1
Let k be 83/1494 + 2/(-36). Suppose 0*a**2 + 3/4*a**3 + 0 + k*a = 0. What is a?
0
Let u be 2 - -9*8/24. Let c(o) be the third derivative of 0*o**3 - 1/105*o**7 + 0*o**u + 0*o - 3*o**2 + 0 + 0*o**4 - 1/60*o**6. Factor c(x).
-2*x**3*(x + 1)
Find v such that -14/13*v**3 + 80/13*v**2 + 24/13*v + 0 = 0.
-2/7, 0, 6
Let y(f) be the third derivative of -f**8/2016 - 11*f**7/1260 - f**6/72 + 53*f**5/180 - 133*f**4/144 + 49*f**3/36 - 108*f**2. Factor y(x).
-(x - 1)**3*(x + 7)**2/6
Let m(k) be the second derivative of -k**4/3 + 6*k**3 - 16*k**2 - 15*k. Suppose m(z) = 0. What is z?
1, 8
Let p(s) be the second derivative of -s**7/378 + s**6/54 - s**5/30 - s**4/54 + 7*s**3/54 - s**2/6 + 58*s. Let p(c) = 0. Calculate c.
-1, 1, 3
Let f(g) be the second derivative of 2*g**4 + 14*g**3/3 - 26*g**2 + g - 191. Let f(r) = 0. Calculate r.
-13/6, 1
Let q(f) be the first derivative of 0*f + 5/12*f**4 + 6 + 8/9*f**3 + 2/3*f**2 + 1/15*f**5. Let q(y) = 0. What is y?
-2, -1, 0
Let z(c) be the third derivative of 6*c**2 + 1/20*c**5 + 0*c**4 + 0*c + 0*c**3 + 0. Factor z(r).
3*r**2
Find q such that 0 + 1/3*q**4 - 1/3*q**2 + 1/3*q**3 - 1/3*q = 0.
-1, 0, 1
Solve 1/7*k**3 - 3*k - 36/7 + 17/7*k**2 - 1/7*k**4 = 0.
-4, -1, 3
Let y be (2/(-5))/((-21)/15). Let g be -11*(154/(-121))/7. Factor -y*z + 2/7*z**3 + 0*z**g + 0.
2*z*(z - 1)*(z + 1)/7
Factor -2592 - 434/9*f**2 - 2/9*f**3 - 2640*f.
-2*(f + 1)*(f + 108)**2/9
Let k(j) be the first derivative of j**4/34 - 2*j**3/51 - 8*j**2/17 + 24*j/17 - 29. Find g such that k(g) = 0.
-3, 2
Let c(q) be the second derivative of q**6/15 - 19*q**5/170 + q**4/51 + 123*q - 1. Factor c(b).
2*b**2*(b - 1)*(17*b - 2)/17
Let a(x) = 3*x**3 - 129*x**2 - x + 43. Let c be a(43). Factor c - i - 1/4*i**3 - i**2.
-i*(i + 2)**2/4
Let i(f) = 6*f. Let m be i(1). Suppose -10*z = -m*z - 24. Determine c so that 11 + 6*c**2 + z*c - 2 + 0*c - 9*c**2 = 0.
-1, 3
Let l(z) be the third derivative of z**6/24 - 7*z**5/2 + 135*z**4/8 - 100*z**3/3 - 27*z**2. Factor l(t).
5*(t - 40)*(t - 1)**2
Suppose 40000/3 + 800*o**2 + 16000/3*o + 4/3*o**4 + 160/3*o**3 = 0. What is o?
-10
Factor 0 - 1/2*v**4 + 13/2*v**2 + 6*v + 0*v**3.
-v*(v - 4)*(v + 1)*(v + 3)/2
Let x be (6 - 1)*1 - (-7 - -12). Let p(y) be the first derivative of 4 + 1/8*y**4 - 1/10*y**5 + x*y**2 + 0*y**3 + 0*y. Determine i, given that p(i) = 0.
0, 1
Let d(g) be the first derivative of -2*g**3/15 - 94*g**2/5 - 4418*g/5 + 34. Factor d(q).
-2*(q + 47)**2/5
Let u(c) be the second derivative of 4/7*c**6 + 8/7*c**4 - 25/294*c**7 + 0 - 12*c + 0*c**2 - 8/21*c**3 - 46/35*c**5. Factor u(x).
-x*(x - 2)**2*(5*x - 2)**2/7
Let p(q) = -5*q**2 + 79*q - 95. Let x(f) = 4*f**2 - 80*f + 90. Let r(z) = -4*p(z) - 6*x(z). Factor r(n).
-4*(n - 40)*(n - 1)
Let -800/17 - 2/17*p**2 - 80/17*p = 0. Calculate p.
