 1)**2/2
Let s = -1973/105 + 299/15. Find t, given that -s*t**3 + 2/7*t + 2/7*t**2 + t**4 - 2/7*t**5 - 1/7 = 0.
-1/2, 1
Let y(b) be the third derivative of -b**5/30 + 21*b**4/2 - 1323*b**3 - 170*b**2. Factor y(j).
-2*(j - 63)**2
Let l(m) = -4*m**3 - m**2 - 2*m - 1. Let d(k) = k**2 - k - 1. Let z(s) = -2*d(s) + l(s). Let b be z(-2). Factor 0 - 21*y**2 + b*y - 9*y**3 - 7 + 16.
-3*(y - 1)*(y + 3)*(3*y + 1)
Let s = 17606 + -17606. Solve s + 2/5*j**3 + 1/5*j**2 + 0*j + 1/5*j**4 = 0.
-1, 0
Let c = 287 - 66. Suppose -2*u + 4*p + 42 = -32, c = 5*u + 2*p. Solve -37 - 13*n**2 + 40*n + 8*n**2 - u = 0 for n.
4
Factor 21/5*y + 24/5 - 3/5*y**2.
-3*(y - 8)*(y + 1)/5
Let n = -192 - -192. Let j(i) be the second derivative of -2*i - 1/15*i**5 - 8/3*i**2 + 1/9*i**4 + 8/9*i**3 + n. Factor j(y).
-4*(y - 2)*(y - 1)*(y + 2)/3
Suppose 31*b - 10 = 27*b - 5*f, 4*b + 4 = 2*f. Let -2/11 + b*h**2 + 4/11*h + 2/11*h**4 - 4/11*h**3 = 0. Calculate h.
-1, 1
Factor -39 - 331 - 30 - h**2 - 40*h.
-(h + 20)**2
Let r be (-2)/(5 - 6) - 18/10. Let h(j) be the second derivative of 0*j**4 + 1/14*j**7 + 3/20*j**5 + r*j**6 + 6*j + 0*j**3 + 0 + 0*j**2. Solve h(x) = 0.
-1, 0
Let b(f) = 3*f**2 + 198*f - 3078. Let r(i) = 2*i**2 + 197*i - 3077. Let y(c) = -5*b(c) + 6*r(c). Solve y(o) = 0.
32
Let b(j) be the first derivative of j**8/5040 - j**7/1260 - j**6/360 - 19*j**3/3 - 29. Let l(c) be the third derivative of b(c). Suppose l(v) = 0. What is v?
-1, 0, 3
Suppose -12 = -4*v - 4*h, -2*h - 9 = 3*v - 18. Determine r, given that 3/10*r**2 + 1/10 - 1/10*r**v - 3/10*r = 0.
1
Let p(f) be the first derivative of -f**8/12 - 6*f**7/35 - f**6/15 - 13*f**2/2 + 6. Let z(k) be the second derivative of p(k). Factor z(h).
-4*h**3*(h + 1)*(7*h + 2)
Let g = -125529/5 - -25113. Factor -3/5*n**4 - g*n**3 - 138/5*n**2 - 15 - 36*n.
-3*(n + 1)**2*(n + 5)**2/5
Determine z so that 1/2*z**4 + 2*z + 0 - 2*z**3 - 1/2*z**2 = 0.
-1, 0, 1, 4
Let m = 42 + -37. Let f(k) = -80*k**4 + 32*k**3 + 68*k**2 - 8*k. Let w(a) = -32*a**4 + 13*a**3 + 27*a**2 - 3*a. Let y(c) = m*f(c) - 12*w(c). Factor y(q).
-4*q*(q - 1)*(q + 1)*(4*q - 1)
Factor -35*z + 2*z + 75 + 5*z**2 - 7*z.
5*(z - 5)*(z - 3)
Let o(b) be the second derivative of -b**6/165 + 3*b**5/22 + b**4/2 + 17*b**3/33 + 137*b. Find s such that o(s) = 0.
-1, 0, 17
Let a(y) = y**2 + 46. Let o be a(0). Suppose -3*g + o = 34. Factor 0 + 52/7*w**2 + 108/7*w**3 + 8/7*w + g*w**5 + 92/7*w**4.
4*w*(w + 1)**3*(7*w + 2)/7
Let t be (-4)/(-3)*(182/(-78))/((-70)/30). Factor 2/9*k**2 + 10/9 + t*k.
2*(k + 1)*(k + 5)/9
Find u, given that -20 - 111*u**3 - 112*u**3 + 0 - 28*u**2 + 219*u**3 - 44*u = 0.
-5, -1
Let v(r) be the third derivative of 1/280*r**8 + 25*r**2 + 1/50*r**6 + 0 + 2/25*r**5 - 3/20*r**4 + 0*r**3 - 4/175*r**7 + 0*r. Determine w so that v(w) = 0.
