r - 8/5 - 6/5*r**2 = 0.
-2
Let q(r) be the second derivative of 0 - 7/12*r**4 - 3*r**2 + 11*r - 23/6*r**3. Factor q(y).
-(y + 3)*(7*y + 2)
Let v(t) be the third derivative of t**6/160 + 213*t**5/80 + 15123*t**4/32 + 357911*t**3/8 - 429*t**2. Factor v(w).
3*(w + 71)**3/4
Let i be 1/3 + (-44)/(-12). Suppose -5*r = i*u - 35, -5*u + r = -15 - 7. Suppose u*w**4 + 3*w**3 + 0*w**4 - w**3 - 3*w**4 = 0. What is w?
-1, 0
Suppose -13*b + 9*b = -40. Suppose -3*z - z + 5*x - b = 0, 8 = -z + 4*x. Suppose z + 1/2*u**2 + 1/4*u**3 + 0*u = 0. What is u?
-2, 0
Let c(p) be the first derivative of p**3/21 + 5*p**2 + 175*p - 111. Let c(j) = 0. What is j?
-35
Let p(u) be the first derivative of u**6/90 - u**5/15 - u**4/2 - 7*u**3/3 + 7. Let h(s) be the third derivative of p(s). Factor h(v).
4*(v - 3)*(v + 1)
Let v(m) be the second derivative of 0*m**3 + 0 + 14*m - 4/45*m**6 + 0*m**2 - 1/6*m**5 - 1/9*m**4 - 1/63*m**7. Factor v(s).
-2*s**2*(s + 1)**2*(s + 2)/3
Let w(p) be the first derivative of p**4/12 + 20*p**3/9 - 7*p**2/2 + 323. Factor w(z).
z*(z - 1)*(z + 21)/3
Let v(r) be the first derivative of r**5/25 - r**4/2 + 16*r**3/15 - 149. What is j in v(j) = 0?
0, 2, 8
Let c(o) be the second derivative of 27/2*o**2 + 19*o + 0 - 6/5*o**5 + 1/10*o**6 + 11/2*o**4 - 12*o**3. Determine j so that c(j) = 0.
1, 3
Factor -1/5*t**2 + 2/5*t - 1/5.
-(t - 1)**2/5
Let d be 123/21 + -6 - 13/(-7). Factor -2/7*a**2 - 18/7 + d*a.
-2*(a - 3)**2/7
Let -5*f**4 + 22*f + 35 + 25*f + 123*f**2 + 20*f**3 + 53*f - 33*f**2 = 0. What is f?
-1, 7
Let f = -9 + 16. Let m(y) = 4*y + 4. Let c be m(f). Factor -3*k - 2*k**2 - 17*k - 18 + c*k.
-2*(k - 3)**2
Let v = 3550/7 + -508. Let n = -4/7 - v. Solve n*y**5 + 2/7*y**4 + 0*y + 0 + 0*y**2 + 0*y**3 = 0.
-1, 0
Let m be ((-1)/2)/(87/18 + -5). Let s(n) be the second derivative of 0 + 0*n**m + 1/9*n**4 - 8*n + 0*n**2. Factor s(a).
4*a**2/3
Factor -242*f**2 - 200*f**3 + 33*f**2 - 195*f**2 - 4 - 208*f.
-4*(f + 1)**2*(50*f + 1)
Let g be 21/63 + -4 + (-13)/(-3). Let u = 4 + -2. Factor 0 - 4/3*h**u + 0*h**3 + 4/3*h**4 - g*h**5 + 2/3*h.
-2*h*(h - 1)**3*(h + 1)/3
Let g(i) = -168*i**3 - 332*i**2 - 160*i - 28. Let n(a) = -56*a**3 - 111*a**2 - 54*a - 9. Let u(h) = -5*g(h) + 16*n(h). Factor u(w).
-4*(w + 1)**2*(14*w + 1)
Factor 5/4*g**3 + 25/4*g**2 + 45 - 40*g.
5*(g - 2)**2*(g + 9)/4
Solve -18*x + 123/7*x**2 + 0 + 3/7*x**3 = 0 for x.
-42, 0, 1
Find p, given that -130*p - 25/4*p**4 + 165*p**2 - 55/2*p**3 - 80 = 0.
-8, -2/5, 2
Let j(f) be the third derivative of 2/3*f**3 - 11/12*f**4 + 3/10*f**5 + 0 + 0*f - 4*f**2. What is h in j(h) = 0?
2/9, 1
Let q be (16/6 - 6)/(4/(-18)). Let k be (-10)/q - 0 - 26/(-12). Factor -z - z**3 + 1/4*z**4 + 1/4 + k*z**2.
