). Factor 15*t + 6*t**2 + 30*t**f + 3*t**2 + 5*t**5 + 16*t**2 + 25*t**2 + 60*t**3.
5*t*(t + 1)**3*(t + 3)
Let o = -5/119 - 907/1071. Let v = 94/45 + o. Let -9/5*m - v + 3/5*m**3 + 0*m**2 = 0. What is m?
-1, 2
Let z(t) = -5*t**2 - 14*t. Let r(h) be the third derivative of -h**5/6 - 29*h**4/24 + 15*h**2. Let q(j) = 4*r(j) - 9*z(j). Suppose q(d) = 0. Calculate d.
-2, 0
Let c = -24 - 10. Let n = c - -171/5. What is l in -3/5*l**3 + 3/5*l**5 + 0*l - n*l**2 + 0 + 1/5*l**4 = 0?
-1, -1/3, 0, 1
Let j(a) be the first derivative of -5/3*a**3 - 4*a + 1/4*a**4 + 4*a**2 - 17. Suppose j(b) = 0. Calculate b.
1, 2
Let d be -2 - -2 - -1*(-1 + 0). Let a be d + 0 + (6 - (-7 - -9)). Factor 0 + 1/3*c + 23/6*c**4 + 7/6*c**5 + 9/2*c**a + 13/6*c**2.
c*(c + 1)**3*(7*c + 2)/6
Let i(u) be the second derivative of u**5/110 + 7*u**4/66 - u**3/33 - 7*u**2/11 - 170*u. Factor i(l).
2*(l - 1)*(l + 1)*(l + 7)/11
Let o(v) = -v**3 + v**2 + 6*v - 1. Let z be o(-2). Let q be 19/76*z*(-8)/10. Factor 0 + 1/5*w**4 - q*w**2 + 0*w**3 + 0*w.
w**2*(w - 1)*(w + 1)/5
Factor -9*z**3 + 3*z**4 + 12*z - 4 + 6 - 2.
3*z*(z - 2)**2*(z + 1)
Let 6*d**4 - 2*d**4 - 32 - 120*d**2 - 68*d**3 + 272*d + 20*d**4 + 8*d**4 = 0. What is d?
-2, 1/8, 2
Factor -4*q - 10 - 2/5*q**2.
-2*(q + 5)**2/5
Let v(j) = -2*j**2 - 33*j - 134. Let c be v(-8). Suppose 1/9*b**3 + 1/9*b**5 - 2/9*b**4 + 0*b**c + 0*b + 0 = 0. Calculate b.
0, 1
Let s(g) = -g**3 + 2*g**2 - 5*g + 24. Let a be s(3). Let f(j) be the first derivative of j**2 + a*j - 4/3*j**3 + 1/2*j**4 - 4. Factor f(z).
2*z*(z - 1)**2
Let q(k) be the first derivative of -35/4*k**4 + 5*k**3 - 36 + 0*k + 5*k**5 + 0*k**2 - 5/6*k**6. Suppose q(a) = 0. Calculate a.
0, 1, 3
Let d(z) = -z**3 - 3*z**2 + 28*z + 2. Let t be d(-7). Let v = -22 - -24. Factor 2 + t*a + 1/2*a**v.
(a + 2)**2/2
Let w(t) = 3*t**2 + t - 1. Let k(s) = -2*s**4 + 16*s**3 - 40*s**2 - 20*s + 34. Let o(m) = k(m) + 4*w(m). Suppose o(q) = 0. Calculate q.
-1, 1, 3, 5
Suppose -3*q = -9, -4*s + 3*q = -0*q - 3. Let t = 74 + -71. Let -1 + 4*b**2 + 1 - 70*b**t + 72*b**s = 0. What is b?
-2, 0
Let z be ((-2)/35)/(158/(-553)). Factor -z*o**2 + 14/5 + 13/5*o.
-(o - 14)*(o + 1)/5
Let s(h) be the first derivative of 2*h**3/15 + 2*h**2/5 + 2*h/5 - 165. Let s(l) = 0. Calculate l.
-1
Let o(w) be the third derivative of -w**7/70 - 17*w**6/120 - 17*w**5/30 - 7*w**4/6 - 4*w**3/3 - 33*w**2. Factor o(l).
-(l + 1)*(l + 2)**2*(3*l + 2)
What is h in -21/2*h + 441/4 + 1/4*h**2 = 0?
21
Let t(q) be the first derivative of -2/3*q - 2/3*q**4 - 8/15*q**5 + 2/3*q**2 - 17 + 2/3*q**3. Let t(a) = 0. Calculate a.
-1, 1/2
Determine a so that 3/4*a**2 + 3/8 + 3*a**3 - 15/8*a = 0.
-1, 1/4, 1/2
Factor 100352/9 + 2/9*c**2 - 896/9*c.
