Suppose -6*i + 38 = -22. Suppose -p + i + 5 = -3*y, p = y + 5. Factor 1/2*n**4 - 1/2 + p*n**2 + n - n**3.
(n - 1)**3*(n + 1)/2
Let k(d) = 5*d**3 + 10*d**2 + 7*d + 14. Let x be k(-2). Find u such that x + 0*u**3 + 4/13*u**4 + 0*u - 2/13*u**5 + 0*u**2 = 0.
0, 2
What is q in -3/4*q + 0 + q**3 + 1/2*q**2 - 1/4*q**5 - 1/2*q**4 = 0?
-3, -1, 0, 1
Let k(u) = -4*u + 5. Let x be k(-5). Solve q + 29*q + 27 - 27 + 5*q**3 - x*q**2 = 0 for q.
0, 2, 3
Let r(v) = 4*v**3 + 248*v**2 + 243*v - 59. Let g be r(-61). Find l, given that 9/4 + 1/4*l**g + 3/2*l = 0.
-3
Let c = 2/4329 - -1439/8658. Suppose 0 + 1/6*w - c*w**3 + 1/6*w**4 - 1/6*w**2 = 0. What is w?
-1, 0, 1
Let a(x) be the third derivative of 0*x + 1/4*x**3 + 0 - 21*x**2 - 17/96*x**4 + 1/48*x**5. Factor a(g).
(g - 3)*(5*g - 2)/4
Let i(m) be the second derivative of -4/5*m**2 - 1/60*m**4 + 3/10*m**3 - 19*m + 0. Factor i(c).
-(c - 8)*(c - 1)/5
Let b(d) be the second derivative of -15*d + 3/100*d**5 + 1/50*d**6 - 1/10*d**3 + 0 + 0*d**2 - 1/20*d**4. Factor b(p).
3*p*(p - 1)*(p + 1)**2/5
Suppose -v + 2*v = -l - 7, -15 = v + 3*l. Let p be 20/(-30)*(-1)/v*-5. What is n in 2/9*n**3 + p*n + 4/9 + 8/9*n**2 = 0?
-2, -1
What is y in 2*y**2 + 4*y - 3 - 19*y**4 - 4*y**3 + 0*y**4 + 5*y**4 + 8*y**4 + 7*y**4 = 0?
-1, 1, 3
Let d(i) be the second derivative of 4/11*i**2 + 13*i + 1/66*i**4 + 0 + 5/33*i**3. Factor d(p).
2*(p + 1)*(p + 4)/11
Let o(s) be the third derivative of s**6/120 + s**5/15 + s**4/8 - s**2 - 13*s. Factor o(c).
c*(c + 1)*(c + 3)
Let -1849/3 - 86/3*v - 1/3*v**2 = 0. What is v?
-43
Let w(n) be the second derivative of 1/2*n**6 + 13*n + 0*n**2 + 7/4*n**4 + 27/20*n**5 + n**3 + 1/14*n**7 + 0. Factor w(b).
3*b*(b + 1)**3*(b + 2)
Let d be 16/14 + 0/(-5) + -1. Let y(c) be the first derivative of 0*c + 0*c**3 + d*c**4 - 5 + 0*c**2 + 2/35*c**5. Factor y(i).
2*i**3*(i + 2)/7
Let v be 5/(-1)*1/(-2 + 1). Solve 437*b - 16*b**2 + 24*b**4 + 12*b**3 - 8*b**4 + 4*b**v - 453*b = 0 for b.
-2, -1, 0, 1
Let v be 70/(-220)*20/(-35). Let 0 - 2/11*m**2 + v*m = 0. What is m?
0, 1
Let y(k) = k**5 + 11*k**4 - 22*k**3 + 19*k**2 + 3*k + 3. Let d(s) = s**5 + 9*s**4 - 22*s**3 + 18*s**2 + 2*s + 2. Let l(z) = -3*d(z) + 2*y(z). Factor l(g).
-g**2*(g - 2)*(g - 1)*(g + 8)
Let x(s) be the third derivative of -1/80*s**6 - 18*s**2 - 1/16*s**4 + 0 + 0*s + 0*s**3 - 1/20*s**5. Factor x(v).
-3*v*(v + 1)**2/2
Let t(s) be the first derivative of 2*s**5/35 + s**4/14 - 4*s**3/7 - 4*s**2/7 + 16*s/7 - 4. Factor t(z).
2*(z - 2)*(z - 1)*(z + 2)**2/7
Let w(u) be the third derivative of -9*u**2 - 1/120*u**5 - 1/4*u**3 + 0*u + 19/96*u**4 - 1/160*u**6 + 0. Factor w(h).
-(h - 2)*(h + 3)*(3*h - 1)/4
Let a be (3 - 1)/((-11)/((-132)/48)). Factor a + 1/2*b**2 + b.