-20
Let f(s) be the third derivative of -s**7/1260 - s**6/120 + s**5/24 - s**4/18 + 5*s**2 - 15*s. Let f(o) = 0. What is o?
-8, 0, 1
Factor 12/7 + 8/7*y + 1/7*y**2.
(y + 2)*(y + 6)/7
Let y(h) be the third derivative of h**5/15 - 3*h**4/2 - 44*h**3/3 - 61*h**2 + 2*h. Factor y(n).
4*(n - 11)*(n + 2)
Let c(m) = m**3 - m. Let f = -85 + 80. Let s(v) = -3*v**3 + 24*v**2 + 101*v + 128. Let k(y) = f*c(y) - s(y). Factor k(r).
-2*(r + 4)**3
Let j(l) be the first derivative of -7*l**4/34 - 346*l**3/51 + 232*l**2/17 - 104*l/17 + 606. Let j(f) = 0. Calculate f.
-26, 2/7, 1
Factor 16/5 - 2/5*s**2 + 14/5*s.
-2*(s - 8)*(s + 1)/5
Suppose 2*p + 2*p = 4, 3*f + 2*p = 20. Let 3*o + 5*o**2 - 2*o**2 - f*o = 0. What is o?
0, 1
Let m(v) be the first derivative of -3*v**4/8 + 9*v**2/4 - 3*v + 54. Solve m(i) = 0 for i.
-2, 1
Determine p so that -167*p - 579 - 409*p + 46875*p**4 - 6600*p**2 - 20000*p**3 + 563 = 0.
-2/25, 2/3
Factor 31/8*w**2 + 46 - 25*w - 1/8*w**3.
-(w - 23)*(w - 4)**2/8
Let y(j) be the third derivative of j**7/1260 + j**6/144 + j**5/60 + 22*j**2 - 2. Solve y(z) = 0 for z.
-3, -2, 0
Suppose 12*z - 16*z + 8 = 0. Let 4*m - 8*m**2 - 14*m + 15 + 3*m**z = 0. Calculate m.
-3, 1
Let d(g) be the first derivative of 3*g**4/28 - 2*g**3/7 + 3*g**2/14 + 439. What is i in d(i) = 0?
0, 1
Let v(h) be the first derivative of -h**3 + 73*h**2/2 + 50*h + 25. Factor v(t).
-(t - 25)*(3*t + 2)
Let i(k) = k**5 + k**3 + 2*k**2 + k - 1. Let b(s) = -s**5 + 79*s**4 + 368*s**3 + 470*s**2 + 127*s - 43. Let v(l) = 5*b(l) + 30*i(l). Solve v(n) = 0.
-7, -1, 1/5
Find j, given that j**3 + 3*j**4 + 5738*j**2 - j**3 - 2*j**3 - 5739*j**2 = 0.
-1/3, 0, 1
Let m(u) be the first derivative of -8 + 1/4*u + 1/4*u**3 + 3/8*u**2 + 1/16*u**4. Determine c so that m(c) = 0.
-1
Let k(c) be the first derivative of -24 + 0*c + 3/2*c**3 - 3/2*c**2 - 3/8*c**4. Factor k(t).
-3*t*(t - 2)*(t - 1)/2
Let q = 8 - 5. Determine t so that -6*t**3 + 5 + 1 - 3*t + 3*t**3 + 6*t**q - 6*t**2 = 0.
-1, 1, 2
Let f = -1723357/132 - -78247/6. Let l = f + 59/4. Suppose -2/11*p**2 + 0 + l*p = 0. Calculate p.
0, 1
Let n be 0*(0 + (-3)/12). Suppose -6*y + n*y = 0. Factor y*d**2 + 0*d + 0 - 3/5*d**5 + 0*d**4 + 3/5*d**3.
-3*d**3*(d - 1)*(d + 1)/5
Let k(j) be the third derivative of -j**6/120 + j**5/20 - j**4/8 + j**3/6 + 6*j**2 - 10*j. Determine t so that k(t) = 0.
1
Let n = -7542 - -22654/3. Find p such that 0 + 6*p**5 - n*p**3 - 8*p**2 + 16/3*p + 10*p**4 = 0.
-2, -1, 0, 2/3
Let k(b) be the third derivative of 0*b + 0 + 17*b**2 + 4/21*b**3 + 1/14*b**4 + 1/105*b**5. Factor k(z).
4*(z + 1)*(z + 2)/7
Let h(y) be the first derivative of 0*y - 3/2*y**2 + 0*y**3 + 1/48*y**4 + 6 + 1/60*y**6 + 1/24*y**5. Let w(u) be the second derivative of h(u). Factor w(a).
a*(a + 1)*(4*a + 1)/2
What is c in -306/7*c + 540/7 + 24/7*c**2 + 6/7*c**3 = 0?
