)*(r - 1)
Let i(u) = u**3 - 26*u**2 - 54*u - 61. Let z be i(28). Let v be (11/z - -1)/((-14)/77). Find a, given that 3*a - v*a**2 + 12/5*a**3 + 6/5 = 0.
-1/4, 1, 2
Suppose 53/4*h**3 + 1/4*h**4 + 855/4*h**2 - 6859 + 2527/4*h = 0. What is h?
-19, 4
Let l(t) be the first derivative of 4*t**3/9 - 68*t**2/3 + 124*t + 160. Factor l(j).
4*(j - 31)*(j - 3)/3
Let y(n) be the first derivative of 7*n**2/2 + 5*n - 9. Let c be y(3). Let -38*v**4 - 42*v**5 - c*v**4 - 30*v**3 - 4*v**4 - 4*v**2 = 0. What is v?
-1, -1/3, -2/7, 0
Suppose 4*z - 2032 = -2*w, -5*w + 1419 + 2125 = 7*z. Let x(p) be the first derivative of 96*p**2 + 12 + 8*p**3 + 1/4*p**4 + z*p. Factor x(f).
(f + 8)**3
Let h(x) be the third derivative of -x**8/840 - 17*x**7/525 - 17*x**6/75 - 2*x**5/3 - 4*x**4/5 + 2792*x**2. Find r, given that h(r) = 0.
-12, -2, -1, 0
Suppose -2*w + 16 = 2. Suppose 0 = w*n - 3*n - 28. Factor -n*o**2 + 6*o**3 - 5*o**4 + 2*o**2 + 4*o**3.
-5*o**2*(o - 1)**2
Suppose -38 = b - s - 66, -13*b = 4*s - 41. Factor -2*h**2 + 15/2*h + b - 2*h**3.
-(h - 2)*(2*h + 3)**2/2
Let n(i) = 6*i**4 - 27*i**3 - 45*i**2 + 39*i + 33. Let c(k) = 7*k**4 - 24*k**3 - 46*k**2 + 40*k + 31. Let q(d) = 3*c(d) - 4*n(d). Factor q(j).
-3*(j - 13)*(j - 1)*(j + 1)**2
Suppose -5*w - 2*u = -6*u - 25, 4*w + 4*u = 20. Factor -3*h**4 - h**3 - h**3 - h**5 + 5*h**3 - w*h**3.
-h**3*(h + 1)*(h + 2)
Suppose -414 = 7*i - 491. Let c = -43/4 + i. Factor 0 - 1/4*m**2 - c*m**3 + 1/2*m.
-m*(m - 1)*(m + 2)/4
Let z(c) be the first derivative of -c**6/2520 - 17*c**5/280 - c**3/3 + 221. Let y(q) be the third derivative of z(q). Solve y(r) = 0 for r.
-51, 0
Determine x so that -188/3 + 43/3*x + 1/3*x**2 = 0.
-47, 4
Let c = 13 + -14. Let p = c + 3. Determine i so that 0*i + 3/4*i**p + 0 = 0.
0
Let t(k) be the second derivative of -3/35*k**6 - 73*k + 6/7*k**2 + 9/14*k**3 - 6/35*k**5 + 1/14*k**4 + 0 - 1/98*k**7. Find h such that t(h) = 0.
-4, -1, 1
Let u(v) be the third derivative of v**7/630 + 11*v**6/90 + 19*v**5/10 + 73*v**4/12 + v**3/6 + 204*v**2. Let h(g) be the second derivative of u(g). Factor h(p).
4*(p + 3)*(p + 19)
Let t(l) be the third derivative of -1/17*l**3 + 0 - 1/102*l**4 - 27*l**2 + 1/510*l**5 + 0*l. Factor t(d).
2*(d - 3)*(d + 1)/17
Solve 3986*b**2 + 5*b**3 - 32*b - 28*b - 3966*b**2 = 0.
-6, 0, 2
Let r be (1/(24/26))/((-107)/(-1712)). Let b = r - 14. Factor 0 + 8/3*x**3 + b*x**2 - 4*x.
2*x*(x + 2)*(4*x - 3)/3
Factor 140807*x**3 - 140806*x**3 + 3*x + 1182*x**2 - 4*x - 528 - 647 - 7.
(x - 1)*(x + 1)*(x + 1182)
Let i(y) be the first derivative of y**6/30 - 19*y**5/100 + 7*y**4/20 - y**3/6 - y**2/5 - 123*y + 86. Let q(b) be the first derivative of i(b). Factor q(a).
(a - 2)*(a - 1)**2*(5*a + 1)/5
Let b = -51177/20 + 2559. Let q(t) be the second derivative of b*t**5 - 18*t + 0 - 6*t**2 + 9/2*t**3 - 3/2*t**4. Factor q(p).