(b + 1)**2/2
Let j(v) be the first derivative of v**6/24 - v**5/20 - v**4/8 + v**3/6 + v**2/8 - v/4 - 179. Factor j(f).
(f - 1)**3*(f + 1)**2/4
Let t(a) = -a**2 - 4*a - 10. Let x be t(6). Let u be (7/x)/((-3)/(18/3)). Solve u*o**2 + 0 + 0*o - 2/5*o**3 + 1/5*o**4 = 0.
0, 1
Suppose -3*f = f - 8. Let w(l) = -l**2 - 4*l - 3. Let n(t) = -t**2 - 5*t - 4. Let c(i) = f*n(i) - 3*w(i). Factor c(h).
(h + 1)**2
Let d be (61/(-122))/(5/(-4)). Find i such that d*i**2 + 0 - 6/5*i = 0.
0, 3
Let i = 20492 + -20492. Factor 8/5*s + i + 2/5*s**2.
2*s*(s + 4)/5
Let r(h) be the third derivative of 1/9*h**3 - 1/90*h**6 + 0*h + 0*h**5 + 0 + 1/18*h**4 - 1/315*h**7 - 9*h**2. What is u in r(u) = 0?
-1, 1
Suppose -135 = -5*p + s, 3*p + 0*s - 99 = -3*s. Find f such that -12 - 125*f**3 + 19*f**2 + 40*f**4 - 5*f**5 - p*f - 112*f + 52 + 171*f**2 = 0.
1, 2
Suppose 24*k + 48 + 2/9*k**3 + 4*k**2 = 0. Calculate k.
-6
Let y = -38 - -40. Factor 16*o**y - 21*o**2 + 0*o - 5*o.
-5*o*(o + 1)
Let v(w) be the second derivative of 1/20*w**6 + 0 + 3/20*w**5 + 9/4*w**2 + 12*w - 1/2*w**3 - 1/2*w**4. Factor v(q).
3*(q - 1)**2*(q + 1)*(q + 3)/2
Let s(i) be the second derivative of 3*i**7/28 + i**6/20 - 63*i**5/40 + 11*i**4/8 + 3*i**3/2 - 279*i. Find r, given that s(r) = 0.
-3, -1/3, 0, 1, 2
Find z, given that 134/3*z**3 - 72 + 2/3*z**5 + 144*z - 26/3*z**4 - 114*z**2 = 0.
2, 3
Determine m, given that -4/15*m + 0 + 2/15*m**2 = 0.
0, 2
Let u(n) = -9*n + 9. Let y(l) be the first derivative of -l**3/3 + 5*l**2 - 10*l - 12. Let v(f) = 2*u(f) + 3*y(f). Find j, given that v(j) = 0.
2
Let b(m) = m**3 + 7*m**2 + m + 10. Let k be b(-7). Let -100*a**2 - 130*a**k + 26*a + 8*a**4 + 14*a - 34*a**4 - 9*a**4 = 0. Calculate a.
-2, 0, 2/7
Let b(g) be the second derivative of -g**4/4 + 231*g**3 - 160083*g**2/2 - 15*g + 4. Determine h so that b(h) = 0.
231
Suppose 4*s - 5*f + 1 = 0, 5*s + 86*f = 83*f + 8. Let z(x) be the first derivative of s - 4/21*x**3 - 4/7*x**2 + 12/7*x. Solve z(g) = 0.
-3, 1
Find k, given that 0 + 2/5*k + 2/5*k**3 - 4/5*k**2 = 0.
0, 1
Suppose 2*q - 70 = 200. Let y be (-51)/q - 9/(-15). Factor -2/9*h**2 + 0 - y*h.
-2*h*(h + 1)/9
Let i(l) = 2*l - 4. Let m be i(3). Factor h**m - 35*h + 35*h.
h**2
Let 3/8*l**4 + 87/8*l**2 - 399/8*l - 441/4 + 39/8*l**3 = 0. What is l?
-7, -2, 3
Let l(r) be the second derivative of r**4/54 - 58*r**3/27 - r - 83. Let l(d) = 0. What is d?
0, 58
Factor -10/7*g + 0 - 2/7*g**3 - 12/7*g**2.
-2*g*(g + 1)*(g + 5)/7
Let p(m) be the third derivative of -m**6/270 + 2*m**5/45 - 11*m**4/54 + 4*m**3/9 - 39*m**2. Find o such that p(o) = 0.
1, 2, 3
Factor 0*a**2 + 0 + 18/5*a**3 + 6/5*a**4 - 24/5*a.
6*a*(a - 1)*(a + 2)**2/5
Let r(t) be the second derivative of -t**4/78 + 478*t**3/39 - 57121*t**2/13 - 309*t - 2. Suppose r(w) = 0. Calculate w.
