t derivative of -1/12*w**4 + 0*w**2 + 0*w + 1 - 2/9*w**p. Factor c(g).
-g**2*(g + 2)/3
Let -158*i + 331*i - 4*i**2 - 132 - 3*i**2 - 117*i + 3*i**2 = 0. What is i?
3, 11
Find i, given that 2/9*i**2 + 800 + 80/3*i = 0.
-60
Let x = 2 - -1. Suppose x*m + 0*m = 6. Find w, given that 0 - 3 + 3*w**m + 3 = 0.
0
Let c(v) be the third derivative of v**7/315 + v**6/45 + v**5/45 - v**4/9 - v**3/3 + 65*v**2. Let c(j) = 0. Calculate j.
-3, -1, 1
Let i(b) be the second derivative of b**5/100 + 29*b**4/60 + 8*b**3/3 + 26*b**2/5 + 2*b + 107. Factor i(m).
(m + 1)*(m + 2)*(m + 26)/5
Suppose 18*h + 9 = 9*h. Let c be (3/(-25))/(h/(-5)*-1). Solve c*o**3 + 0 - 4/5*o + 4/5*o**2 = 0 for o.
-2, 0, 2/3
Let o(w) be the second derivative of 3*w**5/100 - w**4/5 + 230*w. Let o(f) = 0. What is f?
0, 4
Let y(c) be the second derivative of -7*c**6/30 + 3*c**5/5 + 25*c**4/12 + c**3 - 44*c. Factor y(z).
-z*(z - 3)*(z + 1)*(7*z + 2)
Let b(p) = 7*p**4 + 36*p**3 - 132*p**2 + 122*p - 48. Let l(w) = 13*w**4 + 72*w**3 - 264*w**2 + 250*w - 96. Let f(s) = -5*b(s) + 3*l(s). Factor f(t).
4*(t - 1)**3*(t + 12)
Let v be (-98)/(-4) - 123/(-82) - 10. Factor -v*a - 16/3 + 28/3*a**2.
4*(a - 2)*(7*a + 2)/3
Let o(k) = -10*k**4 + 4*k**3 - 46*k**2 + 36*k - 12. Let g(v) = -7*v**4 + 2*v**3 - 31*v**2 + 24*v - 8. Let y(m) = 7*g(m) - 5*o(m). Factor y(q).
(q - 2)**2*(q - 1)**2
Let b = -859 - -864. Let t(g) be the third derivative of 0*g + 0*g**4 + 1/150*g**6 + 0 + 0*g**3 + 1/75*g**b + g**2. Determine y so that t(y) = 0.
-1, 0
Let o be (-1 + -6)/(25 + -26). Let n(b) be the second derivative of -1/12*b**4 - 1/10*b**6 + 0 + 0*b**2 + 9*b - 3/20*b**5 - 1/42*b**o + 0*b**3. Factor n(a).
-a**2*(a + 1)**3
Let i(d) be the second derivative of -1/6*d**3 - 1/4*d**2 - 1/24*d**4 - 1 - 5*d. Determine p, given that i(p) = 0.
-1
What is f in -4*f**3 - 16*f**2 - 7 + 44*f + 3 - 20 + 0 + 0*f = 0?
-6, 1
Find q such that -859*q**2 - 858*q**2 + 3*q**3 + 1729*q**2 - 63*q = 0.
-7, 0, 3
Let t(f) be the third derivative of 0*f + 11/450*f**6 + 0*f**3 + 0 + 4/75*f**5 + 1/20*f**4 + 8/1575*f**7 + 1/2520*f**8 + 14*f**2. Factor t(r).
2*r*(r + 1)**2*(r + 3)**2/15
Determine w, given that -3/5*w**4 + 0 + 0*w**2 + 6/5*w**3 + 0*w = 0.
0, 2
Let v = 13498 - 175458/13. Suppose v*p + 2/13*p**3 + 8/13 + 10/13*p**2 = 0. What is p?
-2, -1
Let g(i) be the third derivative of i**7/525 + i**6/150 + i**5/150 - 5*i**2 - 3. Let g(w) = 0. What is w?
-1, 0
Factor 36*k + 13 - 84 + 3*k**2 + 15 - 7*k**2.
-4*(k - 7)*(k - 2)
Let n be (3 - 3)/(-3 - -7). Factor 1/5*s**3 + n + 0*s + 0*s**2.
s**3/5
Let a = -45 - -35. Let q be -2*(-16)/20*a/(-4). Find z, given that 6/5*z**3 + 21/5*z + 6/5*z**q - 24/5*z**2 - 6/5 - 3/5*z**5 = 0.
-2, 1
Let h(s) be the first derivative of -s**7/840 + s**6/180 + 56*s**3/3 + 26. Let n(t) be the third derivative of h(t). Factor n(f).