-1, 0, 1, 3
Let y(a) = -11*a - 112. Let j(i) = 6*i + 56. Let g(m) = -5*j(m) - 3*y(m). Let d be g(-17). Factor 4/5*z**d + 0*z + 2/5*z**4 + 0*z**2 - 2/5*z**3 + 0.
2*z**3*(z + 1)*(2*z - 1)/5
Suppose 0 = -n + 3*q - 22 + 7, n + q = 5. Let m(t) be the third derivative of -8*t**2 + t**3 - 1/8*t**4 + n + 0*t - 1/20*t**5. Solve m(l) = 0 for l.
-2, 1
Let c(o) be the second derivative of -o**5/70 + 5*o**4/42 - 2*o**3/7 + 2*o - 16. Factor c(i).
-2*i*(i - 3)*(i - 2)/7
Let q(m) be the third derivative of m**7/1260 - m**6/360 + m**4/4 - 5*m**2. Let w(j) be the second derivative of q(j). Factor w(t).
2*t*(t - 1)
Let p(h) be the first derivative of h**5 + 5*h**4/4 + 5*h + 7. Let v(x) = x**3 + x**2 - 1. Let a(n) = p(n) + 5*v(n). Factor a(d).
5*d**2*(d + 1)**2
Let y(g) be the third derivative of 1/16*g**4 + 12*g**2 - 3/8*g**3 + 1/80*g**5 + 0*g + 0. Suppose y(d) = 0. Calculate d.
-3, 1
Let a(i) = 4*i**3 - 3*i**2 + 5*i - 3. Let q be a(1). Let -19/3*o**2 + 7/3*o**q + 4/3 + 8/3*o = 0. What is o?
-2/7, 1, 2
Let -16/3*u + 0 + 56*u**3 - 37/3*u**4 - 20/3*u**5 - 20/3*u**2 = 0. What is u?
-4, -1/4, 0, 2/5, 2
Let v(f) = f**4 + 7*f**3 + 2*f**2 - 2*f. Let z(u) = 6*u**4 + 36*u**3 + 11*u**2 - 11*u. Let d(b) = 33*v(b) - 6*z(b). Determine x, given that d(x) = 0.
0, 5
Let t(o) be the first derivative of o**6/36 - o**4/8 + o**3/9 + 49. Suppose t(d) = 0. What is d?
-2, 0, 1
Let i(t) be the third derivative of -t**8/672 + t**7/42 - 11*t**6/80 + 3*t**5/10 + 47*t**2. Factor i(y).
-y**2*(y - 4)*(y - 3)**2/2
Let c be 192/27 + -16 + 9. Factor 2/9 + 0*z**2 + 1/3*z - c*z**3.
-(z - 2)*(z + 1)**2/9
Suppose -2*z + 21 = -d + 15, 4*z - 6 = -d. Let a(f) be the first derivative of -3*f + z*f**3 + 3 - 5/8*f**4 + 11/4*f**2. Factor a(h).
-(h - 3)*(h + 1)*(5*h - 2)/2
Let z(p) = -21*p + 175. Let u be z(8). Let i(w) be the third derivative of 0*w**3 + u*w**2 - 1/60*w**5 - 1/48*w**4 + 0*w + 0 - 1/240*w**6. Factor i(h).
-h*(h + 1)**2/2
Let h be 88/(-20) + 1 + (3 - 26/(-13)). Let 4/5*g**4 - 6/5*g**3 + 0 + 2/5*g**5 + 8/5*g - h*g**2 = 0. What is g?
-2, 0, 1
Factor -55/2*b + 14 + 13*b**2 + 1/2*b**3.
(b - 1)**2*(b + 28)/2
Let l(v) be the second derivative of v**7/189 - v**6/27 - v**5/90 + 5*v**4/54 - v + 36. Suppose l(d) = 0. Calculate d.
-1, 0, 1, 5
Let t(q) be the third derivative of -q**8/1512 + q**6/270 - q**4/108 - q**2 - 220. What is f in t(f) = 0?
-1, 0, 1
Let v = 905/6 - 68789/456. Let u = v + 471/760. Factor 3/5*l**2 - 6/5*l + u.
3*(l - 1)**2/5
Let k(j) be the second derivative of 17/40*j**5 + 20*j - 9*j**2 - 14/15*j**6 + 4/21*j**7 - 2*j**3 + 0 + 83/24*j**4. Let k(c) = 0. What is c?
-3/4, 1, 2
Let i(l) = 7*l**2 - l - 9. Let b be i(3). Solve -u**4 + 2*u**3 + b*u - 51*u - u**2 = 0.
0, 1
Factor 20*d**4 + 16 - 31*d**4 - 16*d**2 + 14*d**4 + d**5 - 4*d**3.
