*r + 161. Factor x(f).
3*(f - 27)**2
Let p(q) be the second derivative of 5*q**7/42 + q**6/2 - q**5/4 - 35*q**4/12 + 10*q**2 + 253*q. Suppose p(g) = 0. What is g?
-2, -1, 1
Let b(a) be the first derivative of a**5/4 + 15*a**4/16 - 15*a**3/4 + 25*a**2/8 - 180. Determine v so that b(v) = 0.
-5, 0, 1
Suppose 2 = -10*m + 11*m. Solve -24*f - 12 - 22*f**m + 7*f**2 + 12*f**3 - 15*f**3 = 0.
-2, -1
Let d(m) = 9*m**5 - 40*m**4 + 32*m**3 + 45*m**2 - 36*m. Let o(p) = -8*p**5 + 40*p**4 - 32*p**3 - 44*p**2 + 36*p. Let s(v) = -4*d(v) - 5*o(v). Factor s(b).
4*b*(b - 9)*(b - 1)**2*(b + 1)
Let c be 20/5 - (2 + 0). Suppose -8*s**3 + 39*s - 42*s**c - 6*s**2 + 4*s**5 - 3*s + 18*s**4 - 2*s**4 = 0. Calculate s.
-3, 0, 1
Let m(k) be the first derivative of -4*k**3/3 - 54*k**2 + 232*k - 228. What is s in m(s) = 0?
-29, 2
Let m(s) be the third derivative of s**7/1890 - 2*s**5/135 + 8*s**3/27 - 48*s**2. Determine n so that m(n) = 0.
-2, 2
Suppose -8*m - 10 = -10*m, -5*o = -m - 10. Let w = 3 + -3. Suppose 0*d + 2/5*d**4 + 0 + w*d**o + 0*d**2 = 0. Calculate d.
0
Let c be (2/6)/(9/135). Suppose -c*y - q = -3*q - 43, -3*q + 48 = 5*y. What is n in 4*n - 3 + n**2 + 2*n**2 + y - 5*n**2 = 0?
-1, 3
Let u(h) be the third derivative of h**7/490 - 11*h**6/56 + 783*h**5/140 - 729*h**4/56 + 463*h**2. Factor u(k).
3*k*(k - 27)**2*(k - 1)/7
Solve -162/7 - 14*g**4 - 96*g**3 - 864/7*g - 1404/7*g**2 = 0 for g.
-3, -3/7
Let a be 1/98 + 0/6. Let t(y) be the second derivative of 3/7*y**2 - 1/7*y**4 + 5*y + 1/35*y**6 + 0 + 3/70*y**5 - a*y**7 - 1/14*y**3. Solve t(h) = 0.
-1, 1, 2
Let z(x) be the third derivative of x**8/294 + x**7/245 - x**6/105 - x**5/70 + 59*x**2 + 2. What is c in z(c) = 0?
-1, -3/4, 0, 1
Let z(d) be the third derivative of d**6/30 + 8*d**5/15 + 17*d**4/6 + 20*d**3/3 + 82*d**2 - 1. Factor z(t).
4*(t + 1)*(t + 2)*(t + 5)
Let u(r) be the third derivative of -r**6/360 - 19*r**5/90 - 11*r**4/2 - 36*r**3 - 54*r**2 - 3. Solve u(a) = 0 for a.
-18, -2
Let c(h) be the second derivative of h**7/2520 - h**6/360 + h**5/120 + h**4/3 + 10*h. Let o(d) be the third derivative of c(d). Solve o(n) = 0.
1
Suppose 18 = c + 5*o - 12, 0 = -4*c + 2*o + 54. Factor 2*b**5 - c*b**5 - 4*b**5 + 3*b**5 - 4*b**4.
-2*b**4*(7*b + 2)
Let r(n) = 12*n**2 - 255*n + 84. Let x(u) = u**2. Let p(a) = -r(a) + 3*x(a). Determine f, given that p(f) = 0.
1/3, 28
Suppose 19*q = -172*q + 382. Let m be 2 + (-2)/(-14) + -2. Factor 3/7*w**q - 3/7*w + m - 1/7*w**3.
-(w - 1)**3/7
Let r be (-1 + (5 - 24/9))*3. Let q(x) be the third derivative of 0*x + 1/24*x**r + 0*x**3 - 1/120*x**5 - 1/240*x**6 + 0 - x**2. Determine y so that q(y) = 0.
-2, 0, 1
Let a be -1 + (-120)/(-32) - (-3)/(-6). Factor -3/2 - 3/4*b**2 - a*b.
-3*(b + 1)*(b + 2)/4
Factor -22/5*f - 3/5*f**3 + 0 + 67/5*f**2.
-f*(f - 22)*(3*f - 1)/5
Factor -3*h**2 + 3/5*h**4 - 9/5*h + 9/5*h**3 + 12/5.
