-1). Factor j**b - 16/7*j**2 + 6/7 - 17/7*j.
(j - 3)*(j + 1)*(7*j - 2)/7
Let k = 1363/91 + -191/13. Factor 0*f**2 + 0 + k*f**3 - 8/7*f.
2*f*(f - 2)*(f + 2)/7
Let w(a) = -2*a**4 - 6*a**3 - 8*a**2 + 4*a - 8. Let d(l) = -4*l**4 - 12*l**3 - 15*l**2 + 7*l - 14. Let j(o) = -4*d(o) + 7*w(o). Let j(k) = 0. Calculate k.
-2, -1, 0
Solve -1248/5*y - 129792/5 - 3/5*y**2 = 0.
-208
Let b(l) be the first derivative of 9*l**6/14 - 6*l**5/35 - 135*l**4/28 + 10*l**3/7 + 54*l**2/7 - 24*l/7 + 4. Find z such that b(z) = 0.
-2, -1, 2/9, 1, 2
Let w(r) be the third derivative of r**7/1365 - 2*r**6/195 + 23*r**5/390 - 7*r**4/39 + 4*r**3/13 + 99*r**2. Let w(f) = 0. What is f?
1, 2, 3
Let -1/6*m**2 - 4489/6 + 67/3*m = 0. Calculate m.
67
Suppose 5*b - 71 = -56. Let 4*n**3 - b*n**2 + 0 - 36*n**2 + 24 + 5*n**3 + 6*n = 0. Calculate n.
-2/3, 1, 4
Let l = -1/664 - -1333/3320. Find p such that 11/5*p**2 - 21/5*p**4 + 8/5*p**3 + l*p + 0 = 0.
-1/3, -2/7, 0, 1
Let a = 6 - 1. What is x in -117*x + a*x**2 + 101*x + 16 - x**2 = 0?
2
Let l(h) be the second derivative of -h**4/24 + 5*h**3/4 - 11*h**2 + 203*h. Factor l(c).
-(c - 11)*(c - 4)/2
Let x = 1419 - 1411. Let i(z) be the third derivative of 0 + x*z**2 - 1/15*z**5 + 8/3*z**3 + 0*z - 2*z**4 + 1/2*z**6. Suppose i(v) = 0. What is v?
-1, 2/5, 2/3
Let l(p) be the third derivative of -p**5/15 - 5*p**4/3 - 6*p**3 - 41*p**2. Suppose l(b) = 0. Calculate b.
-9, -1
Let x = 2130 + -2127. Let m(z) be the second derivative of -3/4*z**2 + 3/40*z**5 - 1/4*z**x + 0 + z + 1/8*z**4. Factor m(l).
3*(l - 1)*(l + 1)**2/2
Suppose -3*r = 3*y - 6, -8*r = -5*y - 4*r + 28. Let 12*g**2 + 44*g + 0*g**3 - 7*g**3 + 24 - 4*g**4 + y*g**3 - 9*g**3 = 0. What is g?
-3, -1, 2
Let p(t) = -3*t**2. Let v(m) = m**3 - 11*m**2 - 11*m + 18. Let r(o) = 2*p(o) - 2*v(o). Determine g, given that r(g) = 0.
-2, 1, 9
Let k(t) = -12*t - 15*t**2 - 5 + 12 + 4*t. Suppose 6 = -j - 0. Let p(a) = 8*a**2 + 4*a - 4. Let f(i) = j*k(i) - 11*p(i). Factor f(l).
2*(l + 1)**2
Let c(y) = -2*y**3 - 249*y**2 + 384*y + 758. Let u be c(-126). Find b, given that 1/2*b + 0 + b**u = 0.
-1/2, 0
Let p(s) be the second derivative of -49*s**5/130 + 35*s**4/26 - 24*s**3/13 + 16*s**2/13 + 11*s + 8. Determine q, given that p(q) = 0.
4/7, 1
Let w(l) be the second derivative of l**6/70 - 3*l**4/14 + 4*l**3/7 - 9*l**2/14 - 39*l. Determine g so that w(g) = 0.
-3, 1
Let q(r) be the third derivative of r**7/70 - r**6/8 - 6*r**5/5 - r**4/2 + 16*r**3 - 106*r**2 - r. Factor q(t).
3*(t - 8)*(t - 1)*(t + 2)**2
Let d(u) be the first derivative of -u**3 + 3*u**2/2 + 36*u + 282. Suppose d(a) = 0. Calculate a.
-3, 4
Let -980 + 2*k**2 + 458 + 346*k - 40*k**2 + 486 = 0. Calculate k.
2/19, 9
Suppose 7*b = 4 + 24. Solve 50*x**4 - 53*x**b + 0*x**5 - x**5 + x**3 - 3*x**3 = 0.