(z - 1)**4/4
Let f(z) = 16*z + 52. Let x be f(-3). Let i(r) = -4*r + 18. Let v be i(x). Let 2/7*p**4 + 4/7*p**5 + 0 - 6/7*p**3 + 2/7*p - 2/7*p**v = 0. What is p?
-1, 0, 1/2, 1
Let w = -1519 + 7598/5. Suppose 27/5 - 18/5*c + w*c**2 = 0. What is c?
3
Factor -1/3*c**3 + 2*c**2 + 0*c + 0.
-c**2*(c - 6)/3
Let v(u) be the second derivative of u - 1/96*u**4 + 0*u**2 + 1/240*u**6 + 1/40*u**5 + 0 - 1/12*u**3. Factor v(f).
f*(f - 1)*(f + 1)*(f + 4)/8
Let c be 15 - -5*2/(-2). Suppose 14 = c*m - 6. Solve -3/2*j**m + 1/2*j**3 - 1/2 + 3/2*j = 0 for j.
1
Let y(i) be the second derivative of -2*i**6/15 - 12*i**5/5 - 52*i**4/3 - 64*i**3 - 128*i**2 + 83*i - 3. Determine q, given that y(q) = 0.
-4, -2
Let v(o) be the second derivative of -3/11*o**3 - 2/11*o**2 - 17*o + 0 - 7/55*o**5 - 2/55*o**6 - 1/231*o**7 - 8/33*o**4. Factor v(t).
-2*(t + 1)**4*(t + 2)/11
Let i(g) = -g**2 - 24*g + 84. Let k be i(3). Find b, given that -1/3*b**4 + 1/6*b**5 + 1/3 + 4/3*b**2 - 7/6*b - 1/3*b**k = 0.
-2, 1
Let h(d) = -14*d**3 + 2*d**2 + 15*d**3 + 1 - 3*d**2. Let i(j) = 6*j**3 - 7*j**2 + 7*j + 13. Let y(o) = 35*h(o) - 5*i(o). Let y(f) = 0. Calculate f.
-2, -1, 3
Suppose 0 = 10*m - 5*m + 175. Let u = m + 71/2. Let -1/2*k**4 + 0*k + k**2 - u + 0*k**3 = 0. Calculate k.
-1, 1
Let s(l) be the second derivative of -l**5/80 - l**4/8 + 5*l**3/8 - l**2 - 56*l. Let s(u) = 0. What is u?
-8, 1
Suppose 4/3 + 2/9*r**3 - 2/9*r - 14/9*r**2 + 2/9*r**4 = 0. Calculate r.
-3, -1, 1, 2
Let u(a) = a**2 - 26*a + 167. Let h be u(11). Let x be 5/3 + 2/(-2). Suppose 0 - x*i**h - 4/3*i = 0. Calculate i.
-2, 0
Let d(u) be the third derivative of 0*u**5 + 1/525*u**7 - 6*u**2 + 0*u - 1/150*u**6 + 0*u**4 + 0*u**3 + 0. Factor d(p).
2*p**3*(p - 2)/5
Let u(m) be the first derivative of -1 + 5/6*m**3 + 9*m + 1/3*m**4 + 1/20*m**5 + m**2. Let g(i) be the first derivative of u(i). What is a in g(a) = 0?
-2, -1
Factor -33*o**5 + 36*o**5 + 4*o**2 - 4*o**3 - 7*o**4 - 5*o**5.
-o**2*(o + 2)**2*(2*o - 1)
Let h(u) be the third derivative of -u**5/180 - 7*u**4/36 + 5*u**3/6 + 51*u**2. Factor h(b).
-(b - 1)*(b + 15)/3
Let n(o) be the third derivative of 0 + 0*o + 6*o**2 - 1/180*o**5 + 0*o**3 + 0*o**6 + 1/1890*o**7 - 1/108*o**4. Factor n(h).
h*(h - 2)*(h + 1)**2/9
Let o(f) = -2*f**2 - 4*f. Let v(u) = 3*u**2 + 1254*u - 128547. Let m(i) = 3*o(i) + v(i). Let m(d) = 0. Calculate d.
207
Let f(y) = 4*y - 14. Let v be f(4). Suppose 3*d - 2 + 2 = 0. Suppose 1/2*l**v - l + d = 0. Calculate l.
0, 2
Determine c, given that 1/8*c**3 + 1/8*c**2 + 0*c + 0 = 0.
-1, 0
Factor -24 + 24*m**2 - 4/3*m + 4/3*m**3.
4*(m - 1)*(m + 1)*(m + 18)/3
Let m(v) = 3*v**2 - 2*v - 2. Let o be m(4). Let w = 42 - o. Factor 8/3*s - 16/3*s**3 - w*s**2 + 4/3 + 16/3*s**4.
