- 320. Let l be r(5). Factor -1/5*t**l + 0 + 2/5*t**2 + 0*t**3 - 2/5*t**4 + 1/5*t.
-t*(t - 1)*(t + 1)**3/5
Suppose 4*z = -3*y - 11, -3*z + 0 = 15. Suppose 2*d + 6 = y*d. Solve -3*r**2 - 3*r**2 - 4 + 5*r**2 - d*r - r**2 = 0.
-2, -1
Suppose 18 = -2*m - 3*v, 0 = -2*m + 5*v - v - 18. Let u be (1 - -1) + ((-60)/m - 6). Find r such that -1/3*r**4 - u - 7/3*r**3 - 20/3*r - 6*r**2 = 0.
-2, -1
Let f be (-6)/1 - -11 - (-3 + 4). Let g(h) be the first derivative of -4*h - 20/3*h**3 - 5 - 12*h**2 + 12*h**f. Solve g(w) = 0 for w.
-1/3, -1/4, 1
Let v(l) = -l**3 - 2*l**2 + 8*l + 11. Let p be v(-3). Let o be (-12*(-2)/(-4))/(15/p). Factor 16/5 - o*a + 2/5*a**5 - 4*a**2 + 8/5*a**4 + 2/5*a**3.
2*(a - 1)**2*(a + 2)**3/5
Let h(g) = 5*g**5 + 10*g**4 + 95*g**3 + 80*g**2 - 330*g - 400. Let p(i) = 2*i**5 + i**4 - i**3 - 2*i. Let c(w) = h(w) - 5*p(w). Factor c(z).
-5*(z - 5)*(z - 2)*(z + 2)**3
Suppose -15 = -6*d - 8*d + 11*d. Let c = -26/3 + 9. Solve h**3 + 0 + h**4 + 0*h + 1/3*h**2 + c*h**d = 0.
-1, 0
Let b = 7/194 + 615/4462. Let u = b + 26/115. Find n, given that -2/5*n + 0*n**3 + u*n**5 + 4/5*n**2 + 0 - 4/5*n**4 = 0.
-1, 0, 1
Let x be (10 - (-196)/(-21))*9. Let l(c) be the second derivative of 0*c**2 + 1/30*c**4 + 1/50*c**5 - 1/75*c**6 + 0 - 1/105*c**7 + x*c + 0*c**3. Factor l(r).
-2*r**2*(r - 1)*(r + 1)**2/5
Factor -4/3*n**2 + 20/3 + 16/3*n.
-4*(n - 5)*(n + 1)/3
Let k be ((-8)/4 + 0)*53/(-2). Let 25 + k - 45*i + 10*i**3 - 13*i**3 - 3 - 27*i**2 = 0. What is i?
-5, 1
Let u be (-2)/(-33)*3 - ((-7100)/275 - -23). Factor -32/5*y**5 + 0*y**2 + 0*y - 16/5*y**4 + 0 - 2/5*y**u.
-2*y**3*(4*y + 1)**2/5
Suppose -24 = 2*u - 7*u - m, u - 4*m + 12 = 0. Find t, given that -2*t**3 - 278*t**2 + 283*t**2 - 10*t**u - 3*t**3 = 0.
-1, 0, 1/2
Let f(o) be the second derivative of -o**4/9 + 4*o**3/9 + 16*o**2 + o - 65. Determine h so that f(h) = 0.
-4, 6
Suppose -t - 2*t = 2*w + 43, 3*t = 4*w + 95. Let m = 29 + w. Determine f so that 4*f + f**3 - m*f**3 + f**3 = 0.
-1, 0, 1
Let a be (-6 - -4 - -6)/(6*1). Let u(g) be the first derivative of a*g**3 + 3 - g**2 - 4*g. Factor u(i).
2*(i - 2)*(i + 1)
Let k(h) = -5*h - 1. Let y be k(-1). Suppose -5 = -2*c + 3*c, 2*s - y*c = 68. Solve -3*j**3 + 2*j**3 - s*j + 9*j**2 + 0*j**3 + 16 = 0.
1, 4
Let v be ((-78)/5)/(14/20 - 1). Let z be (v/11)/(-2) + 4. Find u, given that 4/11*u**3 + z*u**4 + 0 + 0*u + 14/11*u**5 + 0*u**2 = 0.
-1, -2/7, 0
Factor -3*h**4 + 33*h**2 - 8*h**3 - 4*h**3 - 29 + 36*h + 6*h**3 + 29.
-3*h*(h - 3)*(h + 1)*(h + 4)
Let a(j) be the second derivative of -j**5/10 + 17*j**4/24 - 4*j**3/3 + 3*j**2/4 + 519*j. Factor a(p).
-(p - 3)*(p - 1)*(4*p - 1)/2
Factor 148/3*q**2 + 0 + 4/3*q**4 - 24*q - 80/3*q**3.