-f**2*(f - 2)
Let y(o) be the first derivative of 2/3*o**3 + 0*o**2 - 1/1260*o**6 - 3/28*o**4 - 4 + 1/70*o**5 + 0*o. Let f(c) be the third derivative of y(c). Solve f(z) = 0.
3
Suppose d - 11 = -3*l, -5*l - 2 + 20 = 2*d. Let n(z) be the second derivative of 0*z**2 - 1/130*z**5 - 1/13*z**3 - 6*z + 0 - 2/39*z**l. Factor n(t).
-2*t*(t + 1)*(t + 3)/13
Let l(p) be the first derivative of -p**5/150 + p**4/30 + p**3/5 + 12*p**2 + 1. Let o(v) be the second derivative of l(v). Suppose o(m) = 0. What is m?
-1, 3
Let v = 217 + -212. Let a(i) be the first derivative of 0*i**2 - 6 + 16/3*i**3 + 0*i - 12/5*i**v + 0*i**4 + 2/3*i**6. Let a(h) = 0. Calculate h.
-1, 0, 2
Let b(v) be the second derivative of -v**6/30 + 8*v**5/15 - 8*v**4/3 + 9*v**2/2 - 13*v. Let j(k) be the first derivative of b(k). Factor j(g).
-4*g*(g - 4)**2
Let z = 49 + -44. Suppose 2*u = -z*u. What is h in u*h + 0 - 1/2*h**2 + 1/2*h**4 - 1/2*h**3 + 1/2*h**5 = 0?
-1, 0, 1
Let p = 15 - 13. Let v(a) = 3*a - 16 + 18 - 3*a**2 + 9*a**p. Let l(h) = -7*h**2 - 3*h - 3. Let c(n) = 4*l(n) + 5*v(n). Find g such that c(g) = 0.
-2, 1/2
Let x be (-15)/10*5*32/(-48). Let i(r) be the first derivative of x - 1/20*r**5 - 1/2*r + 1/16*r**4 - 1/8*r**2 + 1/4*r**3. Suppose i(d) = 0. What is d?
-1, 1, 2
Let b(q) = -q**3 + 23*q**2 - 43*q + 21. Suppose 3*w + 252 = 15*w. Let g be b(w). Factor g*h - 8/5*h**4 + 0 + 2/5*h**3 + 0*h**2.
-2*h**3*(4*h - 1)/5
What is d in 14 + 1/3*d - 1/3*d**2 = 0?
-6, 7
Let b(j) = j**2 + j - 1. Let s(w) = -w**2 + 4*w - 1. Let o be s(4). Let t(i) = -4*i**2 + 3*i - 6. Let h(v) = o*t(v) - 3*b(v). Factor h(k).
(k - 3)**2
Let c(l) be the first derivative of -2*l**5/5 + l**4/2 + 6*l**3 + 11*l**2 + 8*l + 111. Find p, given that c(p) = 0.
-1, 4
Let b(l) be the first derivative of -1/18*l**4 + 16 + 0*l**2 - 2/9*l**3 + 8/9*l. Factor b(v).
-2*(v - 1)*(v + 2)**2/9
Let j(c) = 19*c**2 - 8*c - 3. Let n(u) = -19*u**2 + 10*u + 3. Let z(f) = 3*j(f) + 4*n(f). Find w, given that z(w) = 0.
-3/19, 1
Let a be -6*((-176)/(-90) + 162/(-81)). Let t = 8 - 5. Solve -a*y**t + 0*y**2 - 2/15*y**4 + 4/15*y + 2/15 = 0 for y.
-1, 1
Let w(h) = h**3 - 16*h**2 + 14*h + 24. Let f be w(15). Let z = f - 3. Factor -2/3 - z*r**3 - 10*r**2 - 14/3*r.
-2*(r + 1)*(3*r + 1)**2/3
Let u(a) be the first derivative of 1/10*a**5 + 1/8*a**2 - 1/6*a**3 + 6 + 0*a - 1/24*a**6 + 0*a**4. Factor u(s).
-s*(s - 1)**3*(s + 1)/4
Let r = 21/79 - 47/474. Let f(g) be the first derivative of 6 + 1/2*g + 1/4*g**2 - 1/8*g**4 - r*g**3. Suppose f(n) = 0. Calculate n.
-1, 1
Let v be (-12)/30*25/(-120). Let n(f) be the second derivative of 0 + 0*f**3 - v*f**4 - 3*f + 0*f**2. Suppose n(s) = 0. What is s?
0
Let r(w) be the third derivative of -w**8/1344 + w**7/140 - w**6/96 - 23*w**2. Factor r(c).