-10, 3
Let r(u) be the third derivative of u**8/3360 + 19*u**7/8820 + u**6/315 - u**5/105 - u**4/4 + 9*u**2. Let h(g) be the second derivative of r(g). Factor h(k).
2*(k + 1)*(k + 2)*(7*k - 2)/7
Find l, given that 21*l**2 + 3*l - 4*l**2 - 15 - 3 - 7*l**2 - 7*l**2 = 0.
-3, 2
Let w be (-10)/(-60)*30 + 87/(-19). Factor -2/19*h**2 + w + 6/19*h.
-2*(h - 4)*(h + 1)/19
Let d = -844/5 - -169. Let i = 544/55 + -100/11. Factor -i*c - d*c**2 - 3/5.
-(c + 1)*(c + 3)/5
Let j(p) be the first derivative of 60*p**3 - 535*p**2/2 - 15*p + 305. Solve j(b) = 0 for b.
-1/36, 3
Let n(o) = -4*o**2 + 10*o + 14. Let h(p) = p**2 - 3*p - 4. Let m(w) = 22*h(w) + 6*n(w). Determine j so that m(j) = 0.
-2, -1
Let x(j) be the second derivative of 7*j**6/30 - 51*j**5/20 - 7*j**4/2 + 8*j**3/3 + 11*j + 7. Solve x(z) = 0.
-1, 0, 2/7, 8
Let m(y) = -y**3 - y**2 + 1. Let q(u) = -5 - 6*u**2 + 8 - 8*u**4 - 21*u**3 - 2*u**4 + 8*u - 3*u**2. Let t(x) = -6*m(x) - 2*q(x). Factor t(p).
4*(p + 1)**3*(5*p - 3)
Let v(y) be the first derivative of 2*y**3/9 - 11*y**2/3 - 8*y + 44. Suppose v(b) = 0. What is b?
-1, 12
Let t(g) be the second derivative of -g**5/40 - 7*g**4/2 - 196*g**3 - 5488*g**2 - 2*g - 21. Let t(y) = 0. Calculate y.
-28
Let u = 541/7 + -77. Let a = -1/28 + u. Determine c so that c + 3/2*c**2 + c**3 + 1/4*c**4 + a = 0.
-1
Let q(i) = 3*i**2 - 3*i. Let j be (6/4)/(24/(-64)). Let x(k) = k**3 - 3*k**2 + 3*k - 1. Let n(g) = j*q(g) - 3*x(g). What is z in n(z) = 0?
-1, 1
Solve 80616*v + 344*v**2 + 20 - 80916*v + 781*v**2 = 0.
2/15
Find l, given that -372*l**2 + 48 + 10*l + 8*l + 369*l**2 = 0.
-2, 8
Let q be 510/(-34) + (-76)/(-5). Suppose -q*a**2 + 0 + 0*a = 0. Calculate a.
0
Let d = -1042 - -1045. Let f(j) be the first derivative of 6*j + 2*j**2 + 2/9*j**d + 4. Find n, given that f(n) = 0.
-3
Suppose -i - 4 = -3*i. Let a = -53/13 + 423/91. Factor 2/7*t**i - a*t + 2/7.
2*(t - 1)**2/7
Let d(h) be the second derivative of h**4/42 + 20*h**3/21 - 69*h**2/7 + 58*h. Find p, given that d(p) = 0.
-23, 3
Let b(l) = 12*l**2 - 20*l**2 - l**3 + 8*l**2. Let f(t) = -2*t**4 + 44*t**3 - 432*t**2 + 1728*t - 2592. Let w(h) = -4*b(h) + f(h). Let w(x) = 0. Calculate x.
6
Suppose -2*u + 2*k + 2 = 0, -u - 3*k + 7 = -k. Factor -u*j**4 + 8*j**4 - j**3 - 5 + 10*j - 9*j**3.
5*(j - 1)**3*(j + 1)
Let d(g) = 4*g**2 + 8*g + 8. Let u(l) = -l**3 - l**2 + l - 1. Let a(s) = d(s) + 2*u(s). Solve a(o) = 0 for o.
-1, 3
Let v(h) = h**2 - h + 1. Let d be (2 + 10/(-6))/(5/15). Let s(j) = 3*j**5 + 3*j**4 - 9*j**3 - 8*j**2 + 11*j - 5. Let m(y) = d*s(y) + 5*v(y). Factor m(u).
3*u*(u - 1)**2*(u + 1)*(u + 2)
Let u(j) = 2*j**2 - j + 6. Let n be 0 + 10/(2/(-1)). Let h(c) = -3*c**2 + c 