t l(r) be the third derivative of -r**10/30240 + r**9/3780 + 25*r**4/24 + 34*r**2. Let k(f) be the second derivative of l(f). Factor k(m).
-m**4*(m - 4)
Factor -2/9*f**4 - 70/9*f**2 + 0 - 50/9*f - 22/9*f**3.
-2*f*(f + 1)*(f + 5)**2/9
Let r(o) be the second derivative of 0*o**2 - 4*o + 1/45*o**5 + 1/135*o**6 + 0 + 0*o**3 + 1/54*o**4. What is f in r(f) = 0?
-1, 0
Let a(z) be the third derivative of z**8/168 + 5*z**7/21 + 163*z**6/60 + 9*z**5/10 - 54*z**4 + 144*z**3 + 284*z**2. Let a(q) = 0. Calculate q.
-12, -3, 1
Let v(j) be the first derivative of -j**5/270 - 5*j**4/108 + 2*j**3/9 - 2*j**2 + 24. Let d(z) be the second derivative of v(z). Factor d(s).
-2*(s - 1)*(s + 6)/9
Let k be 18/11 - (-216)/594. Factor 4/7*v**3 + 0 + 2/7*v**k - 2/7*v.
2*v*(v + 1)*(2*v - 1)/7
Let x be ((-12)/(-8))/1 + 23/(-18). Suppose 16/9*g + 32/9 + x*g**2 = 0. Calculate g.
-4
Let j be 21 - (-12 + -6 + 13). Suppose 16 = 14*l - j. Factor 1/2*k**2 + 1/2*k**l + 0*k + 0.
k**2*(k + 1)/2
Let u(d) = -d - 4. Let m be u(-6). Let -17*s + 19 + m*s - 14*s**3 - 7*s**3 - 16 + 27*s**2 + 6*s**4 = 0. Calculate s.
1/2, 1
Let x be 5/825*15 + (-2 - (-42)/22). Suppose 7/3*r**2 + x*r - 1/3*r**3 + 0 = 0. What is r?
0, 7
Let y(g) be the second derivative of -g**5/180 + 2*g**4/3 - 407*g**3/18 - 1369*g**2/9 - 508*g. Determine u, given that y(u) = 0.
-2, 37
Let a(j) be the first derivative of -j**6/21 - 16*j**5/35 + 3*j**4/2 + 16*j**3/21 - 20*j**2/7 - 268. What is t in a(t) = 0?
-10, -1, 0, 1, 2
Let r be (-2)/22 - (-65)/110. What is h in 3/2*h**2 + 0*h + 0 - r*h**3 = 0?
0, 3
Suppose -12*x = -9*x - 15. Suppose 15*y = o + 10*y + 10, 5*o + x*y - 10 = 0. Factor -3/2*p**2 + o - p.
-p*(3*p + 2)/2
Let h(x) be the second derivative of 1/120*x**5 - 1/9*x**3 + x + 0 + 1/36*x**4 + 1/2*x**2. Let a(y) be the first derivative of h(y). Let a(i) = 0. Calculate i.
-2, 2/3
Let y = 439 - 436. Let 0*d**2 + 4/5*d**5 - 8/5*d**y + 4/5*d + 0 + 0*d**4 = 0. Calculate d.
-1, 0, 1
Let c(b) be the third derivative of -b**6/80 + 3*b**5/10 - 2*b**4 - 394*b**2 + 2*b. Let c(a) = 0. Calculate a.
0, 4, 8
Let 8/3 + 10/9*h**5 - 172/9*h**2 + 86/9*h + 52/9*h**4 + 0*h**3 = 0. Calculate h.
-4, -3, -1/5, 1
Let f = 18292/12803 + -2/12803. Solve -2/7*m**2 + 0 + f*m = 0.
0, 5
Let g = -7 - -10. Determine n, given that 16*n**g + 15*n**2 - 17*n**3 - 13*n**2 - n = 0.
0, 1
Let i be (-8)/(-36) - (-156)/27. Suppose 2*p + 12 = i*p. Factor -9*n**4 - 16*n + 9*n**2 + 10*n + n**p + 2*n**3 + 3*n**5.
3*n*(n - 2)*(n - 1)**2*(n + 1)
Let m be 64/30 - (-16)/(-120). Suppose 3*t = -3*z - m*t - 11, -3*t = 3*z + 3. Factor 1/4*r**4 + 1/8*r**5 + 0*r**z - 1/8*r + 0 - 1/4*r**2.
r*(r - 1)*(r + 1)**3/8
Let m(j) = 2*j**2 + 38*j + 162. Let z be m(-6). Find o such that 8/9 + 38/9*o**3 - z*o**2 - 8/9*o**4 + 16/9*o = 0.
