2)/2
Let u(x) = -x**3 + x**2 + 3*x + 2. Let z be u(6). Let k be 1/((-6)/4) - z/168. Determine l, given that -4/7*l - k - 2/7*l**2 = 0.
-1
Let n(p) be the third derivative of p**7/180 - 97*p**6/360 + 329*p**5/90 + 49*p**4/18 + 188*p**2. Suppose n(z) = 0. Calculate z.
-2/7, 0, 14
Let s = 3/19 + 2133/209. What is q in 56/11*q**2 + 72/11*q**4 + 0 - 8/11*q - s*q**3 = 0?
0, 1/4, 2/3
Let x(b) be the first derivative of -2*b**5/5 + 9*b**4/2 + 32*b**3 + 52*b**2 - 21. Factor x(k).
-2*k*(k - 13)*(k + 2)**2
Let -22/5*l**2 - 2/5*l**3 + 72/5 - 48/5*l = 0. What is l?
-6, 1
Let s = -2909 + 14492/5. Let z = s - -57/5. Factor 2/5 - 4/5*x + 0*x**2 - 2/5*x**4 + z*x**3.
-2*(x - 1)**3*(x + 1)/5
Suppose 3*h - 16 = -4*x + 14, 4*x = 0. Factor 5*w**4 + 53 + 48 - 96 - h*w**2 + 0*w**4.
5*(w - 1)**2*(w + 1)**2
Let y = -30 + 39. Determine z so that 4 - 2 - 3*z**4 + 12*z + 8 - 12*z**3 + 2 - y*z**2 = 0.
-2, -1, 1
Suppose -59*z - 4 = -61*z. What is o in -15*o**4 - 2*o + 5*o**3 + 20*o**5 - 14*o**3 + 15*o**z - 16*o**3 + 7*o = 0?
-1, -1/4, 0, 1
Let g = 951 - 949. Let o(q) be the third derivative of 1/21*q**7 + 0*q + 0*q**3 + 1/56*q**8 + 0*q**4 - 1/15*q**6 + 0 - 2/15*q**5 + 7*q**g. Solve o(p) = 0.
-2, -2/3, 0, 1
Let z(d) be the third derivative of 0*d + 0 - 2/33*d**3 + 1/330*d**5 + 20*d**2 - 1/132*d**4. Find k, given that z(k) = 0.
-1, 2
Suppose -h - 144 + 149 = 0. Let a(y) be the second derivative of -1/12*y**3 - 1/80*y**h + 1/16*y**4 + 0 + 0*y**2 + 5*y. Factor a(t).
-t*(t - 2)*(t - 1)/4
Let z(u) = -23*u - 135. Let f be z(-6). Let n(v) be the first derivative of -1/2*v + 1 + 0*v**2 + 1/6*v**f. Suppose n(i) = 0. What is i?
-1, 1
Let t = 125 - 46. Let n = t + -49. Find i, given that 6*i**4 - 100*i**3 + 54*i**4 - 14*i**5 + 80*i**2 - n*i - 2 + 6 = 0.
2/7, 1
Let k(i) be the second derivative of -i**6/150 - 13*i**5/100 - 4*i**4/5 - 6*i**3/5 - i + 15. Factor k(x).
-x*(x + 1)*(x + 6)**2/5
Let z(p) = p**4 + p**3 + 1. Let d(a) = a**4 + 8*a**3 - a**2 - 24*a - 14. Let r(i) = -d(i) + 2*z(i). Solve r(m) = 0.
-1, 4
Suppose 3*n + 2*n**3 + 5*n**3 + 3*n**5 + 5*n**4 + 9 - 4*n**5 - 8*n**3 - 14*n**2 - n**3 = 0. Calculate n.
-1, 1, 3
Factor -100*f - 20*f + 180 - 74*f**2 - 13*f**2 - 5*f**3 + 32*f**2.
-5*(f - 1)*(f + 6)**2
Let o(g) = -6*g**3 - 28*g**2 - 22*g - 10. Let w(c) = -2*c**3 - 9*c**2 - 7*c - 3. Let i(y) = 3*o(y) - 10*w(y). Solve i(u) = 0 for u.
-2, -1, 0
Let k = 5/271 + 2404/1897. Factor 3/7*d**2 - k*d + 0.
3*d*(d - 3)/7
Let m(x) be the second derivative of x**5/90 - x**4/27 + x**3/27 + 3*x + 16. Find v, given that m(v) = 0.
0, 1
Let 0 + 1/5*n**2 + 8*n = 0. What is n?
-40, 0
Let m(v) be the second derivative of -v**5/20 + 3*v**4/4 - 13*v**3/3 + 12*v**2 - 392*v. Find c such that m(c) = 0.