2*(c - 224)**2/9
Let b be -2 - (3 - 0) - (0 - 7). Let x be (-108)/(-57) - b/(-19). What is l in 3/5*l**4 + 2/5*l + 0 - 1/5*l**5 - 1/5*l**3 - 3/5*l**x = 0?
-1, 0, 1, 2
Let t be ((-1)/2)/((-5)/3860). Suppose 3*s - t = s. Factor -191*o**2 - o**4 + s*o**2 + 1 - 2.
-(o - 1)**2*(o + 1)**2
Factor -78/7 + 3/7*q**2 - 33/7*q.
3*(q - 13)*(q + 2)/7
Let g(v) = -7*v**2 - 8*v + 3. Suppose 2*r + 2*r - 5*s - 22 = 0, -5*s - 10 = 0. Let b(d) = 6*d**2 + 8*d - 2. Let x(o) = r*b(o) + 2*g(o). Factor x(k).
4*k*(k + 2)
Let z(c) be the second derivative of c**6/60 + c**5/30 - 9*c**2/2 - 7*c. Let r(a) be the first derivative of z(a). Suppose r(g) = 0. What is g?
-1, 0
Let a(q) = 4*q - 24. Let i be a(6). Let l(n) be the first derivative of -1/3*n**6 + 7 - 2/3*n**3 - 3/2*n**4 - 6/5*n**5 + i*n + 0*n**2. Factor l(s).
-2*s**2*(s + 1)**3
Let z(h) be the second derivative of -8*h**2 + 0 - 73/12*h**4 - 28/3*h**3 - 21/10*h**5 + 5*h - 3/10*h**6. Factor z(s).
-(s + 1)**2*(3*s + 4)**2
Factor -15/2*z - 1/2*z**2 + 1/2*z**4 + 15/2*z**3 + 0.
z*(z - 1)*(z + 1)*(z + 15)/2
Let x(c) = -2*c**3 - c - 1. Let p(r) = -r**4 - 10*r**3 + 3*r**2 - 3*r - 5. Let j(t) = -p(t) + 5*x(t). Factor j(i).
i*(i - 2)*(i + 1)**2
Let h be 11/4*16/2. Suppose h = 4*y + 7*y. Determine j, given that 1/5*j**4 + 0 - j**3 + 8/5*j**y - 4/5*j = 0.
0, 1, 2
Solve 4/7*k**2 - 2/7*k + 0 - 2/7*k**3 = 0.
0, 1
Let k(a) = 2*a - 56. Let l be k(0). Let r be (-2)/13 + l/(-26). Factor 0*x**2 + 3*x**3 + x**3 + 4*x**2 + 4*x**r + 4*x.
4*x*(x + 1)**2
Let a(r) be the first derivative of -r**3/6 - r**2/2 + 3*r/2 - 47. Factor a(f).
-(f - 1)*(f + 3)/2
Let n = 86 + -51. Suppose -m = -b - 3*m + 14, 0 = -5*b - 3*m + n. Solve -4*h**2 - 4*h**2 + b*h**2 + 7 - 12*h + 9 = 0.
-4, 1
Let b(h) be the second derivative of h**5/4 + 5*h**4/6 + 5*h**3/6 - 466*h. Factor b(d).
5*d*(d + 1)**2
Let x(f) = -27*f**2 - 219*f + 231. Let d(m) = -22*m**2 - 220*m + 230. Let q(s) = 5*d(s) - 4*x(s). Find n such that q(n) = 0.
-113, 1
Suppose 0 = -5*l, -k - l = -4*l - 1070. Suppose 5*n - 2*q = k, -4*q - 642 = n - 4*n. Factor 7*y**2 + 17*y**2 + 36*y + 230 - n + 4*y**3.
4*(y + 1)**2*(y + 4)
Let s(z) = 2*z**3 + 6*z**2 - 14*z + 10. Let y(c) = -c**3 - c - 2. Let h(v) = s(v) + y(v). Factor h(u).
(u - 1)**2*(u + 8)
Let q(s) be the second derivative of -s**7/28 - 3*s**6/20 + 27*s**5/20 - s**4/2 - 6*s**3 - 296*s. Suppose q(l) = 0. What is l?
-6, -1, 0, 2
Let i(v) = -v**3 + 7*v**2 + 13*v - 23. Let b(u) = -u**3 - u**2 - u + 1. Let m(k) = 6*b(k) - 3*i(k). Find a, given that m(a) = 0.
-5, 1
Let s(k) be the third derivative of -2*k**6/15 + 23*k**5/5 + 55*k**4/6 - 12*k**3 + 49*k**2. Factor s(y).
-4*(y - 18)*(y + 1)*(4*y - 1)
Let y be 25 + -4 + -10 - (-104)/(-10). Let y + 3/5*p**2 + 6/5*p = 0. Calculate p.
