h - 1)**2
Factor -5*z**4 + 0 + 10/3*z - 35/3*z**2 + 40/3*z**3.
-5*z*(z - 1)**2*(3*z - 2)/3
Let c = 2 - -2. Suppose -2*o + 3*y = -15 + 3, 3*y = 0. Determine t, given that 13*t + 2*t**2 - c*t + t**2 + o = 0.
-2, -1
Factor 2*w**4 - 494*w**3 - w**2 - 2*w**2 - w**2 + 492*w**3.
2*w**2*(w - 2)*(w + 1)
Let g(f) be the third derivative of 16/75*f**5 + 0*f**3 - 4/15*f**4 - 2/25*f**6 - 1/840*f**8 + 0*f + 0 + 8/525*f**7 + 13*f**2. Factor g(j).
-2*j*(j - 2)**4/5
Suppose -59*m = 104*m - 3*m. Factor -8/9*k**2 + 2/3*k**4 + 0*k**3 + m*k - 2/9*k**5 + 0.
-2*k**2*(k - 2)**2*(k + 1)/9
Let m(t) be the third derivative of t**4/24 + t**3/6 + 17*t**2. Let c be m(3). Let 1/2*v**2 - 3/4*v**3 + 0*v + 0 + 1/4*v**c = 0. What is v?
0, 1, 2
Let g(s) be the second derivative of -5/4*s**4 - 27*s + 1/6*s**6 - 20/3*s**3 + 1/2*s**5 + 0 - 10*s**2. Factor g(w).
5*(w - 2)*(w + 1)**2*(w + 2)
Let p be 132/88 - (-9)/2. Let i(z) be the second derivative of 1/21*z**4 + 8/105*z**6 - p*z + 0*z**3 + 1/10*z**5 + 1/49*z**7 + 0*z**2 + 0. Factor i(t).
2*t**2*(t + 1)**2*(3*t + 2)/7
Let s = 29/350 + -2/175. Let z(h) be the second derivative of -1/2*h**4 + 1/10*h**6 + 0 + 3/2*h**2 + 1/2*h**3 + s*h**7 + 2*h - 3/10*h**5. Factor z(v).
3*(v - 1)**2*(v + 1)**3
Let g(k) be the first derivative of 0*k + 0*k**3 - 5 - 7/2*k**2 + 1/180*k**5 + 1/72*k**4. Let r(y) be the second derivative of g(y). Factor r(f).
f*(f + 1)/3
Let l(i) = -53*i**3 + 196*i**2 - 128*i + 27. Let n(m) = m**3 - 2*m**2 - 1. Let y(d) = l(d) + 3*n(d). Solve y(q) = 0 for q.
2/5, 3
Let u = -7803 + 7806. Let -2/13*i - 2/13*i**2 + 2/13*i**u + 2/13 = 0. What is i?
-1, 1
Suppose -q - 8 = -5*p, -q = 4*q - p - 8. Solve 3*t**2 + 587*t**4 - 2*t**3 - 589*t**4 + t**q = 0.
-2, 0, 1
Factor -8/9*q**2 - 2/9*q**3 + 10/9*q + 0.
-2*q*(q - 1)*(q + 5)/9
Let o be 36*(3/9)/(3 + -2). Suppose -6*s + 0*s = -o. Solve 4/5*g**s + 0 + 6/5*g**3 + 0*g - 2/5*g**5 + 0*g**4 = 0 for g.
-1, 0, 2
Let d = 7363/28 - 1818/7. Suppose d*j + 9/2*j**3 + 1/4*j**5 - 7/4*j**4 - 3/4 - 11/2*j**2 = 0. What is j?
1, 3
Suppose -2*d - 3 = -z - 16, -3*z + d = 29. Let g be 1/z + (-5)/(-45). Let g + 22/13*o**4 + 70/13*o**5 + 8/13*o**2 - 40/13*o**3 + 0*o = 0. Calculate o.
-1, 0, 2/7, 2/5
Let a(o) be the first derivative of 6 + 0*o - 5/12*o**4 - 2/9*o**3 + 0*o**2 - 1/5*o**5. Factor a(q).
-q**2*(q + 1)*(3*q + 2)/3
Suppose 8 = 4*v + 2*n, -5*v - 51*n = -55*n - 23. Factor 4/7*z - 2/7*z**4 + 2/7 - 4/7*z**v + 0*z**2.
-2*(z - 1)*(z + 1)**3/7
Let x(g) be the first derivative of -3/2*g**2 + 23 + 2*g**3 + 3/4*g**4 - 6*g. Factor x(s).
3*(s - 1)*(s + 1)*(s + 2)
Let w = 31 - 33. Let i(h) = 2*h**2 + 3*h + 1. Let n be i(w). Factor 15*k**2 + n*k**3 + 16*k**2 - 25*k**2.