3*(p - 4)*(p - 1)**2
Suppose 0 = -48*a + 346*a. Solve -11/8*l**3 - 3/4*l**2 + a - 3/4*l**4 + 0*l - 1/8*l**5 = 0.
-3, -2, -1, 0
Let d(f) be the first derivative of -5*f**4/12 - 154*f**3/9 + 191*f**2/6 - 32*f/3 - 10005. Factor d(r).
-(r - 1)*(r + 32)*(5*r - 1)/3
Let f(q) = 3*q**2 - 3*q - 166. Let b be f(8). Let m(t) be the first derivative of -2 + 2*t**2 + b*t**3 - 5/2*t**4 + 0*t. Find o such that m(o) = 0.
-2/5, 0, 1
Let h(g) be the second derivative of 0*g**2 + 1/10*g**5 - 1/63*g**7 + 2/15*g**6 + 4 - 8/9*g**4 - 4/3*g**3 - 2*g. What is o in h(o) = 0?
-1, 0, 2, 6
Let l(o) be the third derivative of 7/6*o**3 - 2/15*o**5 + 0 - 1/24*o**4 + 0*o + 77*o**2. Factor l(k).
-(k + 1)*(8*k - 7)
Let j(x) = -7*x + 9. Let q be j(1). Factor 9*b**2 - 120*b**3 - 5*b**5 + 3*b**5 + 15*b**q + 94*b**3 - 8*b + 12*b**4.
-2*b*(b - 2)**2*(b - 1)**2
Let b be ((-385)/693)/(11/(-561)). Factor -25/3*o**5 - 35*o**3 - 55/3*o**2 - 10/3*o + 0 - b*o**4.
-5*o*(o + 1)**3*(5*o + 2)/3
Let x(s) be the second derivative of -s**4/3 + 58*s**3 - 664*s**2 - 1954*s. Factor x(f).
-4*(f - 83)*(f - 4)
Let k(r) be the third derivative of -r**7/168 + 5*r**6/72 - 151*r**3/6 - 11*r**2 + 4. Let v(g) be the first derivative of k(g). Factor v(y).
-5*y**2*(y - 5)
Let h = -2/3084967 - -1011871178/3088051967. Let x = h - 6/143. Find i, given that 32/7*i + 36/7*i**2 + 10/7 + x*i**4 + 16/7*i**3 = 0.
-5, -1
Let s = 17/4 + -4. Let v = -2995 - -2997. Factor 0 - 9/4*j**3 + 1/4*j**v - j**5 + 11/4*j**4 + s*j.
-j*(j - 1)**3*(4*j + 1)/4
Let u = -9079/660 - -1/165. Let r = u - -299/20. Factor -4/5 - 2/5*c**2 + r*c.
-2*(c - 2)*(c - 1)/5
Let o(h) be the second derivative of 2*h + 1/80*h**6 - 27/160*h**5 - 1 + 21/32*h**4 + 9/8*h**2 - 19/16*h**3. Solve o(i) = 0 for i.
1, 6
Let r(o) be the second derivative of -o**5/5 - 13*o**4/3 - 34*o**3 - 126*o**2 - 3*o + 221. Solve r(l) = 0.
-7, -3
Factor 2533/2*q**2 - 1/2*q**3 + 0 + 0*q.
-q**2*(q - 2533)/2
Let t(v) be the third derivative of 297/8*v**6 + 0 + 243/14*v**7 - 20/3*v**3 - 128*v**2 + 21/2*v**5 + 0*v - 55/6*v**4. Suppose t(w) = 0. Calculate w.
-1, -2/9, 2/9
Factor -1/2*o**3 - 7*o**2 + 15/2*o + 0.
-o*(o - 1)*(o + 15)/2
What is i in 8*i**5 - 48 + 280*i**3 - 60*i**2 - 340*i**3 + 620*i**4 - 592*i**4 + 128*i + 4*i**5 = 0?
-3, -2, 2/3, 1
Let r(i) be the first derivative of -2*i**3/15 - 21*i**2/5 - 196*i/5 + 4739. Find h, given that r(h) = 0.
-14, -7
Let l(h) be the first derivative of 7*h**4/2 + 178*h**3/3 - 124*h**2 + 56*h - 2097. Find m, given that l(m) = 0.
-14, 2/7, 1
Let q(y) be the second derivative of y**4/30 + 19*y**3/5 - 244*y**2/5 + 152*y. Factor q(s).
2*(s - 4)*(s + 61)/5
Suppose 2*o - 2*s - 5 = -3*s, 2*s = -2. Solve 138*x**3 + 7*x + 0 - 2*x - 139*x**3 - x**2 - o = 0 for x.