239
Factor 155*g**4 - 178*g**4 - 108*g**3 - 102*g + 20*g**4 - 207*g**2.
-3*g*(g + 1)**2*(g + 34)
Find p such that 3*p**3 - 1 - 6*p**2 + 1 + 72*p + 14*p**2 + 34*p**2 = 0.
-12, -2, 0
Let w(o) be the third derivative of 1/15*o**5 + 1/3*o**4 + 0*o + 2/3*o**3 + 0 + 18*o**2. Factor w(k).
4*(k + 1)**2
Let m(j) be the first derivative of 2*j**3/3 + 2*j**2 + 360. Find n such that m(n) = 0.
-2, 0
Let m(h) be the third derivative of -h**6/240 - 29*h**5/60 - 7*h**4/3 + 444*h**2. Factor m(x).
-x*(x + 2)*(x + 56)/2
Let g(w) = -20*w**3 - 12*w**2 + 8*w + 24. Let m be 2 - (-2 + 5 + -5 + 12). Let a(q) = -q**3 + q**2 - q + 1. Let l(p) = m*a(p) + g(p). Factor l(c).
-4*(c - 1)*(c + 2)*(3*c + 2)
Let z(o) be the first derivative of -o**5/4 + 5*o**4/12 + 5*o**3/3 - 9*o + 27. Let p(y) be the first derivative of z(y). Factor p(s).
-5*s*(s - 2)*(s + 1)
Determine x so that -4*x**2 + 2*x**2 + 3*x**2 + 3307 - 186*x + 5342 = 0.
93
Factor 140/3 + 35/6*v**3 - 955/6*v**2 - 355/3*v.
5*(v - 28)*(v + 1)*(7*v - 2)/6
Let y(z) be the first derivative of 4*z**3/3 - 4*z**2 - 60*z - 425. Solve y(w) = 0 for w.
-3, 5
Solve 30*s**3 + 4*s**5 - 6*s**5 - 2*s**5 - 24*s**2 + 96 - 112*s + 14*s**3 = 0 for s.
-3, -2, 1, 2
Let a = -799 + 799. Suppose 3/7*r - 3/7*r**4 + 9/7*r**3 - 9/7*r**2 + a = 0. Calculate r.
0, 1
Let s(q) be the first derivative of -q**6/15 - 34*q**5/25 - 9*q**4 - 52*q**3/3 + 91*q**2/5 + 294*q/5 + 310. Suppose s(c) = 0. What is c?
-7, -3, -1, 1
Let i(a) be the third derivative of -a**7/735 + a**6/168 + a**5/420 - a**4/28 + 72*a**2. Factor i(f).
-f*(f - 2)*(f + 1)*(2*f - 3)/7
Let n(i) be the first derivative of -i**6/2 - 21*i**5/5 - 12*i**4 - 12*i**3 - 162. Factor n(s).
-3*s**2*(s + 2)**2*(s + 3)
Let h(u) be the second derivative of -u**5/10 - 4*u**4 + u**3/3 + 24*u**2 - 11*u - 3. Solve h(c) = 0.
-24, -1, 1
Let n(j) be the first derivative of -j**4/18 + 28*j**3/27 - 13*j**2/9 + 306. Factor n(l).
-2*l*(l - 13)*(l - 1)/9
Let r(q) = -q + 9. Let l be r(12). Let h(m) = -6*m**3 + 8*m**2 - 2*m + 4. Let s(x) = 5*x**3 - 7*x**2 + 2*x - 3. Let o(j) = l*h(j) - 4*s(j). Factor o(w).
-2*w*(w - 1)**2
Factor 71/4*k + 35/4 + 37/4*k**2 + 1/4*k**3.
(k + 1)**2*(k + 35)/4
Let y(l) be the second derivative of l**7/42 - 9*l**6/10 - l**5/20 + 9*l**4/4 + 141*l. What is a in y(a) = 0?
-1, 0, 1, 27
Let g(o) be the third derivative of o**8/336 + 3*o**7/56 + o**6/3 + 2*o**5/3 - 2*o**3 + 6*o**2. Let t(d) be the first derivative of g(d). Factor t(m).
5*m*(m + 1)*(m + 4)**2
Let k(x) be the second derivative of -3/11*x**3 + 0*x**2 + 0 + 1/22*x**4 + 7*x. Factor k(m).
6*m*(m - 3)/11
Let u(f) be the second derivative of -f**6/90 + f**5/60 + 2*f + 18. Factor u(m).
-m**3*(m - 1)/3
Let d = -1821 + 56440/31. Let f = 131/155 - d. Factor 2*t + 14/5*t**2 + 2/5 + f*t**3.
2*(t + 1)*