).
-(m - 1)**2*(m + 1)*(7*m + 2)
Let m(w) be the first derivative of -w**6/80 + w**5/20 - 7*w**2 - 4. Let p(u) be the second derivative of m(u). Factor p(h).
-3*h**2*(h - 2)/2
Let t(g) = -5*g**5 - 55*g**4 + 35*g**3 + 25. Let a(y) = y**5 + 9*y**4 - 6*y**3 - 4. Let k(i) = 25*a(i) + 4*t(i). Factor k(q).
5*q**3*(q - 1)*(q + 2)
Let w(c) be the first derivative of 10/3*c + 13 - 5/9*c**3 - 5/6*c**2. Factor w(h).
-5*(h - 1)*(h + 2)/3
Let r(z) be the third derivative of 0*z**3 - 1/3*z**4 + 0 + 0*z - 2/105*z**7 - 6*z**2 + 1/15*z**5 + 1/15*z**6. Factor r(p).
-4*p*(p - 2)*(p - 1)*(p + 1)
Let k(n) be the first derivative of n**6/24 + 9*n**5/20 + 27*n**4/16 + 31*n**3/12 + 3*n**2/2 + 37. Suppose k(w) = 0. Calculate w.
-4, -3, -1, 0
Suppose -7*q + 14 = 0, -2*q = 4*f + 16 - 28. Factor 10/3*m + f*m**2 - 4/3.
2*(m + 2)*(3*m - 1)/3
Factor -1/3*n**2 - 8/3 + 3*n.
-(n - 8)*(n - 1)/3
Determine f so that -1/8*f**5 + 0 + 7/2*f**3 + 5/2*f**2 + 1/8*f**4 - 6*f = 0.
-4, -2, 0, 1, 6
Let s = -85/3 + 29. Let l(y) be the first derivative of y**2 - 4 - 4*y + s*y**3. Factor l(b).
2*(b - 1)*(b + 2)
Let a(n) be the first derivative of -2*n**5/15 + 24*n**4/5 - 2182*n**3/45 + 252*n**2/5 + 392*n/15 - 328. Suppose a(m) = 0. Calculate m.
-1/5, 1, 14
Let r(x) be the first derivative of x**3/27 + 20*x**2/9 + 400*x/9 + 42. Factor r(g).
(g + 20)**2/9
Let x(k) = -155*k**3 - 155*k**2 + 70*k - 15. Let j(l) = l**2 - 3*l**2 - 5*l + 11*l**3 + 13*l**2 + 1. Let r(p) = -85*j(p) - 6*x(p). Factor r(s).
-5*(s - 1)*(s + 1)**2
Let o(u) = u - 6. Let p(x) = -x**2 - 42*x + 73. Let a(s) = 6*o(s) + p(s). Let a(v) = 0. Calculate v.
-37, 1
Let r(l) be the third derivative of 0*l**4 + 1/14*l**7 - 5/336*l**8 + 0*l**5 - 15*l**2 - 1/12*l**6 + 0*l + 0 + 0*l**3. Solve r(d) = 0 for d.
0, 1, 2
Let q(l) = -l**3 + l**2 - 1. Let t(w) = 3*w**4 - 11*w**3 + 5*w**2 + 5*w - 8. Suppose 14 = 7*j + 7. Let k(y) = j*t(y) - 6*q(y). Factor k(n).
(n - 1)**2*(n + 1)*(3*n - 2)
What is t in 4*t**3 + 72/5*t**2 + 24/5 + 76/5*t = 0?
-2, -1, -3/5
Factor 15*z + 184*z**2 + 33*z - 189*z**2 - 13*z.
-5*z*(z - 7)
Let j(s) = -7*s**4 + 2*s**3 + 6*s**2 - 8*s + 1. Let d(y) = y**5 - 7*y**4 + 2*y**3 + 6*y**2 - 7*y + 1. Let w(g) = -3*d(g) + 2*j(g). Factor w(a).
-(a - 1)**3*(a + 1)*(3*a - 1)
Let b(q) be the second derivative of 4/3*q**4 + 6*q - 4*q**5 + 6/5*q**6 + 0*q**2 + 0 + 0*q**3. Suppose b(f) = 0. Calculate f.
0, 2/9, 2
Suppose -5*g - 2*i - 10 = 0, 0 = 2*g - 4*i - 6 - 14. Let y(w) be the second derivative of g*w**2 + 0 - w + 1/33*w**3 + 2/33*w**4. Determine r so that y(r) = 0.
-1/4, 0
Let i(w) be the first derivative of -900*w**3 + 3375/2*w**4 - 16*w - 4 + 180*w**2. Factor i(u).
2*(15*u - 2)**3
Factor 4*x**5 - 132*x**2 + 278*x**4 - 38*x**3 + 14*x**3 - 290*x**4 - 56*x - 68*x**3.