-3, 1
Suppose -4*v - 3*h = 4 - 3, 6 = -2*h. Let r(x) be the first derivative of 6/7*x - 6 - 3/14*x**v + 3/35*x**5 - 3/7*x**3 + 3/28*x**4. Solve r(c) = 0.
-2, -1, 1
Let i = 328566/58685 + 14/11737. Factor 46/5*f - i + 2/5*f**3 - 4*f**2.
2*(f - 7)*(f - 2)*(f - 1)/5
Let h(c) = -1 + 6 - 1 + 8*c**2. Let i = -2069 - -2073. Let o(j) = j**3 - 1. Let a(k) = i*o(k) + h(k). Factor a(y).
4*y**2*(y + 2)
Let n be (-4)/(-10) + 312/195. Find k such that 63*k**2 - 7*k + 83*k - 59*k**n - 8*k = 0.
-17, 0
Solve 33*m**3 - 244*m**5 - 42*m**4 - 84*m**2 + 247*m**5 - 288*m + 126*m**3 = 0.
-1, 0, 3, 4, 8
Let q(z) = 3*z**2 - 74*z - 4. Let w be (2/4 - 1) + (-55)/10. Let l(i) = 2*i**2 - 2*i - 2. Let s(r) = w*l(r) + 3*q(r). Let s(t) = 0. Calculate t.
-70, 0
Let c be -1*9*90/10. Let a = 83 + c. Determine i so that 4/11*i - 2/11*i**3 - 2/11*i**a + 0 = 0.
-2, 0, 1
Let b(a) = 3*a**2 - 138*a - 33. Let g(m) = -m**2 - m - 2. Let l(x) = 283*x + 75. Let p(o) = 6*g(o) + l(o). Let h(j) = -9*b(j) - 4*p(j). Solve h(q) = 0 for q.
-1/3, 45
Factor -141/5*c - 28 - 1/5*c**2.
-(c + 1)*(c + 140)/5
Let c = 306336/1531655 + -1/306331. Find r, given that 7/5*r**2 + 3*r - 18/5 - c*r**4 - 3/5*r**3 = 0.
-3, 1, 2
Let z(f) = 2*f**3 + 17*f**2 - 22*f - 15. Let y(s) = -2*s**3 - 16*s**2 + 22*s + 20. Let r(g) = 3*y(g) + 4*z(g). Factor r(w).
2*w*(w - 1)*(w + 11)
Let j be 6 + -1 - (8 - -1 - 8). Solve -194*z**2 - 386 - 720*z - 14 - 50*z**2 + 72*z**3 - 4*z**j = 0 for z.
-1, 10
Let m(s) be the first derivative of s**6/540 + 5*s**5/9 + 625*s**4/9 - 14*s**3 + 3*s**2/2 + 21. Let z(l) be the third derivative of m(l). Factor z(y).
2*(y + 50)**2/3
Let d(m) be the second derivative of m**7/14 - 11*m**6/10 + 21*m**5/4 - 25*m**4/4 + 11239*m. Factor d(x).
3*x**2*(x - 5)**2*(x - 1)
Find z, given that 1012036 + 82*z**3 - 1819744*z + 1008013*z**2 + 148*z**3 + 1780*z**3 + 487*z**4 - 486*z**4 - 202316*z = 0.
-1006, 1
Let r(y) be the first derivative of 2*y**5/75 - y**4/6 - 2*y**3/45 + y**2/3 + 706. What is p in r(p) = 0?
-1, 0, 1, 5
Let u(k) be the second derivative of -k**7/84 - 41*k**6/60 + k**5/40 + 41*k**4/24 + 6661*k. Suppose u(g) = 0. Calculate g.
-41, -1, 0, 1
Suppose -5*m - 3*b = 9, -b + 1 = 109*m - 106*m. Solve -2/7*n**4 + 18/7*n**2 + 2/7*n**m + 8/7 + 22/7*n = 0 for n.
-1, 4
Suppose -133*t - 1346 = -445*t - 98. Factor 16/17 + 2/17*u**5 - 52/17*u**3 + 88/17*u**2 - 62/17*u + 8/17*u**t.
2*(u - 1)**4*(u + 8)/17
Suppose 3*k + d - 193 = -202, -4*d = 60. Factor 0 + 3*h + 3/7*h**k.
3*h*(h + 7)/7
Let i(h) be the third derivative of -h**7/2520 + h**6/288 + h**5/360 - h**4/12 - 3*h**2 + 2*h - 6. Determine p, given that i(p) = 0.
-2, 0, 3, 4
Let k = 36 - -4. Suppose 3*p - k = -b, 0 = -2*b - 0*b + 8. Let -15*f**4 - 3*f**5 - 3*f**3 -