3*(h - 1)**2*(h + 1)*(h + 4)/5
Let l(x) = 3*x**4 - 106*x**3 + 1807*x**2 - 12000*x + 30000. Let o(v) = -v**4 + 36*v**3 - 602*v**2 + 4000*v - 10000. Let f(z) = 2*l(z) + 7*o(z). Factor f(j).
-(j - 10)**4
Let i(o) = o**2 + 4*o - 3. Let v be (-3)/(-12) - 7/(-4). Let p be i(v). Factor -2*l - 13*l**2 + p*l**2 - 2*l.
-4*l*(l + 1)
Let j(o) be the first derivative of -9 - 3*o**4 + 8/5*o**5 + 2*o**6 - 8/3*o**3 + 0*o + 0*o**2. Solve j(l) = 0.
-1, -2/3, 0, 1
Let a be (-2)/(-3)*-5*(-15)/25. Factor a + 2 - 20*b + 25*b**2 + 7 - 6 - 10*b**3.
-5*(b - 1)**2*(2*b - 1)
Let r(g) be the third derivative of g**6/240 + g**5/12 + 3*g**4/16 - 68*g**2. Find h, given that r(h) = 0.
-9, -1, 0
Let l be ((-75)/10 - -8)*1*2. Let r = l - 1. Solve -3*o**2 + 9/2*o**4 + r - 3/2*o**3 + 0*o = 0.
-2/3, 0, 1
Factor -2 - 12*q + 22 + 2*q - 5*q**2 + 20.
-5*(q - 2)*(q + 4)
Solve 1/4*q**2 + 31/4 + 8*q = 0.
-31, -1
Suppose h + 5*i = 2 + 4, -5*i - 30 = 5*h. Let z be (h/15)/((-3)/15). Factor 3/2*b**4 - 9/2*b**2 - 3/2*b**3 + 3/2*b + z.
3*(b - 2)*(b - 1)*(b + 1)**2/2
Let n be (-2)/(-7) - 38/(-14). Let a be (-20)/(-70) + (-2)/7. Determine b, given that a*b**3 + 2*b**n + 6*b**2 - 10*b**2 = 0.
0, 2
Let k be 42/(-6)*9/(-21). Suppose -3*h = 5*r, r - k*h + 4*h = 0. Factor 0 + r*d + 2/5*d**3 - 1/5*d**4 - 1/5*d**2.
-d**2*(d - 1)**2/5
Suppose 6*a**3 - 8*a**2 - 4*a**3 + 3*a - 6*a**3 + 8*a**4 + a = 0. Calculate a.
-1, 0, 1/2, 1
Let i(x) be the second derivative of 11/14*x**4 + 3*x + 10/21*x**3 + 4/7*x**5 + 1/7*x**2 + 0 + 16/105*x**6. Factor i(t).
2*(t + 1)**2*(4*t + 1)**2/7
Let c(b) = b**3 - 44*b**2 + 28*b + 8. Let q(w) = w + 5. Let j be q(-2). Let h(s) = 15*s**2 - 9*s - 3. Let o(r) = j*c(r) + 8*h(r). Factor o(t).
3*t*(t - 2)**2
Factor -4/7*k + 1/7*k**3 + 136/7 - 34/7*k**2.
(k - 34)*(k - 2)*(k + 2)/7
Let l be ((-154)/(-21))/(4/6). Factor -3*s + 3*s**2 + 9 - l*s + s - 2*s + 3*s**3.
3*(s - 1)**2*(s + 3)
Let z(h) be the third derivative of -h**6/480 + h**5/60 + h**4/8 - 3*h**2 - 28. Find o such that z(o) = 0.
-2, 0, 6
Let v(u) be the first derivative of 1/8*u**3 - 9/8*u + 6 - 3/8*u**2. Factor v(n).
3*(n - 3)*(n + 1)/8
Let s(y) be the first derivative of -5/3*y**3 + 20*y + 1 + 15/2*y**2. Let s(g) = 0. What is g?
-1, 4
Let a(z) = z**3 + 15*z**2 + 23*z - 23. Let u be a(-11). Let c = -206 + u. Factor 2/15 - 2/15*l**c + 0*l.
-2*(l - 1)*(l + 1)/15
Let z(r) = -13*r - 19. Let t be z(-2). Let f be 28/t*1/7. Factor 0 + 2/7*p**4 - 2/7*p**2 + f*p - 4/7*p**3.
2*p*(p - 2)*(p - 1)*(p + 1)/7
Factor 0 - 4/7*p**2 + 6/7*p - 2/7*p**3.
-2*p*(p - 1)*(p + 3)/7
Let y be (-4 - (-64)/10)*(-510)/(-714). Factor -10/7*h - 2/7*h**2 - y.
-2*(h + 2)*(h + 3)/7
Let u be 36/(-30)*-5*1/2. Let f(r) be the third derivative of 1/24*r**4 + 0*r**u + 0 + 0*r + 5*r**2 - 1/80*r**6 - 1/120*r**5. Factor f(v).