-c**3*(c - 5)*(c - 1)/4
Let i be (4 - 1)/((-15)/(-80)). Let d be i/(-20) - 270/(-275). Factor d*n**5 + 2/11*n**3 + 0*n**2 + 0*n + 0 - 4/11*n**4.
2*n**3*(n - 1)**2/11
Solve 100*q**3 - 500*q**4 + 263*q**2 - 501*q**2 - 45 + 390*q - 907*q**2 + 1200*q**3 = 0.
3/10, 1
Let t be 8/3*21/(-4). Let i(v) = v**3 + 14*v**2 - v. Let j be i(t). Solve -15*z + 18 - 2*z**3 - 15*z + j*z**2 + 0*z = 0.
1, 3
Let t(m) = m**2 - 5*m + 3. Let b be t(5). Suppose -2*u = -b*l + 12, 0*u - 3*l + 12 = 2*u. Solve -p**2 + p**4 + 0*p**3 + p**3 + u*p**3 - p**5 = 0.
-1, 0, 1
Let c(b) = -b**2 + 561*b + 1060. Let m(t) = -15*t**2 + 7855*t + 14835. Let v(s) = -85*c(s) + 6*m(s). Let v(w) = 0. Calculate w.
-109, -2
Let l(g) be the first derivative of 0*g - 1/3*g**2 - 1/4*g**4 - 1/15*g**5 + 36 + 5/9*g**3 + 1/18*g**6. Factor l(r).
r*(r - 1)**3*(r + 2)/3
Suppose 0 = -4*f + 4*t + 84, -4*f + 3*t = -3*f - 15. Let h be 15*(f/20 + -1). Factor -2/7*i**2 - 4/7*i**h + 0 + 2/7*i**4 + 4/7*i.
2*i*(i - 2)*(i - 1)*(i + 1)/7
Let f(b) be the second derivative of -b**7/210 - b**6/90 + b**5/30 + b**4/6 + b**3/6 - 6*b. Let w(l) be the second derivative of f(l). Factor w(g).
-4*(g - 1)*(g + 1)**2
Suppose -4 = -4*r + 40. Suppose 4 = -3*z + 10. Find k, given that 2*k**2 + 12*k**3 + r*k**2 + 7*k**z - 16 - 16*k = 0.
-2, -2/3, 1
Let m(d) be the third derivative of d**6/5 - 7*d**5/20 - d**4/8 + 490*d**2. Determine x so that m(x) = 0.
-1/8, 0, 1
Factor -2/3*y**3 - 30*y + 8*y**2 + 100/3.
-2*(y - 5)**2*(y - 2)/3
Let a(m) be the second derivative of m**9/4032 + m**8/1120 - m**6/240 - m**5/160 + 11*m**3/6 + m. Let z(d) be the second derivative of a(d). Factor z(k).
3*k*(k - 1)*(k + 1)**3/4
Solve 18/7 + 2/7*b**3 + 6/7*b - 10/7*b**2 = 0 for b.
-1, 3
Let w = 6888 - 6886. Factor 0*n - 1/2*n**w + 0.
-n**2/2
Let d(w) = 6*w**2 - 188*w - 4842. Let u(a) = a**2 + a - 5. Let i(s) = -d(s) + 8*u(s). Factor i(y).
2*(y + 49)**2
Let i(a) be the second derivative of 1/30*a**6 + 1/15*a**5 + 0 + 0*a**3 + 0*a**4 + a**2 + 6*a. Let h(v) be the first derivative of i(v). Factor h(w).
4*w**2*(w + 1)
Let k(x) = x**2 + 3*x. Let z(h) = h**2 + h + h - h + h. Let c(n) = 3*k(n) - 4*z(n). Solve c(y) = 0.
0, 1
Let n = 838/3 + -279. Determine s so that -1/3*s**3 - n + 1/3*s + 1/3*s**2 = 0.
-1, 1
Let y = -6199 + 6201. Factor 2/5*k**3 + 0*k + 0 + 2/5*k**y.
2*k**2*(k + 1)/5
Let r(u) be the second derivative of -u**5/120 + 3*u**4/8 - 131*u**3/36 + 35*u**2/4 + 153*u + 2. Factor r(i).
-(i - 21)*(i - 5)*(i - 1)/6
Suppose -3*l + 8 = 2. Determine q, given that 20*q**l + 10*q**3 - 7*q**3 - 12*q**4 - 8 + q**3 - 4*q = 0.
-1, -2/3, 1
Solve 1/6*y**2 - 11/6 + 5/3*y = 0 for y.
-11, 1
Let q(k) = -10*k**3 + 26*k**2 - 18*k - 8. Let l(m) = 5*m**3 - 13*m**2 + 8*