4*x*(x - 7)*(x + 1)**2*(x + 2)
Let i(n) be the third derivative of 1/6*n**4 + 0 + 0*n - 2/3*n**3 - 1/60*n**5 - 6*n**2. Determine l so that i(l) = 0.
2
Let n = -1783 + 90929/51. Let x = n - -67/204. Factor -x*w**3 + 1/4*w - 1/2 + 1/2*w**2.
-(w - 2)*(w - 1)*(w + 1)/4
Let w be ((-50)/70 - -1)*35. Factor w*o - 1/2*o**4 - 4 - 9*o**2 + 7/2*o**3.
-(o - 2)**3*(o - 1)/2
Let d(a) = -9 + 0*a**3 + 3*a**3 + 8 + 2*a. Let g be d(1). Find b such that 0*b**2 + 7*b**3 - 2*b**3 - 4*b**3 - 4*b**2 + g*b = 0.
0, 2
Let p(m) be the first derivative of m**3/3 - 5*m**2 - 9*m + 10. Let f be p(11). Factor 3/5*u - 3/5*u**f + 0.
-3*u*(u - 1)/5
Suppose 738 = 7*m - 116. Factor 3*w**5 + w**3 - 4*w**3 + 2*w**4 + m*w**2 - 124*w**2.
w**2*(w - 1)*(w + 1)*(3*w + 2)
Let c = -34 - -16. Let k be (-9)/c - (-127)/2. Solve 66 + 2*l - l**3 - k + l = 0.
-1, 2
Let q(r) = -3*r**3 - r**2 - r. Let a be q(-1). Let y be 2 - (-2 + (0 - -1)). Factor -z**4 + a*z**4 + 14*z**2 - 13*z**2 - 6*z**4 + y*z**3.
-z**2*(z - 1)*(4*z + 1)
Let y(n) = 2*n**2 - 10*n + 2. Let o be y(5). Factor 6*b**2 - 2*b**3 + 0*b**4 + 10*b**3 + o*b**4.
2*b**2*(b + 1)*(b + 3)
Let m = -43995 - -43997. Suppose 12/7*k**4 + 16/7 + 4/7*k**3 - 4*k**m - 4/7*k**5 + 0*k = 0. Calculate k.
-1, 1, 2
Let u(v) = 316*v - 5996. Let y be u(19). Factor 4/5*t**2 + y*t + 20.
4*(t + 5)**2/5
Suppose -h = -0*h - 3, -4*t - 5*h = -35. Let g be ((-12)/30)/(4/(-15)). Factor 0 + 0*x + g*x**3 + 1/2*x**2 + 3/2*x**4 + 1/2*x**t.
x**2*(x + 1)**3/2
Let -144/5 + 14/5*d**3 - 1/5*d**4 + 168/5*d - 73/5*d**2 = 0. Calculate d.
3, 4
Let r(h) be the second derivative of 1/25*h**6 + 7/5*h**2 + 19/15*h**4 - 1/105*h**7 + 9/5*h**3 + 0 + 16*h + 11/25*h**5. Find u such that r(u) = 0.
-1, 7
Let k(u) = -6*u**2 - 167*u - 1003. Let s(w) = -708 - 36*w**2 + 33*w**2 + 207 - 84*w. Let q(g) = 6*k(g) - 11*s(g). Find y such that q(y) = 0.
-13
Let y(b) be the third derivative of -1/210*b**5 - 1/2205*b**7 + 0 - 1/315*b**6 + 4/63*b**3 + 0*b + 1/63*b**4 + 27*b**2. What is k in y(k) = 0?
-2, -1, 1
Let g(k) be the first derivative of 0*k + 1/6*k**3 + 3 - 1/10*k**5 + 0*k**2 - 1/16*k**4 + 1/24*k**6. Factor g(u).
u**2*(u - 2)*(u - 1)*(u + 1)/4
Let i(g) be the second derivative of -g**4/4 + 2*g**3 + 18*g**2 + 424*g. Factor i(z).
-3*(z - 6)*(z + 2)
Let y(n) be the second derivative of -n**6/45 - n**5/5 - 2*n**4/9 + 2*n**3/3 + 5*n**2/3 + 16*n - 4. Solve y(a) = 0.
-5, -1, 1
Let w(i) = -103*i**2 - 824*i. Let h be w(-8). Factor -1/2*r + h + r**2 - 1/2*r**3.
-r*(r - 1)**2/2
Let w(n) = -3*n - 7. Let r be w(-4). Let -4 + 5*b**3 + 14 + 5*b**4 - r*b - 10*b**2 + 0*b**3 - 5*b**2 = 0. Calculate b.
-2, -1, 1
Let l = -11 + 14. Factor l*s**4 + s**4 + s**3 + 7*s**5 - 8*s**5 - 5*s**3.