-2, -1, 0
Suppose 5*i + 7 = -4*f, 0*i + 4*i + 22 = 5*f. Determine x so that 11*x + 2*x**3 + 2*x**3 + 15*x**f + x**3 - x = 0.
-2, -1, 0
Let y(j) = -3900*j**3 - 9255*j**2 - 3160*j - 300. Let i(c) = -300*c**3 - 712*c**2 - 243*c - 23. Let d(t) = 40*i(t) - 3*y(t). Find w, given that d(w) = 0.
-2, -1/4, -2/15
Let q(j) = j**4 - 8*j**3 + j**2 + 8*j - 7. Let l(n) = -n**3 + n - 1. Let c(s) = -5*l(s) + q(s). Factor c(o).
(o - 2)*(o - 1)**2*(o + 1)
Let m(l) = 15*l**4 - 40*l**3 - 10*l**2 + 35*l. Let s(i) = -i**2 + i. Let q(p) = -m(p) + 25*s(p). Find a, given that q(a) = 0.
-1/3, 0, 1, 2
Let t be 4/(-38) - (-208)/6916*13. Determine h, given that -1/7*h - 1/7*h**5 - 1/7 + 2/7*h**3 - 1/7*h**4 + t*h**2 = 0.
-1, 1
Let b(k) be the first derivative of -k**3 - 30*k**2 + 2. Factor b(c).
-3*c*(c + 20)
Let u(s) be the first derivative of 3*s**4/10 - 43*s**3/5 - 33*s**2/5 + 120. Factor u(t).
3*t*(t - 22)*(2*t + 1)/5
Suppose -15 = 23*w - 84. Factor 0*t + 2/3*t**4 - 1/3*t**w + 1/3*t**5 + 0 - 2/3*t**2.
t**2*(t - 1)*(t + 1)*(t + 2)/3
Let j(c) be the first derivative of -4*c**5/5 + 11*c**4 + 204*c**3 + 1026*c**2 + 2160*c - 289. Let j(b) = 0. Calculate b.
-3, 20
Let d(m) be the second derivative of -m**6/75 - m**5/25 + 3*m**4/10 + 2*m**3/15 - 8*m**2/5 - 595*m. Suppose d(l) = 0. Calculate l.
-4, -1, 1, 2
Let x(o) = o**2 + 2*o + 1. Let u(m) = 8*m**2 + 128*m - 88. Let k(w) = u(w) - 12*x(w). Factor k(q).
-4*(q - 25)*(q - 1)
Let x(f) be the second derivative of 3*f**7/49 - 11*f**6/35 + 13*f**5/70 + 17*f**4/42 - 2*f**3/7 + 157*f. Find a, given that x(a) = 0.
-2/3, 0, 1/3, 1, 3
Suppose 2*s = 5*h - s - 45, -5*s = -5*h + 55. Suppose 5*v - 5*i - 25 = 0, i - 2*i = 2. Factor -4*q**2 - h*q**4 + 7*q**4 - 6*q**4 - 10*q**v - q**4.
-2*q**2*(q + 1)*(3*q + 2)
Let r = 21 - 18. Factor 3*z**r + 3*z**5 - 6*z**5 + 2*z**3 - 2*z**5.
-5*z**3*(z - 1)*(z + 1)
Let x(s) be the third derivative of s**5/40 - 65*s**4/16 - s**2 - s. Factor x(p).
3*p*(p - 65)/2
Suppose -2*p = -3*t + 7*t + 24, 2*t + 30 = -4*p. Let r be (3 + p/4)/3. Factor -1/2*l - 1/2 + r*l**3 + 1/2*l**2.
(l - 1)*(l + 1)**2/2
Let w be 6 + (-16 - -6) + (-138)/(-33). Suppose 3*t = 3*p + 2 + 10, p - 16 = -4*t. Factor 2/11*x**t + w*x**5 + 0*x - 2/11*x**3 + 0 - 2/11*x**2.
2*x**2*(x - 1)*(x + 1)**2/11
Suppose 3*x + 2 = -4*z + 2*z, -20 = 5*z. Let g be x*1 - 156/182. Factor -4/7*o + 0 - g*o**2 - 4/7*o**3.
-4*o*(o + 1)**2/7
Let q(y) be the third derivative of y**8/1176 - 8*y**7/735 + 11*y**6/210 - 4*y**5/35 + 3*y**4/28 + 2*y**2 + 20*y. Suppose q(u) = 0. Calculate u.
0, 1, 3
Let c(f) be the third derivative of f**9/1008 - f**8/80 + 11*f**7/280 - f**6/24 - 4*f**3 + 4*f**2. Let i(t) be the first derivative of c(t). Factor i(h).
3*h**2*(h - 5)*(h - 1)**2
Let n = 54 + -52. Suppose 4*b - 2 = -3*l + 2*l, -b - 4 = -n*l. Suppose 0*x - 1/6*x**3 - 1/6*x**4 + b + 1/6*x**5 + 1/6*x**2 = 0. What is x?
