26*z. Let u(q) = 5*d(q) + 2*r(q). Solve u(s) = 0 for s.
-6, -1, 0
Let v(y) be the first derivative of 2*y**5/15 + 7*y**4/3 - 10*y**3/3 + 358. Factor v(d).
2*d**2*(d - 1)*(d + 15)/3
Let n = 5467 - 5464. Let v be -1*2 - 30/(-8). Solve v*x + 9/4*x**n - 1/4 - 15/4*x**2 = 0.
1/3, 1
Let m(x) be the third derivative of -x**7/105 - 11*x**6/180 - 2*x**5/15 - x**4/9 + 294*x**2 + x. Determine t, given that m(t) = 0.
-2, -1, -2/3, 0
Let w(g) = -6*g**4 + 33*g**3 - g**2 - 13*g + 16. Let o(b) = b**3 + b**2 + b. Let m(i) = 22*o(i) - 2*w(i). What is t in m(t) = 0?
-1, 2/3, 2
Suppose -3*n = z - 5, 0*n + 3 = z + n. Suppose 0 = 5*o - 5*s + s - 45, -2*o + 3*s + 18 = 0. Factor 2*l**3 + 4*l - 6*l**3 + 3*l**2 - 2*l**z + 8 - o*l**2.
-4*(l - 1)*(l + 1)*(l + 2)
Factor -8/3*r - 2/9*r**2 - 40/9.
-2*(r + 2)*(r + 10)/9
Let c = 112/5 + -316/15. Find r such that -4/3*r - c - 1/3*r**2 = 0.
-2
Let b = 17 - 13. Factor -4*g**b + 2*g**5 - g**3 - 48*g**2 - g**3 + 52*g**2.
2*g**2*(g - 2)*(g - 1)*(g + 1)
Let z(u) = 4*u**2 - 4*u. Let c be z(4). Let f = 487 + -434. Factor -f*s**2 - s + s + c*s**2.
-5*s**2
Let g be 3/(-2)*((-6360)/210 - -30). Let d(i) = i**3 - 4*i**2 - 6*i + 5. Let k be d(5). Find u, given that -3/7*u + g*u**2 + k = 0.
0, 1
Let 18*p + 18/7*p**4 - 20/7 + 50/7*p**3 - 174/7*p**2 = 0. Calculate p.
-5, 2/9, 1
Let f(c) be the second derivative of c**5/80 - c**4/6 + 7*c**3/24 + 238*c. Factor f(x).
x*(x - 7)*(x - 1)/4
Let b(l) = -140*l**3 + 1025*l**2 + 6600*l + 5500. Let z(m) = -13*m**3 + 93*m**2 + 600*m + 500. Let g(a) = -6*b(a) + 65*z(a). Factor g(u).
-5*(u + 1)*(u + 10)**2
Let j(t) be the first derivative of 53 + t**4 - 8*t**2 + 0*t + 16/3*t**3 - 4/5*t**5. Solve j(u) = 0 for u.
-2, 0, 1, 2
Let s(d) be the third derivative of 0 + 1/120*d**5 - 1/4*d**3 + 0*d - 1/24*d**4 + 23*d**2. Suppose s(g) = 0. What is g?
-1, 3
Determine b so that 36/5*b - 9/5*b**3 + 24/5 - 3/5*b**4 + 6/5*b**2 = 0.
-2, -1, 2
Let l(y) be the second derivative of -2/21*y**3 - 4/35*y**5 + 0 + 0*y**2 - 13/42*y**4 + 16/35*y**6 - 14*y. Determine r so that l(r) = 0.
-1/4, 0, 2/3
Let t(i) be the second derivative of -i**7/35 - 2*i**6/15 - 7*i**5/50 + 2*i**4/15 + 4*i**3/15 + 32*i - 2. Solve t(r) = 0.
-2, -1, 0, 2/3
Let h(j) = 2*j**2 + 22. Let x be h(0). Suppose 2*u = -3*n, -4*n - n + x = -4*u. Factor -o**n - 8*o - 3*o**2 - 2 + 2.
-4*o*(o + 2)
Let l = 729 - 727. Suppose -2*p + 25 = 5*j - 7*p, -5*p - 25 = j. Let -6/13*u**l - 2/13*u**3 + j + 0*u = 0. What is u?
-3, 0
Let u = 6064 + -30318/5. Factor 14/5*j + 12/5 + u*j**2.
2*(j + 1)*(j + 6)/5
Factor -2/5*a + 2/5*a**3 - 72/5 + 72/5*a**2.
2*(a - 1)*(a + 1)*(a + 36)/5
Determine f, given that -1/2*f**3 - 56*f - 19/2*f**2 - 96 = 0.
