3*o*(o + 1)*(o + 3)
Factor 4*f**3 + 10*f - 11*f - 7*f**2 + 2*f**2 + 2*f.
f*(f - 1)*(4*f - 1)
Factor -25/4 - 45/8*u - 1/8*u**3 - 3/2*u**2.
-(u + 2)*(u + 5)**2/8
Let p = 891/5 + -1777/10. Factor 0 - p*o**3 + 0*o - o**2.
-o**2*(o + 2)/2
Factor 4/15*z**2 - 2/15*z + 0 - 2/15*z**3.
-2*z*(z - 1)**2/15
Let i(x) = -36*x**3 - 6*x**2 + 4*x**4 + 24*x + 4*x**4 + 10*x**2. Let j(z) = -z**4 + z**3 - z. Let l(g) = -i(g) - 24*j(g). Solve l(k) = 0 for k.
-1, 0, 1/4
Let d(c) be the third derivative of 3*c**7/245 + 23*c**6/84 - 13*c**5/105 - 155*c**2. Factor d(v).
2*v**2*(v + 13)*(9*v - 2)/7
Let q = 2456 - 9819/4. Factor 0 + 5/2*m - q*m**2.
-5*m*(m - 2)/4
Let i(d) be the first derivative of -14 + d**2 + 2/21*d**3 + 12/7*d. Factor i(t).
2*(t + 1)*(t + 6)/7
Let b(z) be the first derivative of 3*z**4/32 - 11*z**3/4 + 63*z**2/16 + 334. Find l such that b(l) = 0.
0, 1, 21
Let b(h) = 6*h**3 - 3*h**2 + 5*h + 10. Let f(j) = 5*j**3 - 2*j**2 + 5*j + 9. Let x(d) = -6*b(d) + 7*f(d). Let g be x(5). Factor 6*r**2 + r - 3*r + g*r**3 - 7*r.
3*r*(r - 1)*(r + 3)
Let b(o) be the third derivative of -o**7/210 - 2*o**6/45 - 2*o**5/15 - 5*o**3/2 + 19*o**2. Let p(f) be the first derivative of b(f). Find n such that p(n) = 0.
-2, 0
Factor 36*t**3 - 129*t + 7*t**2 - 5*t**2 + 67*t**2 - 36.
3*(t + 3)*(3*t - 4)*(4*t + 1)
Let z(o) = -28*o**3 + 2*o + 1. Let a be z(-1). Let d = 48 - a. Factor -18*c + 13*c**3 + 18 - d*c + 12*c**2 - 4*c**3.
3*(c - 1)*(c + 3)*(3*c - 2)
Suppose 2*d = -2*p - 20, 4*d - 4*p = p + 5. Let j(b) = 8*b**2 + 26*b - 20. Let k(r) = -3*r**2 - 9*r + 7. Let q(u) = d*j(u) - 14*k(u). Let q(x) = 0. Calculate x.
1
Let r(v) be the second derivative of -v**4/24 - 14*v**3/3 - 196*v**2 + 16*v. Factor r(j).
-(j + 28)**2/2
Solve 4416/17*w - 4608/17 + 190/17*w**2 + 2/17*w**3 = 0 for w.
-48, 1
Factor -10*v**2 + 68*v**3 - 16*v**3 - 25*v - 5 - 19*v**3 - 13*v**3 - 5 + 20*v**4 + 5*v**5.
5*(v - 1)*(v + 1)**3*(v + 2)
Let o**2 + 14*o + 844*o + 0*o**2 - 5*o**2 - 44944 - 10*o = 0. What is o?
106
Let l = 3 - 3. Suppose -3*m + 0*m + 21 = l. Factor 3 - 12*q - 2*q**4 - 18*q**2 + 19*q**3 + 17*q**4 - m*q**3.
3*(q - 1)*(q + 1)**2*(5*q - 1)
Let p(n) be the first derivative of -n**5 + 15*n**4/2 - 40*n**3/3 - 15*n**2 + 45*n + 58. Let p(r) = 0. What is r?
-1, 1, 3
Let m(v) be the third derivative of -v**8/168 - 19*v**7/105 + 21*v**6/20 - 13*v**5/6 + 11*v**4/6 - 35*v**2 + 3*v. Factor m(r).
-2*r*(r - 1)**3*(r + 22)
Let x(t) be the third derivative of -t**7/560 + 3*t**5/160 - t**4/32 - 2*t**2 - 7. Determine y so that x(y) = 0.
-2, 0, 1
Let v(s) be the third derivative of -s**5/600 + s**4/6 + 41*s**3/60 + 2*s**2 + 28. Factor v(n).
-(n - 41)*(n + 1)/10
Let k be 443/1772 + 14/8. Determine p so that 1/3 - k*p + 5/3*p**2 = 0.