3*k**2*(k + 2)
Let o(q) be the second derivative of -q**4/48 + 11*q**3/4 - 1089*q**2/8 + 249*q. Factor o(l).
-(l - 33)**2/4
Let u(z) be the first derivative of 3*z**5/5 - 21*z**4/2 - 51*z**3 - 6*z**2 + 204*z - 471. Find b, given that u(b) = 0.
-2, 1, 17
Let s(m) be the third derivative of m**5/15 + 92*m**4/3 + 16928*m**3/3 - 476*m**2. Factor s(w).
4*(w + 92)**2
Suppose -l - 10 = -6*l. Factor -2*j**3 + 2*j**l + 6*j - 8*j - 2*j**4 + 4*j**3.
-2*j*(j - 1)**2*(j + 1)
Let q be 6/2*4/6. Let f(a) = -10*a + 3. Let l be f(0). Factor -4*v**2 - 6*v + 3*v**l - 2*v**3 + 11*v + 0*v**q - 2.
(v - 2)*(v - 1)**2
Let o(r) = -5*r - 25. Let i be o(-9). Suppose d - i = -18. Factor 0 - 4/11*g + 14/11*g**d + 6/11*g**4 - 16/11*g**3.
2*g*(g - 1)**2*(3*g - 2)/11
Factor 0 - 2/3*p**2 + 8/3*p.
-2*p*(p - 4)/3
Factor 3*g**2 - 7/4*g**3 - 4 + g + 1/4*g**4.
(g - 4)*(g - 2)**2*(g + 1)/4
Let r(l) be the first derivative of 3*l**4/28 - 276*l**3/7 + 38088*l**2/7 - 2336064*l/7 - 342. Factor r(d).
3*(d - 92)**3/7
Factor -75*u - 145/2 - 5/2*u**2.
-5*(u + 1)*(u + 29)/2
Suppose -4*n - 4*j = -8, 2*n + 7 = 2*j + 3. Suppose 0 = 2*u - 4*d - n*d - 10, -3*u + 2*d = -11. Factor 0*z**2 + 4/7*z**4 + 0*z + 0 + 2/7*z**5 + 2/7*z**u.
2*z**3*(z + 1)**2/7
Suppose -3*z + 6 = -3. Let w(b) = 2*b**2 + 14*b + 22. Let v be w(-5). Factor 4*o**2 - 2*o**3 + o**v + o**3 + 6*o**z.
5*o**2*(o + 1)
Let c(m) be the third derivative of -m**6/280 + 3*m**5/20 - m**4 + 18*m**3/7 + 44*m**2. Factor c(i).
-3*(i - 18)*(i - 2)*(i - 1)/7
Let h(g) = g**2 - 16*g + 17. Let j be h(15). Factor t + 25 + t**j + 0*t - 11*t.
(t - 5)**2
Let r be 135/100 + 6/(-8). Let w(o) be the first derivative of 3/20*o**4 + 1/5*o**3 - 3/10*o**2 - 5 - r*o. Factor w(i).
3*(i - 1)*(i + 1)**2/5
Let f(k) be the third derivative of k**5/30 - k**4/6 - 8*k**3/3 + 123*k**2. Factor f(h).
2*(h - 4)*(h + 2)
Let m = 1/270 - -3667/135. Let a = m - 27. Factor -1/3 + 1/3*z**2 - 1/6*z**3 + a*z.
-(z - 2)*(z - 1)*(z + 1)/6
Let y(i) be the second derivative of -i**10/30240 + i**9/10080 - i**8/13440 + 7*i**4/4 - 33*i. Let n(t) be the third derivative of y(t). Factor n(f).
-f**3*(f - 1)*(2*f - 1)/2
Let d = -110 - -114. Let f(s) be the first derivative of 7/5*s**d - 8/15*s**3 + 0*s + 9 - 8/5*s**2 + 1/5*s**6 + 26/25*s**5. Determine k, given that f(k) = 0.
-2, -1, 0, 2/3
Factor 2/17*b**3 + 128/17*b - 192/17 - 28/17*b**2.
2*(b - 6)*(b - 4)**2/17
Let d(g) be the second derivative of -g**7/168 - g**6/72 + g**5/12 - 13*g**3/6 + 10*g. Let o(a) be the second derivative of d(a). Factor o(m).
-5*m*(m - 1)*(m + 2)
Suppose -2*w = w - 24. Suppose 0 = -4*a - w + 20. Find p, given that 4*p**2 - 3 - 7*p - 6*p**a - 19*p**2 - 5*p = 0.
-1, -1/2
Let t(q) = q**3 + 2*q**2 + 1. Let u(r) = 2*r**4 + 2*r**3 - 6*r**2 - 8*r - 14. Let f(j) = 6*t(j) + u(j). Factor f(v).