-1/4, 1, 2
Let d(a) be the second derivative of 1/240*a**6 - 7/24*a**3 - 5*a + 0 - 1/80*a**5 - 5/16*a**2 - 1/8*a**4. Suppose d(h) = 0. Calculate h.
-1, 5
Solve -2/9*p**5 + 8/9*p**2 + 8/9*p - 8/9*p**4 + 0 - 2/3*p**3 = 0.
-2, -1, 0, 1
Let t be 2 + (0 - 3 - -12). Let q = t - 9. What is g in -2*g + 2*g**2 + 0*g**2 + 2*g**2 - g**3 - q*g = 0?
0, 2
Suppose -3*m - 43 = -2*l, -33 = -3*l - 4*m + 6. Factor x**3 + 18*x**5 + 2 - 5*x**3 - l*x**5 + 3*x - 2*x**2.
(x - 2)*(x - 1)*(x + 1)**3
Let l(y) = y**5 + y**4 - 2*y**2 + y - 1. Let w(m) = -16*m**5 + 12*m**4 - 56*m**3 + 88*m**2 - 48*m + 20. Let c(h) = -12*l(h) - w(h). Find o, given that c(o) = 0.
1, 2
Factor 9*k + 2*k**2 + 0*k - 19*k + 6*k.
2*k*(k - 2)
Let l(f) be the first derivative of 2/5*f**5 + 2*f + 22 + 4*f**3 - 4*f**2 - 2*f**4. Factor l(g).
2*(g - 1)**4
Let r(c) = -c**3 + 18*c**2 - 3*c + 21. Let u(o) = -o**2 + o. Let y(f) = r(f) + 2*u(f). Let a be y(16). Solve -82 + 18 - a*z + 37*z - 4*z**2 = 0.
4
Let w be (2 + 44/(-12))*(-3)/15. Let i(x) be the second derivative of 0*x**2 + 0*x**3 - 3*x + 1/10*x**5 + 0 - w*x**4 + 1/15*x**6. Let i(h) = 0. What is h?
-2, 0, 1
Factor 9/4 - 15/4*q + 4*q**3 - 2*q**2.
(q + 1)*(4*q - 3)**2/4
Let h(m) be the first derivative of -m**4/2 + 5*m**3/9 + 13*m**2/6 + 2*m/3 - 49. Factor h(g).
-(g - 2)*(g + 1)*(6*g + 1)/3
Let t(n) be the second derivative of n**4/18 + 16*n**3/9 + 5*n**2 + n + 3. Let t(p) = 0. Calculate p.
-15, -1
Let p be 53/14 + (-2)/7. Let l(b) = -b**3 + 17*b**2 + 18*b + 2. Let o be l(18). Solve -1/2*z**3 - p*z - 3/2 - 5/2*z**o = 0.
-3, -1
Suppose -74*t**3 + 10*t**2 + 0*t**2 + 10*t - 44*t**2 + 3*t**4 + 7*t**2 + 40*t = 0. What is t?
-1, 0, 2/3, 25
Let a be (-52)/(-20) + -2 + 710. Let i = a - 707. Suppose -2*f - 6/5*f**2 - 2/5 + i*f**3 = 0. What is f?
-1/3, 1
Determine b so that -5*b**3 + 37*b + 35*b**2 + 40 - 48*b - 59*b = 0.
1, 2, 4
Suppose -p - 10 = -2*n, p - 61*n = -63*n + 14. Factor 3*y + 0 + 5/2*y**p + 1/2*y**3.
y*(y + 2)*(y + 3)/2
Let u = -2/17249 - -207002/120743. Factor -3*f - 1/7*f**3 - u*f**2 - 10/7.
-(f + 1)**2*(f + 10)/7
Let o = 170 + -168. Let r be o/(0 + 8/20). Determine h so that 0 + 2/3*h**3 + 0*h**2 - 1/3*h + 0*h**4 - 1/3*h**r = 0.
-1, 0, 1
Let r = 2 + -4. Let q be (-12)/r - 2 - 4. Let 2*o**3 - 3*o**2 - 5*o**3 + 3*o + 3 + q*o**3 = 0. What is o?
-1, 1
Let r(h) be the first derivative of 1/20*h**6 - 1/24*h**4 - 2 + 0*h**3 + 3*h + 0*h**2 - 1/20*h**5. Let b(d) be the first derivative of r(d). Factor b(x).
x**2*(x - 1)*(3*x + 1)/2
Let q(f) be the second derivative of -f**6/45 - f**5/15 + f**4/6 + 75*f. Factor q(n).
-2*n**2*(n - 1)*(n + 3)/3
Factor -340*p**2 + 1590*p + 126405 + 679*p**2 - 334*p**2.
5*(p + 159)**2
Suppose 35 - 32 = l. Solve -76/7*i**l + 100/7*i**2 + 16/7 + 4*i**4 - 64/7*i - 4/7*i**5 = 0.