4*(s - 1)**2*(2*s + 1)**2/3
Let u(t) be the second derivative of -t**7/21 - 4*t**6/15 - t**5/2 - t**4/3 + 18*t. Factor u(c).
-2*c**2*(c + 1)**2*(c + 2)
Let d = -91 - -170. Suppose 2*a + t = -a + d, -5*t = 10. Find s such that -s**3 - s**3 + a - 24*s**2 + 18*s - 15*s**3 - s**3 - 3*s**4 = 0.
-3, -1, 1
Factor 72/5*f + 48/5 + 27/5*f**2 + 3/5*f**3.
3*(f + 1)*(f + 4)**2/5
Let b(l) = -l**3 - 13*l**2 + 2*l - 35. Let w be b(-12). Let k = w - -206. Factor 3/2*m**4 + 0 + 0*m + 1/2*m**5 + 3/2*m**k + 1/2*m**2.
m**2*(m + 1)**3/2
Let i(s) be the third derivative of s**8/14 - 62*s**7/105 + 3*s**6/2 - s**5 - 11*s**4/6 + 4*s**3 - 51*s**2. Suppose i(y) = 0. Calculate y.
-1/2, 2/3, 1, 3
Let t(s) be the third derivative of s**6/40 - 13*s**4/2 + 48*s**3 + 458*s**2. Factor t(c).
3*(c - 6)*(c - 2)*(c + 8)
Let f(q) be the first derivative of -q**3/3 + 61*q**2/6 - 20*q/3 + 69. What is h in f(h) = 0?
1/3, 20
Let z(t) be the third derivative of -t**5/40 + 3*t**4/16 - 64*t**2 - 1. Determine c so that z(c) = 0.
0, 3
Let c(l) be the third derivative of l**7/42 - l**6/12 - 5*l**5/12 + 5*l**4/4 + 26*l**2. Determine r so that c(r) = 0.
-2, 0, 1, 3
Suppose -37*i + 38*i - 2 = 0. Let a be (-2)/4*-3*i. Suppose 1/4 + 11/4*y**2 + 7/4*y - 3*y**4 - 7/4*y**a = 0. What is y?
-1, -1/3, -1/4, 1
Let n(s) = -11*s**4 + 11*s**3 - 2*s**2 - 48*s. Let h(d) = 2*d**4 - d**3 - d**2. Let x(b) = -6*h(b) - n(b). Factor x(g).
-g*(g - 3)*(g + 4)**2
Factor -49 + 52 - 3*p**2 + 278*p + 309 + 31*p.
-3*(p - 104)*(p + 1)
Suppose 4*v + 34 = -50. Let q = 25 + v. Suppose q*k + k**4 - 3*k - k**2 - k = 0. What is k?
-1, 0, 1
Suppose -2*k + 9 = 5*t, -3*t = -5*k + 6*k - 6. Suppose 45*v**4 - 41*v**4 - 4*v**2 + 4*v**5 - 4*v**t + 0*v**5 = 0. Calculate v.
-1, 0, 1
Let i be (-395)/316*(-2)/55. Let x(s) be the first derivative of 0*s**2 + 2/33*s**3 - 8 + 0*s - i*s**4. Suppose x(t) = 0. Calculate t.
0, 1
Suppose 138 = 11*t - 5. Let h(u) be the first derivative of -1/2*u**3 + 3*u**2 - 6*u + t. Suppose h(l) = 0. Calculate l.
2
Let s = -7 - -12. Let w = s + -3. Suppose -4/7*p**w - 16/7 - 16/7*p = 0. What is p?
-2
Factor 24/5*b - 3/5*b**3 + 36/5 - 3/5*b**2.
-3*(b - 3)*(b + 2)**2/5
Let -44/5*m**3 - 32/5*m**4 + 12/5 + 44/5*m + 4*m**2 = 0. What is m?
-1, -3/8, 1
Let j(o) be the second derivative of -o**6/90 - o**5/15 + 5*o**4/36 + 534*o + 2. Factor j(l).
-l**2*(l - 1)*(l + 5)/3
Let t(y) be the second derivative of y**5/4 + 5*y**4 - 395*y**3/6 + 255*y**2 - 5*y + 2. Find n such that t(n) = 0.
-17, 2, 3
Let l(k) be the first derivative of -5*k**4/54 + 68*k**3/27 + 28*k**2/9 - 43*k + 56. Let s(q) be the first derivative of l(q). Factor s(p).
-2*(p - 14)*(5*p + 2)/9
Let d(b) be the third derivative of -b**6/30 + b**5/15 + 7*b**4/3 - 16*b**3 - 746*b**2. Factor d(r).
-4*(r - 3)*(r - 2)*(r + 4)
Let r = -2892 - -2895. Factor 2/7*b**5 + 2/7*b**4 + 0 - 2/7*b**2 - 2/7*b**r + 0*