-8, -3
Let m(r) be the third derivative of -r**7/70 - r**6/4 - 21*r**5/20 + r**4/2 + 14*r**3 + 6*r**2 + 1. Find a, given that m(a) = 0.
-7, -2, 1
Let a be 33880/2100 - (0 + 0)/1. Solve 88/15*x + 8/15 + a*x**2 = 0 for x.
-2/11
Determine d so that 6292*d**2 + 26645*d**3 + 19740*d**2 - 5 + 6148*d**2 + 25 - 1440*d - 6995*d**2 = 0.
-1, 2/73
Let v be 1*6/(-2) - 3. Let d be 1/(10/v + 2). Find j, given that 0*j**5 - 5*j**d - 2*j**5 - 4*j**4 + 3*j**3 = 0.
-1, 0
Solve -80 - 3*y**2 + 5*y**2 + 378 + 1270 + 112*y = 0 for y.
-28
Factor -2/3*b - 5/6 + 1/6*b**2.
(b - 5)*(b + 1)/6
Let k = 823/2 - 410. Let m(u) be the second derivative of 0 + 1/4*u**4 + k*u**2 + u**3 - 3*u. Factor m(y).
3*(y + 1)**2
Let w(c) = 8*c**5 - 12*c**4 + 12*c**3 + 11*c**2 - 10*c + 1. Let p(t) = t**5 + t**2 + t - 1. Let d(s) = 5*p(s) - w(s). Factor d(h).
-3*(h - 2)*(h - 1)**3*(h + 1)
Let v = 456053/190020 - 1/38004. Determine x so that -v*x - 8/5 + 18/5*x**2 - x**3 = 0.
-2/5, 2
Suppose -4 = -3*c + t, 5*c - 30 = -2*t - t. Suppose 0 = -c*d + d. Suppose 3*w**2 - 2*w + d*w**2 - 4*w**2 + 0*w**2 = 0. What is w?
-2, 0
Let q(f) be the second derivative of -f**9/3024 - f**8/672 + f**7/126 + f**6/18 - 31*f**4/12 + 32*f. Let k(u) be the third derivative of q(u). Factor k(a).
-5*a*(a - 2)*(a + 2)**2
Let g(d) be the second derivative of d**7/525 - 7*d**6/375 - 19*d**5/125 + 97*d**4/75 + 469*d**3/75 + 49*d**2/5 - 615*d. Solve g(y) = 0 for y.
-5, -1, 7
Let x(m) = 11*m**5 + 3*m**4 + 2*m**3 + 3*m**2 - 8*m - 11. Let q(v) = 13*v**5 + 3*v**4 + 2*v**3 + 4*v**2 - 9*v - 13. Let i(t) = -5*q(t) + 6*x(t). Factor i(g).
(g - 1)*(g + 1)**4
Suppose -16*u + 20*u = 0. Let t(o) = -2*o. Let d be t(u). Let 0 - 1/2*m**4 - m**5 + d*m**2 + 0*m**3 + 0*m = 0. What is m?
-1/2, 0
Factor -1/8*m**2 - 9/8*m - 1.
-(m + 1)*(m + 8)/8
Solve -3*i**3 + 0*i + 0*i**2 + 0 - 27/4*i**4 + 15/8*i**5 = 0.
-2/5, 0, 4
Let v be 245/20 - (-20)/(-16). Factor -2*q + 7*q + 5*q**3 - 8 + v + 13*q**2 + 6*q.
(q + 1)**2*(5*q + 3)
Let t(d) = -63*d**4 - 51*d**3 + 81*d**2 + 27*d - 90. Let x(s) = 13*s**4 + 10*s**3 - 16*s**2 - 5*s + 18. Let m(q) = 5*t(q) + 24*x(q). Factor m(c).
-3*(c - 1)**2*(c + 1)*(c + 6)
What is p in -36/5 + 6/5*p**3 + 42/5*p**2 - 6/5*p - 6/5*p**4 = 0?
-2, -1, 1, 3
Let w(l) = l**2 + 14*l - 3. Let t(c) = c**2 + 13*c - 2. Let v(q) = 5*t(q) - 4*w(q). Let k be v(-9). Factor -4*g**k + 2*g**3 + 5*g**2 - 5*g**2 + 8*g**4 - 6*g**5.
-2*g**2*(g - 1)**2*(3*g + 2)
Factor 4*a**5 + 103432*a**3 + 0*a**5 - 12*a**4 - 103424*a**3.
4*a**3*(a - 2)*(a - 1)
Let a(v) = v**2 + 48*v + 134. Let w(h) = -12*h**2 - 528*h - 1472. Let r(o) = 32*a(o) + 3*w(o). Factor r(t).
-4*(t + 4)*(t + 8)
Let x(u) be the second derivative of 8/45*u**3 + 16*u - 8/45*u**4 + 0 - 1/15*u**2. Let x(z) = 0. What is z?