-1, 0, 1
Suppose 3*z - 2*t + 3 = 9, t - 2 = -z. Find h such that -4/3*h**4 - 8/3*h**3 + 0*h - 4/3*h**z + 0 = 0.
-1, 0
Let g = 9 - 6. Suppose -123*c + 8*c**3 + 0*c**2 + 138*c - 3*c**g - 15*c**2 - 5 = 0. What is c?
1
Let d(a) = -2*a**2 - 12*a + 3. Let l be d(-6). Let 3*s**4 + 3*s**2 + 170*s - 158*s - 9*s**l - 3*s**2 = 0. What is s?
-1, 0, 2
Suppose 0 = 5*i - 3 - 7. Suppose -2*z - 3*u + 11 = -0*u, -4*z - i*u + 34 = 0. Factor -3*d**5 - 4*d**2 + 9*d**3 - z*d**2 - 4*d**2 + 6*d + 3*d**2 + 3*d**4.
-3*d*(d - 1)**3*(d + 2)
Let j = -17725/7 - -2533. Factor -j*u - 4/7 + 2/7*u**3 + 0*u**2.
2*(u - 2)*(u + 1)**2/7
Let g(k) be the second derivative of k**4/24 + k**3/4 - 5*k**2/2 + 63*k. What is w in g(w) = 0?
-5, 2
Let 10/3*d**3 + 12*d**2 - 16/3 + 8*d = 0. What is d?
-2, 2/5
Let o be (-7)/(((-12)/(-20))/3). Let b be -5 + -6 + (-415)/o. What is s in 2/7*s**3 + b*s**2 + 6/7*s + 2/7 = 0?
-1
Factor -35378/3 - 532/3*n - 2/3*n**2.
-2*(n + 133)**2/3
Let g(w) be the first derivative of 4*w**3 - 9*w**2/2 + 160. Solve g(k) = 0.
0, 3/4
Let p be ((-9)/(-15) - 0)*(-70)/(-98). Let y(o) be the first derivative of 1 - 1/7*o**3 - 3/14*o**2 + p*o + 3/28*o**4. Find c such that y(c) = 0.
-1, 1
Let u = -6463/2040 - -54/17. Let x(n) be the third derivative of 0*n + 0*n**3 + 0*n**4 + u*n**6 + 0*n**5 - 5*n**2 + 0 + 1/210*n**7. Factor x(k).
k**3*(k + 1)
Suppose -9*y - 47 = -4*k - 10*y, -2*y = -4*k + 38. Suppose 2*p - k*p = p. Factor 1/6*c**3 + 1/6*c**2 + p*c + 0.
c**2*(c + 1)/6
Suppose 2*m = -2*m - m. Suppose m = -3*r + 9 - 9. Let 3/5*n**2 + 0*n + r = 0. Calculate n.
0
Let d = 35262 + -35259. Let 4/3 + 8/3*w - d*w**3 - w**2 = 0. Calculate w.
-2/3, 1
Let j = 8196 + -8194. Find f, given that 1/2*f**j + 3/2*f + 0 = 0.
-3, 0
Let k(q) be the third derivative of q**5/60 - 5*q**4/8 + 7*q**3/3 - 3*q**2 - 5*q. Factor k(j).
(j - 14)*(j - 1)
Let n = -39 + 98. Let f = -117/2 + n. Factor f*x**2 + 1/2*x**4 + 3/2*x**3 - 1 - 3/2*x.
(x - 1)*(x + 1)**2*(x + 2)/2
Let i(z) be the first derivative of -z**5/20 - 8*z**4 - 661*z**3/2 + 1040*z**2 - 4225*z/4 - 457. Let i(c) = 0. What is c?
-65, 1
Let x = -22475/21 + 1069. Let r = -19/21 - x. Factor 0 - 2/3*i - r*i**2.
-i*(i + 2)/3
Suppose 3237 = 21*q + 3174. Solve -q - 3/4*a**2 + 3*a = 0 for a.
2
Let l(b) be the third derivative of -b**5/20 - 97*b**4/4 - 9409*b**3/2 + 352*b**2. Factor l(w).
-3*(w + 97)**2
Let y(x) = -8*x**3 - 88*x**2 + 98*x + 104. Let w(d) = -15*d**3 - 89*d**2 + 99*d + 104. Let m(b) = -2*w(b) + 3*y(b). Factor m(i).
2*(i - 13)*(i - 2)*(3*i + 2)
Let d be -1 + -1 + 2 + 0 - -2. Factor 4*k**4 + 2*k**4 + d*k**4 + 2 - 4 - 10*k**3 + 10*k - 6*k**2.
2*(k - 1)**2*(k + 1)*(4*k - 1)
Suppose