4*q*(q - 18)*(q - 1)**2/3
Let s(t) = -4*t - 3. Let l be s(-2). Let f be (l + 903/(-182))/((-1)/(-12)). Factor 2/13*z**2 + 8/13*z + f.
2*(z + 1)*(z + 3)/13
Let m be ((-10)/(-25))/(40/300). Factor 11*v**2 + 10/3*v - 7/3*v**m + 0.
-v*(v - 5)*(7*v + 2)/3
Let c(n) be the first derivative of 1/4*n**2 + 1/4*n + 5 - 1/4*n**3. Factor c(m).
-(m - 1)*(3*m + 1)/4
Let t(d) be the first derivative of -d**4/4 - 2*d**3/3 + d**2 + 8. Let q be t(0). Find x, given that 0*x - 6/7*x**4 - 2/7*x**5 + 0*x**2 + q - 4/7*x**3 = 0.
-2, -1, 0
Let k(y) be the first derivative of y**5/4 + 5*y**4/12 - 5*y**3/6 - 5*y**2/2 - 32*y - 5. Let c(l) be the first derivative of k(l). Factor c(x).
5*(x - 1)*(x + 1)**2
Suppose -2*q + 2*t = -24, -5*t + 75 = 5*q - 25. Suppose 2*c - q = -5*p, p + 5*c = -p + 19. Factor 4*u**p + 0*u**3 - 7*u**2 - 2 + u**3 - u - u**4 + 6*u**2.
-(u - 2)*(u - 1)*(u + 1)**2
Let d(v) be the second derivative of -1/540*v**6 + 2/3*v**3 + 0 - 1/90*v**5 + 0*v**2 - 4*v - 1/36*v**4. Let j(s) be the second derivative of d(s). Factor j(r).
-2*(r + 1)**2/3
Let q be (-2)/(-56) + 10/16*150/375. Factor -q*w + 0 + 4/7*w**2 - 2/7*w**3.
-2*w*(w - 1)**2/7
Suppose -4*z = -3*f - 15, -620*f - 18 = -618*f - 4*z. Let -3/4*u**4 + 3/2*u**2 + f*u**5 + 3*u - 3/4 - 6*u**3 = 0. What is u?
-1, 1/4, 1
Let z(n) be the first derivative of -n**3/9 + 31*n**2/6 - 58*n/3 + 22. Factor z(o).
-(o - 29)*(o - 2)/3
Suppose 0 = 2*v - 0*c - c - 2, 4*c - 8 = 0. Determine w so that 36 - 79 - w**v + 42 - 2*w = 0.
-1
Factor 0 - 3/4*r**4 + 3/8*r**5 + 0*r + 3*r**2 - 3/2*r**3.
3*r**2*(r - 2)**2*(r + 2)/8
Let b be 2/((-16)/(-32)*(-4)/(-6)). Suppose -b = 3*j - 3*a, j - 20 = -3*j - 3*a. Factor 6/7*x**j + 0 - 4/7*x.
2*x*(3*x - 2)/7
Let n be ((-6)/9)/((-18)/135). Let u(k) be the second derivative of 0*k**2 - n*k + 1/30*k**6 + 7/36*k**4 - 1/9*k**3 + 0 - 2/15*k**5. Find h such that u(h) = 0.
0, 2/3, 1
Let w(b) be the first derivative of 4*b**2 + 1 - 8/3*b**3 + 0*b + 4/5*b**5 + 1/3*b**6 - 3/2*b**4. Factor w(t).
2*t*(t - 1)**2*(t + 2)**2
Let k(c) be the third derivative of c**5/90 - 47*c**4/12 - 142*c**3/9 + 408*c**2. Factor k(z).
2*(z - 142)*(z + 1)/3
Suppose -1310*j - 357 = -1429*j. Let -b + 1/2*b**j + 7/4*b**2 + 0 = 0. What is b?
-4, 0, 1/2
Let b be (1/((-15)/9))/((-78)/20). Solve 0 + 2/13*q - 4/13*q**2 + b*q**3 = 0.
0, 1
Let x(f) be the third derivative of -f**5/150 - 47*f**4/180 + 16*f**3/45 + 149*f**2. Find a, given that x(a) = 0.
-16, 1/3
Let y(x) be the third derivative of 0*x - 1/42*x**7 - 10*x**2 + 1/20*x**5 + 0 + 7/120*x**6 - 7/24*x**4 + 1/3*x**3. Determine p, given that y(p) = 0.
-1, 2/5, 1
Let h = 194 - 192. Let c(g) be the first derivative of 3/17*g**h + 2/51*g**3 + 4/17*g - 10. Suppose c(m) = 0. Calculate m.
-2, -1
Let 134/7*u - 4489/7 - 1/7*u**2 = 0. Calculate u.
67
Factor -23104/5 - 4/5*v**2 - 608/5*v.