2, 3, 4
Let t(f) be the second derivative of 30*f + 1/3*f**2 - 1/90*f**5 + 0 + 5/54*f**4 - 7/27*f**3. Solve t(b) = 0 for b.
1, 3
Let x(o) be the second derivative of -o**5/18 - 2*o**4/9 - 4*o**3/27 + 3*o - 5. Let x(i) = 0. Calculate i.
-2, -2/5, 0
Suppose 2997*y - 14 = 2995*y - 4*t, 2*y - 4*t + 2 = 0. Factor -40/7*s**2 + 52/7*s**y - 2*s**4 + 0 - 16/7*s.
-2*s*(s - 2)**2*(7*s + 2)/7
Let q(h) be the second derivative of -1/3*h**4 - 2/3*h**3 + 2*h**2 + 1/5*h**5 + 0 - 6*h. Suppose q(c) = 0. Calculate c.
-1, 1
Let a(u) = -13*u**3 + 4*u**2 + 4. Let s(x) = -10*x**3 + 5*x**2 + 3. Let d(h) = -3*a(h) + 4*s(h). Factor d(o).
-o**2*(o - 8)
Factor -62/15*l + 4 + 2/15*l**2.
2*(l - 30)*(l - 1)/15
Let -1/4*i**4 + 465*i - 15*i**3 - 419/2*i**2 - 961/4 = 0. Calculate i.
-31, 1
Let o(c) be the third derivative of c**5/150 - c**4/4 + 14*c**3/15 + 5*c**2 + 3*c. Factor o(t).
2*(t - 14)*(t - 1)/5
Let x be (-1395)/630 + (-10)/(-4). Factor 0*a**2 + 0*a**4 + 4/7*a**3 + 0 - 2/7*a - x*a**5.
-2*a*(a - 1)**2*(a + 1)**2/7
Let y be (-1 - 30/(-4))*(2 - -2). Find x, given that -y*x**2 + 8*x**3 - 24*x - 2*x**4 - 8 - 10*x**3 - 10*x**3 = 0.
-2, -1
Let k(w) = -38*w - 755. Let v be k(-20). Let a(x) be the first derivative of 12 + 0*x**2 + 0*x**4 - 1/25*x**v + 0*x**3 + 0*x. Factor a(u).
-u**4/5
Let z(n) = 14 - 7 + 4*n - 3*n - 2*n. Let h be z(5). Determine p, given that 36*p - 5 - h*p**2 + 3*p**3 + 20*p**2 + 29 + 0*p = 0.
-2
Let 48*l**2 - 45 + 21*l**4 - 55*l - 17*l**4 - 18*l**4 + 42*l**3 + 11*l**4 + 13*l = 0. What is l?
-1, 1, 15
What is v in 1/6 - 1/2*v**5 + 1/6*v + 5/6*v**4 + 1/3*v**3 - v**2 = 0?
-1, -1/3, 1
Let o(i) be the first derivative of -1/8*i**2 - 1/20*i**5 - 1/24*i**6 - 1/4*i - 8 + 1/8*i**4 + 1/6*i**3. Suppose o(n) = 0. Calculate n.
-1, 1
Let z = 5066 + -5063. Factor 512/3 + 64*p + 8*p**2 + 1/3*p**z.
(p + 8)**3/3
Let x = 27 + -14. Suppose 0 = 2*m + 1 - x. Solve 2*y**5 - 11*y**4 + 62*y**3 + m*y**5 - 2*y - 68*y**3 + 10*y**2 + y**4 = 0 for y.
-1, 0, 1/4, 1
Let z = -35/312 - -2/13. Let i(k) be the third derivative of 1/30*k**5 + 1/120*k**6 + z*k**4 - 7*k**2 + 0*k + 0*k**3 + 0. Factor i(y).
y*(y + 1)**2
Let w(h) be the third derivative of -h**7/210 + h**6/60 + 2*h**5/15 - 3*h**4/4 + 3*h**3/2 + 91*h**2. Factor w(p).
-(p - 3)*(p - 1)**2*(p + 3)
Let k = 13/213 - -2/355. Let j(y) be the second derivative of k*y**3 - 11/60*y**4 + 0 + 0*y**2 + 21/100*y**5 - 17/150*y**6 - 2*y + 1/42*y**7. Factor j(q).
q*(q - 1)**3*(5*q - 2)/5
Let h(a) be the third derivative of 2*a**7/105 + a**6/6 + a**5/5 - 5*a**4/6 - 8*a**3/3 - 33*a**2. Factor h(t).
4*(t - 1)*(t + 1)**2*(t + 4)
Determine w so that 3/4 + 3*w**2 + 1/4*w**4 + 5/2*w + 3/2*w**3 = 0.
