5*h**2.
(h - 1)**3*(2*h + 1)/5
Factor 66*z**2 + 5*z**3 + 3*z**3 + 16*z - 72*z - 485 + 467.
2*(z - 1)*(z + 9)*(4*z + 1)
Let f(s) = 75*s**3 - 285*s**2 + 120*s - 5. Let c(l) = -74*l**3 + 286*l**2 - 119*l + 3. Let z(x) = 5*c(x) + 6*f(x). Factor z(j).
5*(j - 3)*(4*j - 1)**2
Let g(a) be the first derivative of -1/14*a**4 + 0*a + 14 + 2/35*a**5 + 0*a**3 + 0*a**2. Factor g(z).
2*z**3*(z - 1)/7
Let m = -394377264/209 + 1886968. Let s = m + 90/19. Factor -s*b**4 + 6/11*b**3 + 0 - 6/11*b**2 + 2/11*b.
-2*b*(b - 1)**3/11
Let p(h) be the second derivative of h**6/30 + 13*h**5/80 + h**4/16 - 17*h. Factor p(y).
y**2*(y + 3)*(4*y + 1)/4
Let s be 2/(-2 - 0) + 2. Suppose 5*n + s = d, -d - 2 + 3 = n. Factor -9/2*o**3 - 3/2*o**5 - 3/2*o**2 + 0*o + n - 9/2*o**4.
-3*o**2*(o + 1)**3/2
Solve -1007 + 1405*w**2 + 2379*w**2 + 1036*w**2 - 100*w**3 - 3456*w - 440*w**2 + 1695 = 0 for w.
2/5, 43
Let m(f) be the third derivative of 3*f**6/220 + f**5/30 + f**4/66 - 68*f**2. Factor m(x).
2*x*(x + 1)*(9*x + 2)/11
Let c(q) be the second derivative of 5/12*q**4 + 0 - 20*q + 15/2*q**2 - 10/3*q**3. Factor c(a).
5*(a - 3)*(a - 1)
Let f(b) be the second derivative of -9*b**4/16 - b**3 + 3*b**2/8 + 91*b. What is j in f(j) = 0?
-1, 1/9
Let b(x) = 2*x**3 + x - 1. Let p(g) = -5*g**3 + 40*g**2 + 100*g + 95. Let k(f) = 5*b(f) + p(f). Factor k(z).
5*(z + 2)*(z + 3)**2
Suppose -5*w = -3*s - 30, w + s + 11 = 3*w. 