-1
Let j = -4 - -10. Let k be (-15)/j*4/(-5). Suppose -26*a**k + 4*a**3 + 26*a**2 + 2*a**4 - 2 - 4*a = 0. Calculate a.
-1, 1
Let h be ((-51)/34)/(3/268). Let d = -132 - h. Factor 1/5*z**d + 2/5*z + 0.
z*(z + 2)/5
Let z(h) be the first derivative of -4/5*h**5 + 0*h**4 - 1/3*h**6 + 8 + 4/3*h**3 + h**2 + 0*h. Factor z(j).
-2*j*(j - 1)*(j + 1)**3
Let j(n) = n**2 + 8*n + 9. Let u be j(-7). Factor -2*d**u - 71 + 34 - d**5 + 3*d**3 + 37.
-d**2*(d - 1)**2*(d + 2)
Let b(i) be the third derivative of i**6/30 - i**5/3 + 7*i**4/6 - 2*i**3 - 9*i**2. Solve b(f) = 0 for f.
1, 3
Suppose 607*y - 26 = 594*y. Let o(p) be the first derivative of 0*p + 4/21*p**3 - 10 - 2/7*p**y. Determine r so that o(r) = 0.
0, 1
Let o be ((-6)/(-4))/(-1)*-62. Let k = 469/5 - o. Factor -2/5 + k*s - 2/5*s**2.
-2*(s - 1)**2/5
Suppose f - 83 = -4*d + d, -4*d = -3*f - 115. Let n = d + -26. Factor 0*s**4 - 3*s**4 + 2*s**3 - 6*s**n + 6*s**4 + s**3.
3*s**2*(s - 1)*(s + 2)
Let f(q) be the third derivative of -q**9/25200 + q**8/2800 - q**7/1050 + 23*q**4/24 - 26*q**2. Let y(c) be the second derivative of f(c). Factor y(i).
-3*i**2*(i - 2)**2/5
Let u(x) be the first derivative of x**8/560 + x**7/70 + x**6/40 - x**5/10 - x**4/2 - 43*x**3/3 - 4. Let t(z) be the third derivative of u(z). Factor t(w).
3*(w - 1)*(w + 1)*(w + 2)**2
Let t(w) be the second derivative of -3*w**5/80 + 19*w**4/48 - w**3/4 - 16*w. Find m, given that t(m) = 0.
0, 1/3, 6
Let x(t) be the first derivative of t**6/2 - 12*t**5/5 + 15*t**4/4 - 2*t**3 + 84. Factor x(h).
3*h**2*(h - 2)*(h - 1)**2
Let w(b) be the first derivative of 2*b**6/3 - 8*b**5/5 - b**4 + 8*b**3/3 - 58. Solve w(g) = 0.
-1, 0, 1, 2
Let w(z) be the first derivative of z**6/90 + z**5/60 - z**4/12 + 41*z**3/3 + 32. Let o(v) be the third derivative of w(v). Factor o(s).
2*(s + 1)*(2*s - 1)
Let v(i) = i + 3. Let k be v(7). Suppose -2*t + 14 = -k. Suppose t*p**4 - 12*p - 60*p**2 - 63*p**3 + 34*p**4 + 75*p**5 + 14*p**4 = 0. Calculate p.
-1, -2/5, 0, 1
Let v(a) = -4*a**2 + 10*a - 12. Let s(g) = -11*g**2 + 29*g - 37. Let p(u) = -3*s(u) + 8*v(u). Let r be p(6). Let 3 + 1 + r*b**2 - 9*b - 11*b = 0. What is b?
2/9, 2
Let n(k) be the second derivative of 7*k**7/24 + 1393*k**6/120 + 1271*k**5/10 + 431*k**4/6 - 574*k**3/3 + 98*k**2 - 10*k + 5. Suppose n(c) = 0. Calculate c.
-14, -1, 2/7
Let h(g) = g + 7. Let t be h(-5). Suppose -5*q = a - 4*a - 4, 0 = 5*a - 5*q. Factor -4*b**2 + 5*b**t + a + 2*b**4 - 7*b**2 + 2*b**2.
2*(b - 1)**2*(b + 1)**2
Let b(u) = -u**3 + 5*u**2 - 5*u + 4. Let f be b(3). Let k be (f + 2)*2/6. Determine i, given that -8*i**4 + 6*i - k - 6*i**3 - 15*i**4 + 26*i**4 = 0.
-1, 1
Let k(i) be the third derivative of i**9/3780 - i**7/210 - i**6/90 - 5*i**4/24 + 28*i**2. Let t(c) be the second derivative of k(c). Factor t(s).
4*s*(s - 2)*(s + 1)**2
Let n(p) be the third derivat