-4*(v + 76)**2/5
Let c(h) = -2*h - 4. Let q be c(-4). Suppose -2*n - 1 + 171*n**4 + n**3 + n**5 + 1 + 3*n**2 - 174*n**q = 0. What is n?
-1, 0, 1, 2
Suppose -6*g - 10 = -22. Factor g*f**3 - 550 - 6*f**3 + 510 + 76*f - 32*f**2.
-4*(f - 1)**2*(f + 10)
Let v(g) be the second derivative of g**6/10 + 3*g**5 - 33*g**4/2 + 34*g**3 - 69*g**2/2 + 323*g. What is d in v(d) = 0?
-23, 1
Let d = 301/9 - 33. Let z(f) be the first derivative of -d*f**3 + 2/15*f**5 - 1/3*f**2 - 1/9*f**6 + 2 + 1/3*f**4 + 2/3*f. Solve z(c) = 0 for c.
-1, 1
Let h = 165 + -108. Suppose h*p - 62*p = 0. Find m such that 4/7*m**2 + p + 0*m**3 + 2/7*m**5 - 4/7*m**4 - 2/7*m = 0.
-1, 0, 1
Let t(r) = 2*r**2 - r + 5. Let b(g) = 42*g**2 + 93*g + 31. Let p(n) = b(n) - 5*t(n). Factor p(z).
2*(z + 3)*(16*z + 1)
Let i(j) be the second derivative of 7/54*j**4 + 11/90*j**5 - 40*j + 0*j**2 - 7/135*j**6 - 5/189*j**7 - 2/9*j**3 + 0. Determine l, given that i(l) = 0.
-2, -1, 0, 3/5, 1
Suppose 2*b - 4*h - 4 = 0, -4*h = -3*h. Suppose 20 = 6*k - b*k. Solve -63*j**3 + 66*j**3 + k*j - 5*j = 0 for j.
0
Let s(g) = 6*g**3 + 9*g**2 + 41*g - 41. Let d(x) = 2*x**3 + x**2 + x - 1. Let u(r) = 5*d(r) - s(r). Solve u(c) = 0 for c.
-3, 1, 3
Let z(a) = -a**3 + 7*a**2 + 4*a + 4. Let m be z(7). Factor 20*t**3 - 37 + 5*t**2 + 2*t - 22*t + m.
5*(t - 1)*(t + 1)*(4*t + 1)
Let i(b) be the third derivative of b**5/30 - 7*b**4/12 - 59*b**2 - 5*b. Factor i(n).
2*n*(n - 7)
Let x(u) = 11*u**4 - 6*u**3 - 11*u**2 + 6*u. Let a(g) be the first derivative of g**4/4 - g**2/2 + 1. Let d(t) = 4*a(t) + x(t). Factor d(v).
v*(v - 1)*(v + 1)*(11*v - 2)
Suppose -l = l + 2*f, 5*l - 3*f = 8. Solve 7 - 5*j**3 + 5*j - 1 - 5*j**2 - l = 0.
-1, 1
Let 0*f - 200/3*f**3 + 0 + 2500*f**2 + 4/9*f**4 = 0. What is f?
0, 75
Let n(i) = -i + 4. Let v be n(2). Factor v - s**4 - 2*s + 2*s**3 + 3 - 4.
-(s - 1)**3*(s + 1)
Let j(h) = -h**3 + 1. Let n(s) = -2*s**3 - 20*s**2 - 21*s + 4. Let u(m) = -6*j(m) + 2*n(m). Let d be u(21). Solve 2/3*w - 1/3*w**d + 1 = 0.
-1, 3
Let m(u) be the first derivative of u**6/80 - 3*u**5/40 + 3*u**4/16 - u**3/4 - 10*u**2 + 28. Let x(y) be the second derivative of m(y). Solve x(z) = 0 for z.
1
Let b be (4/(-8))/((1/1)/(-20)). Find m such that 70*m**3 - 30*m**4 + 2*m - 80*m**2 - b + 2*m**5 + 23*m + 20*m + 3*m**5 = 0.
1, 2
Let l be (60/(-50))/((-2)/5). Let p(x) be the first derivative of -6 + 1/3*x**l + 1/4*x**2 - 1/2*x. What is b in p(b) = 0?
-1, 1/2
Factor 258*k**3 - 156*k - 532*k**3 + 620*k**2 + 290*k**3.
4*k*(k + 39)*(4*k - 1)
Let h = -88 + 88. Let o be h*(57/(-152) - (-2)/(-16)). Factor 3/4*g**3 + 0 + o*g + 1/2*g**2 + 1/4*g**4.
g**2*(g + 1)*(g + 2)/4
Let j(q) be the third derivative of q**6/280 + q**5/140 - 17*q**4/56 + 15*q**3/14 - 15*q**2 - 2*q. Suppose j(o) = 0. Calculate o.
-5, 1, 3