*z**3 - 3*z**3 + d*z**3 = 0.
-1, 0
Let a = 30 + -15. Find m, given that -m**2 + 12*m**4 - 3*m**4 + a*m**3 + 7*m**2 = 0.
-1, -2/3, 0
Let o(h) be the first derivative of -24/11*h - 12/11*h**2 - 2/11*h**3 + 6. Let o(s) = 0. Calculate s.
-2
Let c(h) be the third derivative of -h**5/330 + h**4/33 - h**3/11 + h**2 - 29*h. Determine r, given that c(r) = 0.
1, 3
Find f such that 3*f**5 - 2415*f**2 + 2523*f**2 - f**4 + 144*f**3 + 40*f**4 = 0.
-6, -1, 0
Let i(x) be the first derivative of -6 + 27/5*x**5 - 81/2*x**2 - 12*x - 53*x**3 - 63/4*x**4. What is w in i(w) = 0?
-1, -1/3, 4
Let i(b) be the first derivative of -b**4 + 152*b**3/3 - 640*b**2 - 3200*b - 141. Suppose i(d) = 0. Calculate d.
-2, 20
Find a, given that 256/3*a + 134/3*a**2 - 32/3 + 17/3*a**3 = 0.
-4, 2/17
Let b = -1 - -3. Let l be 5/(-10) + 1 - 1/b. Factor 1/5*n**3 - 1/5*n + 1/5*n**4 - 1/5*n**2 + l.
n*(n - 1)*(n + 1)**2/5
Let n(k) = 6*k**4 - 64*k**3 + 17*k**2 + 509*k + 432. Let y(q) = 3*q**4 - 33*q**3 + 9*q**2 + 255*q + 216. Let v(p) = 3*n(p) - 5*y(p). Factor v(o).
3*(o - 6)**2*(o + 1)*(o + 2)
Factor -16/9*z**3 - 32/9*z + 40/9*z**2 + 2/9*z**4 + 0.
2*z*(z - 4)*(z - 2)**2/9
Let x(r) be the third derivative of r**5/12 + 5*r**4/8 - 15*r**3 + 278*r**2. Find j such that x(j) = 0.
-6, 3
Find q such that -112/5*q**3 + 0 - 4/5*q**4 - 24*q + 236/5*q**2 = 0.
-30, 0, 1
Let x = -6514105/28 + 232602. Let c = x + 183/4. Factor -8/7*o**2 + 0*o - 2/7*o**4 + c*o**3 + 0.
-2*o**2*(o - 2)**2/7
Let t = 33130 - 33126. Factor 6*c**2 + 6*c - 3/2*c**3 + 0 - 3/2*c**t.
-3*c*(c - 2)*(c + 1)*(c + 2)/2
Let f = -146 - -293/2. Let r = 7/10 + f. Factor r*z - 4/5 + 14*z**2.
2*(5*z - 1)*(7*z + 2)/5
Let b(m) be the third derivative of -m**7/420 + 29*m**6/360 - 19*m**5/360 + 672*m**2. Factor b(k).
-k**2*(k - 19)*(3*k - 1)/6
Let a(o) be the second derivative of -1/80*o**5 + 0*o**2 - 1/24*o**3 - 1/24*o**4 - o + 0. Factor a(d).
-d*(d + 1)**2/4
Let m = -2153/2 - -1078. Let k = 0 + 3. Find f, given that -3/2*f + m*f**2 - k = 0.
-1, 2
Let j(l) = -l**3 - l - 4. Let g be j(-2). Factor -3/2*s**2 - 9/2*s + g.
-3*(s - 1)*(s + 4)/2
Let u be -4 + 3 + 2790/12. Let j = u - 231. Let -c + j*c**2 + 1/2 = 0. Calculate c.
1
Let r(y) be the first derivative of y**4/4 + 7*y**3/3 - y**2/2 - 7*y + 22. Let r(s) = 0. What is s?
-7, -1, 1
Let n(b) = 5*b**5 + 28*b**4 - 140*b**3 + 194*b**2 - 6*b + 6. Let w(l) = l**5 + l**4 - l**2 - l + 1. Let t(o) = n(o) - 6*w(o). Factor t(r).
-r**2*(r - 10)**2*(r - 2)
Let c be ((-15)/(-12))/(850/1632). Factor 36/5*v + 18/5*v**3 + 3/5*v**4 + c + 39/5*v**2.
3*(v + 1)**2*(v + 2)**2/5
Let n(f) = -f**3 + 15*f**2 - 10*f - 176. Let h be n(13). Let p(l) be the second derivative of -7*l + 0 - h*l**2 - 8*l**3 - l**4 - 1/20*l**5. Factor p(b).