(d - 2)*(d - 1)*(d + 2)**3
Let 26/19*j + 2/19*j**2 + 0 = 0. Calculate j.
-13, 0
Let n be (-2 + 2)/(-2*(0 + 1)). Let l(q) be the first derivative of -7 + n*q + 4/15*q**3 + 6/5*q**5 + 0*q**2 + 11/10*q**4. Factor l(k).
2*k**2*(3*k + 1)*(5*k + 2)/5
Let x(n) be the second derivative of 0*n**3 + 0*n**2 + 0 - 13*n + 1/4*n**5 + 0*n**4 + 5/42*n**7 + 1/3*n**6. Factor x(r).
5*r**3*(r + 1)**2
Let v(n) be the third derivative of -n**9/2352 + n**8/490 - 3*n**7/980 + n**5/280 - 8*n**3/3 + 12*n**2. Let p(m) be the first derivative of v(m). Factor p(c).
-3*c*(c - 1)**3*(3*c + 1)/7
Factor 2/3*q + 1/2 + 1/6*q**2.
(q + 1)*(q + 3)/6
Suppose -10*i = -14*i + 8. Suppose -r = i*s - 6, 0 = -s + 2*r - 2. Find a, given that 0*a + 2/7*a**s + 0 = 0.
0
Let j(h) be the third derivative of 1/140*h**5 + 0*h + 1/14*h**3 + 0 + 12*h**2 - 1/28*h**4. Factor j(u).
3*(u - 1)**2/7
Determine k, given that 3/2*k**2 - 45/2 - 3*k = 0.
-3, 5
Let x(c) be the third derivative of c**7/105 + c**6/20 - c**5/30 - c**4/4 + 210*c**2. Find w such that x(w) = 0.
-3, -1, 0, 1
Let b(l) = -2*l**2 - 3*l. Let y(z) = -z. Suppose -3*r - 3 + 0 = 0. Let c(a) = r*b(a) + 3*y(a). Let c(u) = 0. Calculate u.
0
Let d be 22/6 - 20/(-15). Factor -d*n - 13*n**2 + 2 + 19*n**2 - 3*n**2.
(n - 1)*(3*n - 2)
Suppose 0*m - 8 = -m + 5*z, 20 = 5*m - 5*z. What is i in -3*i**2 + i**3 + 0*i**3 - i**m - 3*i**3 = 0?
-1, 0
Factor 17672*h - 2*h**2 - 17471*h - h**2.
-3*h*(h - 67)
Let q(r) be the third derivative of r**5/240 + r**4/24 - r**3/2 + 2*r**2 + 19*r. Factor q(v).
(v - 2)*(v + 6)/4
Let r(m) be the third derivative of m**6/120 - 11*m**5/60 + 11*m**4/24 - 5*m**3/3 - 35*m**2. Let l be r(10). Factor 2/9*x**4 + 0*x**2 + 0*x + 2/9*x**3 + l.
2*x**3*(x + 1)/9
Let -32/13*b + 2/13*b**2 - 72/13 = 0. What is b?
-2, 18
Find j, given that 1/4*j**2 + 33/4 - 7/2*j = 0.
3, 11
Factor -1 + 1/5*w**2 - 4/5*w.
(w - 5)*(w + 1)/5
Let q(f) = -f**2 + 11*f + 16. Let w be q(12). Factor 8*j**2 + w*j**5 + 8*j**4 - 12*j**2 + 4*j**2 + 4*j**3.
4*j**3*(j + 1)**2
Suppose 30*n = 12*n. Factor -3/7*f**4 + 0 + n*f + 0*f**3 + 0*f**2.
-3*f**4/7
Factor 0 - 5/2*h**2 - 275/2*h.
-5*h*(h + 55)/2
Let h(g) = 20*g**4 - 4*g**3 + 26*g**2. Let s(o) = -7*o**4 + o**3 - 9*o**2. Let v(t) = 5*h(t) + 14*s(t). What is j in v(j) = 0?
0, 1, 2
Let z(f) be the third derivative of 1/240*f**5 + 0*f - 1/96*f**4 + 7*f**2 + 0 + 0*f**3. Factor z(d).
d*(d - 1)/4
Let o = 52/103 + 50/309. Let f = -2/69 - -94/69. Find y, given that -2/3*y + f - o*y**2 = 0.
-2, 1
Let c(z) be the first derivative of -4/5*z**5 - 11 - 12*z**3 + 5*z**4 - 8*z + 14*z**2. Solve c(l) = 0 for l.
1, 2
Let p(s) be the first derivative of 0*s - 17 - 1/3*s**2 - 2/15*s**5 + 2/9*s**3 + 1/6*s**4. Factor p(r).
-2*r*(r - 1)**2*(r + 1)/3
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