2*(v - 1)*(v + 1)*(v + 2)**2
Let l(u) be the first derivative of -u**6/6 - 2*u**5/5 + 3*u**4/4 + 8*u**3/3 + 2*u**2 - 72. Determine p, given that l(p) = 0.
-2, -1, 0, 2
Let g(k) be the first derivative of -5*k**6/6 + 6*k**5 - 65*k**4/4 + 20*k**3 - 10*k**2 - 100. Find u, given that g(u) = 0.
0, 1, 2
Suppose -4*p + 24 = -0*p. Factor -4*c**3 + p - 15*c**2 - 8*c + 12 - 15.
-(c + 1)*(c + 3)*(4*c - 1)
Suppose -4*x + 48 = -10*x, -2*x = 4*z + 4. Factor 1014/11*n + 2/11*n**z + 78/11*n**2 + 4394/11.
2*(n + 13)**3/11
Let r(q) be the first derivative of 2*q**3/3 - 18*q**2 - 80*q - 140. Factor r(l).
2*(l - 20)*(l + 2)
Let y = 42294/5 + -8457. Factor 0 - y*u - 3/5*u**2.
-3*u*(u + 3)/5
Let b(h) be the second derivative of h**6/240 + h**5/40 - 3*h**3/2 - 3*h. Let l(y) be the second derivative of b(y). Determine g, given that l(g) = 0.
-2, 0
Let x(z) be the first derivative of -17*z**5/20 + 19*z**4/8 - z**3 - 27*z**2/2 + 13. Let h(k) be the second derivative of x(k). What is a in h(a) = 0?
2/17, 1
Let g = 146 - 143. Let h(w) be the second derivative of -1/30*w**6 - 5/12*w**4 + 0*w**2 - 1/3*w**g + 7*w + 0 - 1/5*w**5. Let h(a) = 0. Calculate a.
-2, -1, 0
Suppose 9 = -u + 3*l, 3*u - 2*l + 14 = 5*u. Suppose -16 = -7*f + u*f. Factor 5*q**3 - 149*q**2 - 2*q**4 + 0*q**f + 3*q**4 + 158*q**2 + 7*q + 2.
(q + 1)**3*(q + 2)
Factor -39*f**4 - 407*f + 117*f**3 - 97*f**2 + 36*f**4 - 3310*f - 2646 - 350*f**2 - 504*f**2.
-3*(f - 21)**2*(f + 1)*(f + 2)
Let f be 112/(-64)*(-10)/(-28)*-2. Determine m so that -7/4*m**2 + 1/2 + f*m = 0.
-2/7, 1
Let b(d) be the third derivative of -d**7/1680 + d**6/320 + d**5/480 - d**4/64 - 639*d**2. Factor b(v).
-v*(v - 3)*(v - 1)*(v + 1)/8
Let a(g) be the third derivative of 24*g**2 + 0 + 0*g - 1/70*g**7 + 0*g**4 - 1/40*g**6 + 0*g**3 + 0*g**5. Factor a(i).
-3*i**3*(i + 1)
Let p(y) be the third derivative of y**7/357 - 13*y**6/1020 + y**5/85 - 179*y**2. Factor p(g).
2*g**2*(g - 2)*(5*g - 3)/17
Let x(t) be the third derivative of -t**9/3024 - t**8/1680 + t**7/840 + t**6/360 - t**3/2 + 15*t**2. Let p(b) be the first derivative of x(b). Factor p(d).
-d**2*(d - 1)*(d + 1)**2
Let g = -643 + 35367/55. Let x(v) be the first derivative of 0*v**3 + 1/22*v**4 + 0*v + g*v**5 + 0*v**2 - 6. Suppose x(p) = 0. What is p?
-1, 0
Let x be 26/7 + -4 - (-82)/140. Let u(f) be the second derivative of -3/25*f**5 - 2/5*f**3 - 3/10*f**4 + 0 - 1/50*f**6 - x*f**2 + 4*f. Factor u(w).
-3*(w + 1)**4/5
Let m(x) = 17*x**2 - 120*x + 37. Let o be m(7). Find r such that 50/3*r - 2/3*r**4 - o*r**2 + 500/3 - 26/3*r**3 = 0.
-5, 2
Suppose 5*m - 293 = -3*k, 3*m + 0*m - 178 = -4*k. Let l = m - 58. Factor l + 0*y + 0*y**2 + 1/4*y**3.
y**3/4
Let b(x) = x**3 + 19*x**2 - 18*x + 42. Let l be b(-20). Let j(a) be the first derivative of -6 - 6*a + 3/2*a**l + a**3. Factor j(g).
3*(g - 1)*