-(b + 4)**3
Factor -192 - 18*j**2 - 18*j**2 - 144*j - 316*j**3 + 313*j**3.
-3*(j + 4)**3
Let c = 421/900 + -7/300. Determine a so that -2/9*a**4 + 2/9 - c*a**3 + 0*a**2 + 4/9*a = 0.
-1, 1
Suppose -5*d = 3*x - 10, -2*d + 4*d + 15 = -5*x. Let m(h) be the second derivative of 3*h + 0 + 0*h**2 - 1/90*h**d + 1/27*h**4 - 1/27*h**3. Factor m(a).
-2*a*(a - 1)**2/9
Let n = -5680 - -5683. Suppose 0*w + 0 + 1/9*w**2 + 1/9*w**4 + 2/9*w**n = 0. What is w?
-1, 0
Let k(m) be the first derivative of -m**6/210 - 4*m**5/35 - 6*m**4/7 - 45*m**2/2 + 4. Let d(h) be the second derivative of k(h). Factor d(f).
-4*f*(f + 6)**2/7
Let w(o) be the second derivative of -2*o - 1/48*o**4 - 1/6*o**3 + 0*o**2 - 3. Factor w(k).
-k*(k + 4)/4
Let f(a) be the third derivative of a**8/20160 - a**7/1008 - a**6/120 + 7*a**5/30 + 2*a**2. Let w(o) be the third derivative of f(o). Factor w(x).
(x - 6)*(x + 1)
Suppose -4*v + 62 = -2*v. Let y = -92/3 + v. Factor 1/6*d**2 + 0 + y*d.
d*(d + 2)/6
Let a be (2/3)/(13/78). Determine h, given that 38*h**2 - 12*h + 19*h**2 + 39*h**3 + 13*h**2 - 35*h**a - 8 = 0.
-1, -2/7, 2/5, 2
Let f = 1452 + -1450. Let -20/7 - 2/7*q**2 + f*q = 0. What is q?
2, 5
Factor -41/3*f - 20/3 - 1/3*f**3 - 22/3*f**2.
-(f + 1)**2*(f + 20)/3
Factor 289/6 + 1/6*t**2 - 17/3*t.
(t - 17)**2/6
Let c be 13110/(-513)*((-34)/28 + 1). Let w = -36/7 + c. Factor -2/3*f**2 + 1/3*f**4 + 2/3*f**3 - 1/3*f - 1/3*f**5 + w.
-(f - 1)**3*(f + 1)**2/3
Let m(d) = -d**2 - d - 1. Let j(s) = -5*s**3 - 15*s**2 + 10*s - 5. Let b = 18 - 13. Let h(q) = b*m(q) - j(q). Factor h(g).
5*g*(g - 1)*(g + 3)
Let y(n) = 20*n**4 - 11*n**3 - 66*n**2 + 61*n - 10. Let v(u) = -180*u**4 + 100*u**3 + 595*u**2 - 550*u + 90. Let k(z) = 6*v(z) + 55*y(z). Factor k(h).
5*(h - 1)**2*(h + 2)*(4*h - 1)
Let c(s) = -5*s**2 + 25*s - 50. Let i(d) = -5*d**2 + 26*d - 49. Let q(v) = 4*c(v) - 5*i(v). Factor q(b).
5*(b - 3)**2
Let p(n) be the second derivative of n**4/4 - 6*n**3 + 105*n**2/2 + 6*n + 38. Factor p(l).
3*(l - 7)*(l - 5)
Let c(l) be the third derivative of 0 + l**2 + 0*l**3 - 169/960*l**6 + 0*l - 13/120*l**5 - 1/48*l**4. Factor c(j).
-j*(13*j + 2)**2/8
Let l(j) be the second derivative of -j**5/85 - 7*j**4/204 - j**3/51 + 2*j**2 + 6*j. Let m(s) be the first derivative of l(s). Let m(v) = 0. What is v?
-1, -1/6
Let o = 820 - 814. Let n(i) be the first derivative of -2 + 2/3*i**o + 8*i - 10*i**2 + 4*i**4 - 16/5*i**5 + 8/3*i**3. Factor n(p).
4*(p - 2)*(p - 1)**3*(p + 1)
Let z = -671 - -687. Let k(o) be the first derivative of 8*o**2 - 4*o**4 - 2 + z*o - 4/5*o**5 - 4*o**3. Factor k(w).
-4*(w - 1)*(w + 1)*(w + 2)**2
Let n(x) = x**3 + x**2 + 9*x - 3. Let c(r) be the second derivative of r**4/6 + 4*r**3/3 - r**2 + 3*r. Let a(z) = -3*c(z) + 2*n(z). Find u, given that a(u) = 0.