1/5, 1
Let t(d) be the third derivative of -d**5/60 - 4*d**4/3 - 56*d**3/3 + 48*d**2 + 3. Determine y so that t(y) = 0.
-28, -4
Find i, given that 1/2*i**5 + 0 + 45/2*i**3 + 11*i**2 + 0*i + 12*i**4 = 0.
-22, -1, 0
Let m be (-16)/28*21/(-6). Suppose m*n + 28 = 5*r + 11, -3*n = -5*r + 18. Solve -2*t**4 - 8*t - 16*t**2 - 14*t**3 + 5*t**r - 3*t**3 + 2*t**3 = 0 for t.
-2, -1, 0
Let p(x) = -24*x**4 + 24*x**3 + 126*x**2 + 200*x + 122. Let y(m) = -m**4 + m**3 + 2*m**2 - m - 1. Let r(f) = 2*p(f) - 44*y(f). Factor r(v).
-4*(v - 8)*(v + 1)*(v + 3)**2
Let u = -274 - -1105/4. Let o = 575/4 + -137. Factor -u*p**2 + o*p - 27/4 + 1/4*p**3.
(p - 3)**3/4
Let z(n) be the second derivative of -n**4/72 - 7*n**3/36 + 2*n**2/3 - 56*n. Suppose z(p) = 0. What is p?
-8, 1
Let x(b) be the second derivative of -b**7/504 - b**6/144 + b**4/4 - 18*b. Let o(d) be the third derivative of x(d). Factor o(v).
-5*v*(v + 1)
Factor -32/3 - 1/3*j**2 - 4*j.
-(j + 4)*(j + 8)/3
Factor 1/9*s**2 - 1/3 - 2/9*s.
(s - 3)*(s + 1)/9
Suppose -4*z - 4*i + 19 = -9, 4*i - 19 = -z. Find w, given that 74*w**z + 27*w + 20*w**2 + 16 - 70*w**3 + 5*w = 0.
-2, -1
Let g = 5054/15 + -55324/165. Solve -30/11*z**2 + g*z + 6/11*z**3 + 54/11 = 0.
-1, 3
Let q(g) be the second derivative of -g**4/48 - 3*g**3/8 - 7*g**2/4 + 13*g. Factor q(c).
-(c + 2)*(c + 7)/4
Let i be -1 - (-1)/(3/12). Let 56*w**4 + 152*w**2 - 1 + 9 + 156*w**i + 60*w + 1 - 1 = 0. Calculate w.
-1, -1/2, -2/7
Let s(a) be the second derivative of a**5/100 + a**4/20 - a**3/30 - 3*a**2/10 - 2*a + 2. Solve s(g) = 0 for g.
-3, -1, 1
Find y such that 3*y**4 + 21*y**2 + 72/5*y**3 + 36/5*y - 12/5 = 0.
-2, -1, 1/5
Let r = 78 + -74. What is k in -14*k + 17*k**2 - 15 + r*k - 12*k**2 = 0?
-1, 3
Let w(x) be the third derivative of -x**7/105 - 2*x**6/15 - 8*x**5/15 - 14*x**2 + 1. Factor w(i).
-2*i**2*(i + 4)**2
Let p = -99 + 126. Let y = p - 25. Factor 0*r + 2/7*r**y - 2/7.
2*(r - 1)*(r + 1)/7
Let r(d) = 20*d**3 - 2*d**2 - 3*d + 3. Let u(a) = a + 35 - 2*a - 25*a**2 + 240*a**3 - 10*a - 24*a. Let p(x) = 35*r(x) - 3*u(x). Find b, given that p(b) = 0.
0, 1/4
Let u(x) be the third derivative of x**9/90720 + x**8/10080 + x**7/2520 + x**6/1080 + 7*x**5/60 - 3*x**2. Let k(d) be the third derivative of u(d). Factor k(l).
2*(l + 1)**3/3
Let t = 21 - 19. Suppose -4*q + 4*a = 0, -5*q + 3*a + t = -q. Factor -5*h**4 + 4*h**q - 6*h**4 - h**5 - 4*h + 7*h**4 + 2*h**5 + 3*h**3.
h*(h - 2)**2*(h - 1)*(h + 1)
Let f(r) be the second derivative of r**4/32 - 9*r**3/16 + 3*r**2/2 + 15*r. What is v in f(v) = 0?
1, 8
Suppose 6*k - 45 + 3 = 0. Let h(s) be the second derivative of 8/35*s**5 - 2/21*s**6 + 2/147*s**k + 0*s**3 + 0 - 4/21*s**4 + 4*s + 0*s**2. Factor h(g).
4*g**2*(g - 2)**2*(g - 1)/7
Let i(u) be the third derivative of 2*u**7/105 - u**6/15 - u**5/5 + 9*u**2. Factor i(x).