-3, -1
Let b(o) = 3*o**4 + 12*o**3 + 7*o**2 - 5*o - 5. Let v(l) = 12*l**4 + 48*l**3 + 27*l**2 - 21*l - 21. Let d(p) = -21*b(p) + 5*v(p). Let d(c) = 0. Calculate c.
-2, 0
Let h(i) be the third derivative of -i**7/735 - 23*i**6/420 - 11*i**5/105 - 2*i**2 - 205. Suppose h(s) = 0. Calculate s.
-22, -1, 0
Let d = 5 + 1. Suppose 2*o = d*o - 20. Determine p so that -15*p**o + 0 + 4/5*p + 28/5*p**2 + 53/5*p**3 - 2*p**4 = 0.
-2/5, -1/3, 0, 1
Let t = -151/2 + 1665/22. Suppose 2309*z - 14 = 2302*z. Factor -2/11*u**z + 0 - t*u.
-2*u*(u + 1)/11
Let a(s) be the first derivative of -3/5*s**5 - 12*s - 21/4*s**4 - 12 - 15*s**3 - 39/2*s**2. Factor a(j).
-3*(j + 1)**3*(j + 4)
Let u(o) be the third derivative of o**8/1680 - o**7/1050 - o**6/200 + o**5/300 + o**4/60 - 3*o**2 + 8*o. Factor u(p).
p*(p - 2)*(p - 1)*(p + 1)**2/5
Let w(g) = g**2 + 9*g - 12. Let r be w(-11). Suppose -30 = -r*s + 5*s. Let 44 - 4*m - 2*m**3 - 44 - s*m**2 = 0. Calculate m.
-2, -1, 0
Let -15*r**2 + 30*r - 6*r**2 + 5*r**3 - 14*r**2 = 0. What is r?
0, 1, 6
Let m(k) be the first derivative of 5*k**4/12 + 10*k**3/3 + 10*k**2 - 14*k + 6. Let o(p) be the first derivative of m(p). Factor o(s).
5*(s + 2)**2
Let o(u) = -10*u + 74. Let h be o(7). Let w(b) be the third derivative of -1/12*b**h + 0*b**3 + 0*b + 1/60*b**5 + 0 + 5*b**2. Suppose w(a) = 0. What is a?
0, 2
Let c(w) = 8*w**4 - 48*w**3 + 12*w**2 - 12*w - 20. Let z(a) = -a**4 - a - 1. Suppose 10 = -2*r, -5*n + 5*r = -117 - 8. Let q(p) = n*z(p) - c(p). Factor q(h).
-4*h*(h - 1)**2*(7*h + 2)
Let 0*d**2 - 2/3*d**3 + 2*d + 4/3 = 0. Calculate d.
-1, 2
Let v(o) = -3*o**2 + 156*o - 2190. Let m(z) = -6*z**2 + 314*z - 4379. Let r(d) = -3*m(d) + 5*v(d). Find t, given that r(t) = 0.
27
Let k(f) be the second derivative of f**3 + 19*f**2 + 7*f. Let m be k(-6). Factor 8/7 + 2/7*o**m + 8/7*o.
2*(o + 2)**2/7
Let o(s) = s**2 - 7*s + 3. Let l be o(7). Suppose 12 = 6*j - l*j. Factor -j*g**2 - g**4 + g**2 + 0*g**2 + 0*g**2 + g + 3*g**3.
-g*(g - 1)**3
Let t = 18 + -18. Let h(f) be the first derivative of 2 + 4/15*f**5 - 7/12*f**4 + 2/9*f**3 + t*f + 1/6*f**2. Determine v, given that h(v) = 0.
-1/4, 0, 1
Let t = -12 - -15. Let k be (-2 - 14/(-16))/(12/(-8)). Factor 3/4*o**2 + 1/4*o**t + k*o + 1/4.
(o + 1)**3/4
Let t = -785/4 + 197. Let i(a) be the first derivative of -8/3*a**6 + 0*a + 3 + 1/12*a**3 - t*a**4 + 0*a**2 + 12/5*a**5. Suppose i(x) = 0. Calculate x.
0, 1/4
Let q(g) be the first derivative of -g**5/10 + 23*g**4/8 + 49*g**3/6 + 25*g**2/4 - 157. Find b, given that q(b) = 0.
-1, 0, 25
Let t(c) = -6*c**2 + 218*c - 420. Let g(z) = 7*z**2 - 217*z + 418. Let p(k) = 2*g(k) + 3*t(k). Factor p(n).
-4*(n - 53)*(n - 2)
Let f(r) be the second derivative of 4/189*r**7 - 1/135*r**6 + 11/54*r**4 + 0*r**2 - 2/27*r**3 - 6*r + 0 - 2/15*r**5. Suppose f(g) = 0. What is g?
-2, 0, 1/4, 1
Let y(w) be the second derivative of -w**4/132 + 6*w**3/11 + 104*w. Facto