1/4
Let c(w) be the third derivative of 0*w + 13*w**2 + 1/60*w**5 + 1/24*w**4 + 0 + 0*w**3. Solve c(g) = 0 for g.
-1, 0
Let y(o) be the first derivative of 14 - 5/18*o**6 - 11/12*o**4 - 4/3*o - 13/9*o**3 + 8/3*o**2 + 17/15*o**5. Solve y(u) = 0.
-1, 2/5, 1, 2
Let l(m) be the second derivative of m**5/480 - m**4/96 + m**3/48 - 6*m**2 + 8*m. Let i(h) be the first derivative of l(h). Factor i(n).
(n - 1)**2/8
Let z = -3 - -4. Let u be (z*-10*-1)/2. Solve 2*q**5 - q**3 + 2*q - 3*q**3 + 0*q**u = 0 for q.
-1, 0, 1
Let y(f) be the second derivative of f**5/36 - 5*f**4/24 + 5*f**3/9 - 5*f**2/2 - f. Let m(v) be the first derivative of y(v). Solve m(p) = 0 for p.
1, 2
Let s be (14/5)/((-6)/(-75)). Let v be 185/s + -10 + 5. Find z, given that -2/7*z**3 - 6/7*z - 6/7*z**2 - v = 0.
-1
Factor -11 + 3/2*h**2 - 1/2*h**4 - 11/2*h**3 + 31/2*h.
-(h - 1)**2*(h + 2)*(h + 11)/2
Let i = -98 + 138. Let q be ((-2)/(-6))/(i/60). Factor 0*z - q*z**2 + 0.
-z**2/2
Let v(g) be the second derivative of g**9/40320 + 9*g**4/4 + 11*g. Let n(x) be the third derivative of v(x). Factor n(f).
3*f**4/8
Suppose -10*t + 15*t - 15 = 0. Let -4*y**3 - y**t + 8*y + 4*y**5 - 7*y**3 + 0*y**5 + 4*y**2 - 4*y**4 = 0. What is y?
-1, 0, 1, 2
Let g(y) = -11*y - 11. Let t be g(-1). Let h(j) be the first derivative of 3/2*j**4 + 3 + 0*j**2 + t*j - 3/5*j**5 - j**3. Suppose h(f) = 0. Calculate f.
0, 1
Let l(z) be the third derivative of z**5/15 + z**4 + 10*z**3/3 + 56*z**2. Factor l(u).
4*(u + 1)*(u + 5)
Let f(m) = -4*m**2 + m + 3. Suppose 0 = 2*y - 2 - 0. Let w(x) = -x**2 - 1. Let t(h) = y*f(h) - 3*w(h). Factor t(p).
-(p - 3)*(p + 2)
Let m(k) = k**2 - k - 10. Let z be m(5). Find q such that -z*q**3 + 4*q**2 + 2 - 4*q**4 - 7*q**2 + 2*q**2 + 2*q - 5*q**2 = 0.
-1, 1/2
Let u(b) be the third derivative of b**7/4620 - b**6/1980 - 3*b**3 - 10*b**2. Let r(t) be the first derivative of u(t). Solve r(z) = 0.
0, 1
Let f(h) be the first derivative of 49*h**4 - 28*h**3/3 - 66*h**2 - 36*h - 22. Factor f(g).
4*(g - 1)*(7*g + 3)**2
Let p(v) be the second derivative of -v**7/63 + 2*v**6/45 + 2*v**5/5 + 7*v**4/9 + 5*v**3/9 + 1005*v. Factor p(r).
-2*r*(r - 5)*(r + 1)**3/3
Suppose 2 = 4*i - 5*u, i - 4*u = 3*i - 14. Suppose -2*l + 2*v + 12 = 0, -3 = 7*l - 5*l + i*v. Determine h, given that -3/5 - 16/5*h**2 + 4/5*h**l + 13/5*h = 0.
1/2, 3
Let z(k) = 3*k**4 - 39*k**3 - 39*k**2 + 96*k + 303. Let l(q) = -2*q**3 + q**2 + 1. Let g(x) = -15*l(x) + z(x). Determine n, given that g(n) = 0.
-3, -2, 4
Let i(t) be the first derivative of 2*t**3/45 - 4*t**2/15 - 8*t/5 - 252. Factor i(n).
2*(n - 6)*(n + 2)/15
Let s(m) = m**3 - 112*m**2 - 4. Let h(t) = 225*t**2 + 10. Let n(j) = -2*h(j) - 5*s(j). Determine w so that n(w) = 0.
0, 22
Let k(z) be the first derivative of z**3 + z**2/2 - 5*z + 1. Let y(a) = -a**2 - a + 1. Suppose 4 = 7*h + 11. Let i(b) = h*k(b) - 5*y(b). Factor