-s**3*(s - 2)**2
Factor 2*h**2 - 291*h**3 + 289*h**3 + 8*h + 4*h**2.
-2*h*(h - 4)*(h + 1)
Let n(j) be the first derivative of -5*j**4/24 - 5*j**3/9 + 5*j**2/4 - 40. Suppose n(v) = 0. Calculate v.
-3, 0, 1
Suppose 2*h = 5*f - 14, 2*h - 4*f + 1 = -3*h. Factor -2*s**h - 2*s**5 - 2*s**5 + 6*s**3.
-4*s**3*(s - 1)*(s + 1)
Let h(v) be the first derivative of v**5/360 - v**4/48 - 15*v**2/2 + 7. Let t(d) be the second derivative of h(d). Solve t(f) = 0 for f.
0, 3
Determine j, given that -3/2*j + 0*j**2 - 1 + 1/2*j**3 = 0.
-1, 2
Let o(u) = 2*u**2 - 5*u - 22. Let j be o(-3). Determine i so that -8*i**4 - 38*i**5 + 34*i**5 - 16*i**2 - j*i**3 + 39*i**3 = 0.
-4, 0, 1
Let f(n) be the third derivative of -n**8/840 + n**7/175 - n**6/100 + n**5/150 - 4*n**3 + 30*n**2. Let r(p) be the first derivative of f(p). Solve r(a) = 0.
0, 2/5, 1
Let q(a) be the third derivative of a**7/1470 + 3*a**6/280 + a**5/60 - 3*a**4/56 - 4*a**3/21 - a**2 - 22*a. Suppose q(m) = 0. What is m?
-8, -1, 1
Let p(s) be the first derivative of 0*s - 9 + 2*s**2 + 4/3*s**3. Solve p(i) = 0.
-1, 0
Factor -23968*g - 15*g**4 - 140*g**3 + 23968*g + 5*g**5.
5*g**3*(g - 7)*(g + 4)
Let q = 131 + -67. Find j, given that 0*j - q*j**5 + 22*j**4 - 32*j**2 + 60*j**3 + 7*j + 10*j**4 - 3*j = 0.
-1, 0, 1/4, 1
Let c(o) = -102*o - 1323. Let v be c(-13). Let g(a) be the first derivative of 0*a - 12 - 1/6*a**2 + 1/6*a**4 + 0*a**5 + 0*a**v - 1/18*a**6. Factor g(l).
-l*(l - 1)**2*(l + 1)**2/3
Suppose -4*x - 8 + 20 = 0. Suppose 7*p - p - 5*p**x - p = 0. Calculate p.
-1, 0, 1
Let u be (2*2/40)/(72/180). Let c(o) be the first derivative of 1 + 1/24*o**3 + 1/16*o**2 - u*o. Let c(y) = 0. Calculate y.
-2, 1
Let v(i) be the second derivative of -i**6/20 - 3*i**5/80 + i**4/16 + i + 220. Factor v(a).
-3*a**2*(a + 1)*(2*a - 1)/4
Let p be -6 - (-4 - 6) - 31/(3689/420). Find m, given that 2/17*m**3 + 0 + 6/17*m - p*m**2 = 0.
0, 1, 3
Let o = 45127 - 496391/11. Suppose 4/11 - 2/11*f - o*f**2 + 2/11*f**4 + 2/11*f**3 = 0. What is f?
-2, -1, 1
Suppose -3*i - 4*z = -2*i - 21, 3*i + 17 = 4*z. Suppose -5*j + 24 = -i. Factor 3*s + 10 - 2*s**2 - 10 + j*s**2.
3*s*(s + 1)
Suppose -4*w = -z + 7, 2*z + z + 3*w - 6 = 0. Let s(k) be the third derivative of 3*k**2 + k**4 + 0 + 0*k - 2/3*k**z - 1/3*k**5. Factor s(f).
-4*(f - 1)*(5*f - 1)
Let p(l) = -2 + 3 - 2*l**2 + 3*l**2. Let r be 3*((-28)/7)/12. Let f(v) = -6*v**2 - 3*v - 3. Let k(g) = r*f(g) - 3*p(g). Let k(w) = 0. What is w?
-1, 0
Let n(h) = h**3 + 33*h**2 - 108*h + 2. Let t be n(-36). Determine g so that -2/3*g**t - 8/3 - 8/3*g = 0.
-2
Let z(a) = -8*a**5 + 125*a**4 + 3375*a**3 + 43940*a**2 + 285615*a + 742576. Let l(d) = -2*d**5 - d**4 - d**3 + d - 2. Let m(n) = -5*l(n) + z(n). Factor m(t).
2*(t + 13)**5
Let j(r) be the first derivative of 16/3*r**3 + 2*r + 8 - 9/2*r**2 - 1/6*r**6 - 7/2*r**4 + 6/5*r**5. 