1, 2
Factor 9/2*r**2 - 5/2*r - 2.
(r - 1)*(9*r + 4)/2
Let f(y) be the first derivative of -5/2*y + 1/4*y**3 + 34 - 13/8*y**2. Let f(o) = 0. What is o?
-2/3, 5
Let f(l) be the third derivative of 1/60*l**5 + 1/12*l**4 + 0*l + 0 + l**3 - 8*l**2 + 1/720*l**6. Let x(v) be the first derivative of f(v). Factor x(u).
(u + 2)**2/2
Let s(n) be the third derivative of n**7/135 - 89*n**6/90 + 38*n**5 - 722*n**4/27 + 181*n**2 - 2*n. Find b, given that s(b) = 0.
0, 2/7, 38
Let k be 3 - -1 - (-5)/((-5)/2). Let w(b) = -b**3 - 4*b**2 + 2. Let j be w(-4). Factor -j*u**2 - u**3 - 2*u + u + 4*u**k + 0*u**3.
-u*(u - 1)**2
Let j(v) be the second derivative of -v**4/4 + 15*v**3 - 675*v**2/2 + 79*v. Determine l, given that j(l) = 0.
15
Let s(i) be the first derivative of -1/9*i + 0*i**2 + 19 + 1/27*i**3. Factor s(n).
(n - 1)*(n + 1)/9
Suppose -2 + 14 = 4*f. Let j = 45/22 - 203/110. Factor 0*y + 1/5*y**4 - j*y**f + 0*y**2 + 0.
y**3*(y - 1)/5
Factor -36 - 29*g - 97*g**2 - 33*g - 11*g**4 - g**5 + 0*g - 47*g**3 - 34*g.
-(g + 1)*(g + 2)**2*(g + 3)**2
Let k(z) = 19. Let j(g) = g + 1. Let n(m) = -3*j(m) - k(m). Let y be n(-8). Factor -2/5*q**y - 4/5 - 6/5*q.
-2*(q + 1)*(q + 2)/5
Let c be (2/3)/(18/(-1215)*-9). Let k(h) be the first derivative of -2*h**3 + 2*h**2 - 1/5*h**5 + c - h + h**4. Factor k(z).
-(z - 1)**4
Factor 2/13*c**2 + 24/13*c + 72/13.
2*(c + 6)**2/13
Let z(m) be the first derivative of -m**8/3024 - 2*m**7/945 - m**6/360 + 5*m**2 + 2. Let t(l) be the second derivative of z(l). Factor t(x).
-x**3*(x + 1)*(x + 3)/9
Suppose 2*i - l = 18, 2*i = 2*l + 24 - 6. What is j in -4*j**5 + 6*j**4 + 5*j**5 - i*j**4 = 0?
0, 3
Let k = -101 - -103. Let i = -107 + 965/9. Let 2/9*r - 4/9*r**k + 0 + i*r**3 = 0. Calculate r.
0, 1
Let n(z) be the second derivative of 3*z**5/100 + 7*z**4/20 - 9*z**3/5 + 14*z - 4. Factor n(f).
3*f*(f - 2)*(f + 9)/5
Let m = -5 + 9. Suppose m*s = d + 21, -2*s + 2*d + 13 = d. What is w in -8*w**s - 2*w**5 - 2 + 4 - 8*w**3 + 2 + 4*w**2 + 10*w = 0?
-2, -1, 1
Let n be 4/(-4)*(51/21 + 2). Let y = n - -5. Factor 2/7*u**2 + 2/7 - y*u.
2*(u - 1)**2/7
Suppose -5*p + 1 - 21 = 0, u - 2*p = 10. Suppose u*w + w - 12 = 0. Find s such that 3*s + 7*s**2 - w*s**3 - 10*s**2 - 2*s = 0.
-1, 0, 1/4
Factor 50 - 16*a - 6*a + 2*a - 264*a**2 + 266*a**2.
2*(a - 5)**2
Let j(i) = -i**2 - i + 2. Let n(t) = -t**2 - 2*t + 3. Let s(x) = 4*x + 17. Let q be s(-5). Let d(u) = q*n(u) + 2*j(u). Let d(y) = 0. What is y?
-5, 1
Factor 100*j**2 - 46*j**2 - 275 - 49*j**2 - 270*j.
5*(j - 55)*(j + 1)
Factor 56/5 + 2/5*y**2 + 22/5*y.
2*(y + 4)*(y + 7)/5
Let y(t) = t**2 - 17*t - 60. Let f be y(20). Let u(d) be the second derivative of 0*d**3 + 1/18*d**4 + f + 0*d**2 - 6*d + 1/30*d**5. Factor u(q).
2*q**2*(q + 1)/3
Let f(