4*x**2*(x - 3)*(x + 1)
Suppose -3/4*z**2 + 3/2*z**3 - 3/8*z**4 + 9/8 - 3/2*z = 0. Calculate z.
-1, 1, 3
Let m(x) be the third derivative of -1/40*x**6 - 6*x**3 + 0 + 0*x + 23*x**2 - 2*x**4 - 7/20*x**5. What is w in m(w) = 0?
-3, -2
Let g be -3 + (-17 - 1422/(-90))/((-3)/20). Factor 10/3*h**2 - g + 20/3*h**3 + 5/3*h**4 - 20/3*h.
5*(h - 1)*(h + 1)**2*(h + 3)/3
Let f be (-4)/(-26) + (-1106)/91. Let d be (12/(-14))/(-3) + f/(-105). Factor d + 1/5*q - 1/5*q**2.
-(q - 2)*(q + 1)/5
Suppose -2*n - 2*a + 10 = 0, -n + 7*a = 6*a + 1. Let r(i) be the second derivative of -9*i + 0 + 0*i**n + 1/15*i**5 + 1/36*i**4 + 0*i**3. Factor r(u).
u**2*(4*u + 1)/3
Let 11/3*g**2 + 1/3*g**3 + 25/3 + 35/3*g = 0. Calculate g.
-5, -1
Let t(s) be the third derivative of s**6/320 - 11*s**5/80 + 119*s**4/64 - 49*s**3/8 - 169*s**2. Find g, given that t(g) = 0.
1, 7, 14
Let i = 1/5592 + 134201/39144. Find c such that -i + 220/7*c**2 - 4/7*c - 36/7*c**4 + 36/7*c**3 = 0.
-2, -1/3, 1/3, 3
Let s(x) = -1 + 7*x + 3*x**3 - 10*x - 2*x**2 + 0*x**3 + 2*x**4 + 0*x**2. Let q(b) = b**4 - b**2 + 1. Let m(o) = -q(o) - s(o). Suppose m(h) = 0. Calculate h.
-1, 0, 1
Factor -12/7*b - 30 + 6/7*b**2.
6*(b - 7)*(b + 5)/7
Let r(z) be the second derivative of -3/8*z**2 - 5/8*z**4 - 1/8*z**6 + 3/8*z**5 + 5/8*z**3 + 37*z + 0 + 1/56*z**7. Factor r(x).
3*(x - 1)**5/4
Let f = 359/1095 + 2/365. Solve f*u**3 + 0 + 0*u**2 - 1/3*u = 0.
-1, 0, 1
Let a = 3448 + -3446. Determine m so that -3/2 + 6*m**a - 9/4*m**3 - 9/4*m = 0.
-1/3, 1, 2
Let w(u) be the third derivative of -u**6/40 + 133*u**5/20 - 4355*u**4/8 - 4489*u**3/2 - 2*u**2 + 44*u. Let w(k) = 0. Calculate k.
-1, 67
Let a(n) be the third derivative of -n**10/15120 - n**9/7560 - n**4 - 8*n**2. Let c(s) be the second derivative of a(s). Factor c(q).
-2*q**4*(q + 1)
Let k be 18*(1 + 0)/12*4. Let b be (0 - (-1 + -1)) + (-10)/k. Factor b*y**2 - 2/3 - 1/3*y.
(y - 2)*(y + 1)/3
Let a(t) = 2*t**3 - 6*t**2 - t + 5. Let u(m) = -3*m**3 + 9*m**2 + m - 7. Let i(z) = z + 18. Let k be i(-13). Let b(w) = k*u(w) + 7*a(w). Factor b(f).
-f*(f - 2)*(f - 1)
Let s(w) be the first derivative of -w**4/4 - 26*w**3/3 - 146. Factor s(l).
-l**2*(l + 26)
Let r(s) be the first derivative of -9*s + 3/2*s**2 - 6*s**4 - 1 + 10*s**3. Determine p so that r(p) = 0.
-1/2, 3/4, 1
Let y = -5 + 7. Suppose -4 = -y*a + 2. Factor -6 + 2 + 4*q + a*q**2 + 0.
(q + 2)*(3*q - 2)
Let t(m) be the third derivative of m**8/168 + m**7/35 - 2*m**5/15 - 667*m**2. Find r such that t(r) = 0.
-2, 0, 1
Let v be 9/(27/(-42)) + -3. Let l = 20 + v. Factor 4*a**2 - 13*a**l - 4*a**4 + 2*a**5 + 34*a**3 - 21*a**3 - 2*a.
2*a*(a - 1)**3*(a + 1)
Suppose -5*z - 5 = 0, 4*l = -3*z - 47 + 16. Let p = 7 + l. Suppose 6*j**2 + p*j**2 - 2*j - 4*j*