-1, 0, 3
Let o(q) be the second derivative of 0*q**2 + 1/6*q**6 - 1/4*q**5 + 0*q**4 + 0 - 5*q + 0*q**3. Find f, given that o(f) = 0.
0, 1
Let a = -4 + 4. Let v be (-3)/(3/(-2)) + a. Find k such that -2 + 116*k**2 + 3*k - k**3 - 116*k**v = 0.
-2, 1
Let s be (-8 + 36 + -33)*4/(-50). Factor o - s*o**2 - 6/5*o**3 + 1/5*o**5 + 3/5 - 1/5*o**4.
(o - 3)*(o - 1)*(o + 1)**3/5
Let c(j) be the second derivative of -j**7/210 + j**6/30 - 9*j**5/100 + 7*j**4/60 - j**3/15 - 32*j. Factor c(w).
-w*(w - 2)*(w - 1)**3/5
Determine g so that 24/19*g + 6/19*g**2 + 6/19*g**4 - 20/19*g**3 - 8/19 = 0.
-1, 1/3, 2
Let z(q) be the first derivative of -128/5*q + 8/5*q**3 - 32*q**2 + 2/5*q**5 + 5 + 16/5*q**4. Determine n so that z(n) = 0.
-4, -2/5, 2
Let i(r) be the third derivative of -r**8/192 - 317*r**7/840 - 1157*r**6/160 + 2737*r**5/240 + 529*r**4/48 - r**2 - 50*r. Suppose i(u) = 0. What is u?
-23, -2/7, 0, 1
Suppose 74*b - 77*b + 3 = 0. Let f be (b/(-4))/(3 + (-279)/72). Factor -4/7*u + 0*u**2 - 2/7*u**4 + f + 4/7*u**3.
-2*(u - 1)**3*(u + 1)/7
Let p(a) be the third derivative of -a**8/6720 + a**7/560 - a**6/120 + a**5/4 - 5*a**2. Let m(r) be the third derivative of p(r). Solve m(x) = 0 for x.
1, 2
Let h(y) be the third derivative of -y**8/84 + 2*y**7/35 - y**6/15 - 40*y**2 + 2. Find b such that h(b) = 0.
0, 1, 2
Suppose 2*c - 27 + 9 = 0. Let p(u) be the first derivative of 0*u - c + 2/21*u**3 + 0*u**2 - 1/14*u**4. Solve p(r) = 0 for r.
0, 1
Let p = -81 - -89. Factor 94*d**4 - 32*d + 48*d**2 + 4*d**5 - 52*d**4 - p*d**3 - 54*d**4.
4*d*(d - 2)**2*(d - 1)*(d + 2)
Let b be (-44)/(-99)*(-3)/(-8). Let d(f) be the first derivative of -1/8*f**4 + 1/10*f**5 + 1/4*f**2 + 0*f - b*f**3 - 7. Factor d(h).
h*(h - 1)**2*(h + 1)/2
Solve -2 + 18/5*k - 4*k**3 + 2/5*k**5 + 6/5*k**4 + 4/5*k**2 = 0 for k.
-5, -1, 1
Factor -10/7*t**4 + 18/7*t**3 + 2/7*t**5 + 0 + 4/7*t - 2*t**2.
2*t*(t - 2)*(t - 1)**3/7
Let f be (-24)/(-10)*10/4. Let i be 8/f + 85/51. Determine k, given that -k - 4*k - 4*k - i*k**2 = 0.
-3, 0
Let l be ((-6)/(-5))/((-14)/(-10)). Let z = 27250 + -190748/7. Find t such that 6/7*t**2 + 2/7 - l*t - z*t**3 = 0.
1
Factor 3*x**3 - 19*x**2 - 17*x**3 - 21*x**2 - 2*x**3 - 32*x - 2*x**4.
-2*x*(x + 2)**2*(x + 4)
Let r(y) be the third derivative of -y**7/840 - y**6/160 + y**5/80 + 11*y**4/96 + y**3/4 - 4*y**2 - 47. Suppose r(i) = 0. What is i?
-3, -1, 2
Let s be ((-20)/(-52))/(510/204). Solve 0 - 16/13*t**2 - s*t = 0 for t.
-1/8, 0
Let a(q) = q**3 + 5*q + 2. Let m = -53 - -53. Let u be a(m). Factor -1/8*y**5 + 0*y + 1/8*y**3 + 0 + 1/8*y**4 - 1/8*y**u.
-y**2*(y - 1)**2*(y + 1)/8
Let v(n) be the first derivative of -n**4/5 - 8*n**3/5 + 18*n**2/5 + 56*n/5 + 180. Determine l so that v(l) = 0.
-7, -1, 2
Let m(i) = -12*i**2 - 43*i + 25. Let h be m(-4). L