-v*(v + 1)*(3*v - 2)/2
Let u(v) be the third derivative of -4/3*v**3 + 0*v + 1/6*v**4 + 1/84*v**8 - 4/105*v**7 + 3*v**2 - 1/15*v**6 + 4/15*v**5 + 0. Find x, given that u(x) = 0.
-1, 1, 2
Let q(u) = u**3 + 6*u**2 + u + 6. Let d be q(-6). Suppose d = -0*g + 5*g - 15. Factor 2 + 5/3*b - b**g - 8/3*b**2.
-(b - 1)*(b + 3)*(3*b + 2)/3
Let c = 10887022/3 - 25824014381/7116. Let b = c - 2/593. Factor -b*j + 1/4*j**2 + 1/4*j**3 - 1/4*j**4 + 0.
-j*(j - 1)**2*(j + 1)/4
Solve 16 - 30*d**2 + 48*d + 13*d**3 + 82*d**2 + 4*d**4 + 11*d**3 = 0.
-2, -1
Let j(n) = n**3 + 2*n + 2. Let q be j(0). Factor 1/5*p**q - 3/5 - 2/5*p.
(p - 3)*(p + 1)/5
Let b be 1/(-4 + 182/28). What is r in 24/5 + 14/5*r**2 + 32/5*r + b*r**3 = 0?
-3, -2
Suppose -3*d + 27 = -3*n, -2*d + 9 = -n - 4. Let h(l) be the second derivative of -6*l + 0 + 56/3*l**3 + 13/5*l**5 - 10*l**d - 4/15*l**6 - 16*l**2. Factor h(y).
-4*(y - 2)**3*(2*y - 1)
Let k(a) be the first derivative of 0*a - 12 + 1/2*a**2 - 1/3*a**3. Let m(c) = -4*c**2 - 6*c. Let t(i) = k(i) + m(i). Factor t(r).
-5*r*(r + 1)
Let n(g) = 3*g**2 + 84*g + 91. Let t(i) = -i**2 + 2*i + 1. Let q(h) = 2*n(h) + 10*t(h). Factor q(z).
-4*(z - 48)*(z + 1)
Let a(r) = r + 2. Let s be a(0). Let y be (-6)/(-2) - (s + -2). Factor o**3 - 2*o**y - 2*o**3 + 5*o**5 - 2*o**5.
3*o**3*(o - 1)*(o + 1)
Let w(y) = -y - 4. Let l be w(-9). Let t(k) be the first derivative of 0*k**2 - 2*k**3 - 3/5*k**l - 9/4*k**4 + 0*k + 5. Find f such that t(f) = 0.
-2, -1, 0
Suppose 18*i - 298 + 226 = 0. Factor 0*x**3 + 0 - 3/7*x**2 + 0*x + 3/7*x**i.
3*x**2*(x - 1)*(x + 1)/7
Solve 2/13*l**3 + 0*l**2 + 4/13*l**4 + 0 + 0*l + 2/13*l**5 = 0.
-1, 0
Let j(b) = -b**3 + b**2 + 2*b + 1. Let z(c) = 3*c**3 + 4*c**2 + c - 14. Let h(k) = -6*j(k) - 3*z(k). Suppose h(q) = 0. Calculate q.
-4, -3, 1
Let i(s) = s - 5. Let d be i(3). Let l(g) = -3 - 4*g**2 + 20 + 15*g**2 - 18 + 4*g. Let c(y) = 177*y**2 + 63*y - 15. Let u(r) = d*c(r) + 33*l(r). Factor u(z).
3*(z + 1)*(3*z - 1)
Let a(p) be the second derivative of 5*p**8/336 - p**6/8 + p**5/6 - 27*p**2/2 + 27*p. Let l(r) be the first derivative of a(r). Factor l(y).
5*y**2*(y - 1)**2*(y + 2)
Find s, given that 140*s + 201*s**3 - 1080 - 190*s + 954*s - 1470*s**2 + 2804*s - 9*s**4 = 0.
1/3, 6, 10
Factor -4/11*m**3 - 2/11*m**4 + 2/11 + 4/11*m + 0*m**2.
-2*(m - 1)*(m + 1)**3/11
Let b(z) be the third derivative of -1/12*z**6 + 5/8*z**4 + 1/6*z**5 - 1/14*z**7 - 6*z**2 + 0 - 5/336*z**8 + 5/6*z**3 + 0*z. Factor b(d).
-5*(d - 1)*(d + 1)**4
Solve 5*k**3 - k**5 + 10*k**4 + 25*k**2 - 31*k**4 - 44*k**3 - 44*k**2 = 0.
-19, -1, 0
Let r(m) be the first derivative of 0*m**4 - 12 + 0*m**3 - 2/3*m**6 + 0*m