.
u**2*(u + 1)*(u + 2)/8
Let c be ((-7)/((-21)/(-2)))/((-3)/27). Let d be -1 - ((1 - 1) + (2 - c)). Factor 3/5*v**2 + 2/5*v + 0 + 1/5*v**d.
v*(v + 1)*(v + 2)/5
Let f = -658 + 4612/7. Let g(d) be the first derivative of 8/7*d - f*d**3 + 2/7*d**5 - 6 + 4/7*d**4 - 8/7*d**2. Find c, given that g(c) = 0.
-2, -1, 2/5, 1
Suppose 0 = -5*x + 2*q + 4, -21 = -3*x - 12*q + 7*q. Let t be (x + 1)/(60/16 - 3). Factor 8*l**2 - t*l**3 + 2 + 2/3*l**4 - 20/3*l.
2*(l - 3)*(l - 1)**3/3
Let w(b) be the second derivative of -b**6/360 - 7*b**5/60 - 49*b**4/24 + 5*b**3/2 + 5*b. Let m(y) be the second derivative of w(y). Factor m(x).
-(x + 7)**2
Let f be 72/42 - (-2 - 2). Find v, given that 0*v - f*v**3 + 2*v**4 + 18/7*v**5 + 8/7*v**2 + 0 = 0.
-2, 0, 2/9, 1
Suppose 46 = c - 0*c - 4*m, 0 = 3*m. Let y = -26 + c. Let 5*a - y*a**2 + 20*a**4 + 77 - a - 77 - 25*a**5 + 21*a**3 = 0. What is a?
-1, 0, 2/5, 1
Let m = -17 - -24. Suppose 55 = -2*j + m*j. Let -6*y**2 - 12 + 17*y - 16*y + j*y + 3*y**2 = 0. What is y?
2
Let y(m) = -32*m**2 - 3*m - 3. Let u be y(2). Let w = 140 + u. Factor -2/3*s**w + 0 + 0*s**2 + 0*s.
-2*s**3/3
Suppose -25*y + 26*y - 6 = -v, -5*v + 12 = 2*y. Factor v*f + 0 + 3/5*f**2 - 4/5*f**3.
-f**2*(4*f - 3)/5
Let l = -15 - -18. Suppose -5*f - 4*a = -21 - 19, -f - l*a = -19. Determine w so that 8*w**2 - 36*w**f + 16*w**4 - 8*w**3 - 4*w**3 = 0.
-1, 0, 2/5
Let y(n) = -5*n + 102. Let w be y(20). Suppose w = -3*j + 5. Factor 35/2*g**2 - j + 3/2*g.
(5*g - 1)*(7*g + 2)/2
Let j be -30*((-16)/(-12))/2. Let g = -20 - j. Factor -6*x + g + 3 - 8*x**2 - 1.
-2*(x + 1)*(4*x - 1)
Let l(b) = 33*b**3 + 54*b**2 + 84*b - 9. Let o(u) = -15*u**3 - 27*u**2 - 42*u + 4. Let n(j) = 4*l(j) + 9*o(j). Factor n(r).
-3*r*(r + 2)*(r + 7)
Suppose -5 - 7 = -4*h. Factor 3*y**h + 4*y + 115 - 4*y**3 + y**2 - 119.
-(y - 2)*(y - 1)*(y + 2)
Factor -1/3*p**4 + 1/3*p**2 + 1/6*p - 1/6*p**5 + 0*p**3 + 0.
-p*(p - 1)*(p + 1)**3/6
Factor 6*i**4 + 2*i**4 - 16*i**4 + 2*i**4 + 30*i**3 + 40*i**2 + 11*i**4.
5*i**2*(i + 2)*(i + 4)
Suppose -4*c - 8 = -3*y - y, -3*y = c - 18. Suppose -y*q - 5*v = -5 - 5, 0 = q - v. Factor -2*m + 6*m**2 - 2*m + q + m**4 + 8*m + 4*m**3.
(m + 1)**4
Let b = -508 - -512. Let k(f) be the third derivative of 0 - 4*f**2 + 5/6*f**b + 0*f + 1/4*f**5 + 0*f**3 - 1/24*f**6. Factor k(o).
-5*o*(o - 4)*(o + 1)
Let z(t) = -9*t - 440. Let j be z(-49). Determine u, given that -3/2*u**2 - 1/2*u**3 + 1/2*u + 1/2*u**4 + j = 0.
-1, 1, 2
Let h(k) be the first derivative of k**7/560 + k**6/80 - 5*k**3/3 - 4. Let b(r) be the third derivative of h(r). Factor b(j).
3*j**2*(j + 3)/2
Let r(x) be the first derivative of 4 + 8/51*x**3 + 4/17*x - 1/34*x**4 - 5/17*x**2. Factor r(z).
-2*(z - 2)*(z - 1)**2/17
Let j(z) = z**2 + 2*z. Let h be j(0). Suppose h = 5*r + 12 - 22. Factor 2/7*g**r + 4/7*g + 0 - 2/7*g**3.
-2*g*(g - 2)*(g + 1)/7
Let j(n) = -n**4 + 2*n**3 - n**2 - 1. Let c(s) = 3*s**4 - 7*s**3 - 2*s**2 + 2. Let x(b) = c(b) + 2*j(b). Factor x(m).
m**2*(m - 4)*(m + 1)
Suppose -b + 0 + 2 = 0. Suppose 1 = -b*l + 5. What is t in 2*t - 9*t**3 - 5*t - 3*t**4 - 6*t**l + 3*t = 0?
-2, -1, 0
Let x(h) = h**3 - 4*h**2 + h + 2. Let f be x(4). Suppose -f*c = -5*c - 10. Factor -c*a - 14*a + 50 - 2 + 3*a**2.
3*(a - 4)**2
Suppose -28/3*r - 2/9*r**2 - 98 = 0. What is r?
-21
Let l(t) = -t**3 - 116*t**2 - 2580*t + 2. Let o be l(-86). Factor 2*m + 1/3*m**4 + 2*m**3 + 11/3*m**o + 0.
m*(m + 1)*(m + 2)*(m + 3)/3
Factor 2/9*u**2 + 2*u + 16/9.
2*(u + 1)*(u + 8)/9
Find z, given that -36*z - 6*z**2 + 7*z**3 + 6*z**3 + z**3 - 5*z**3 + 54*z**2 = 0.
-6, 0, 2/3
Let h = -19 + 30. Suppose 0 - 5 = -v - 2*b, 5*v - 4*b - h = 0. Factor -3*j**4 + 5*j**5 + 2*j**3 - 4*j**5 - 2*j**5 - j**2 - 5*j**v.
-j**2*(j + 1)**3
Let u be (-3)/(-9) - (-64)/6. Let i = u + -7. Factor 2*h**4 - h**2 + h**3 + 0*h**4 - 5*h**i + 4*h**4 - h**5.
-h**2*(h - 1)**2*(h + 1)
Let w(v) be the first derivative of v**6/66 - 3*v**4/11 - 16*v**3/33 + 227. Factor w(r).
r**2*(r - 4)*(r + 2)**2/11
Let v(x) be the second derivative of -1/3*x**4 - x + 0*x**2 - 2/45*x**6 - 2/9*x**3 + 0 - 1/5*x**5. Factor v(c).
-4*c*(c + 1)**3/3
Let m(l) = -15*l + 555. Let n be m(37). Let g(q) be the third derivative of 0*q**3 + 1/90*q**4 - 1/450*q**5 + 4*q**2 + 0*q + n. Let g(j) = 0. What is j?
0, 2
What is a in 927/2*a**2 - 3/2*a**3 + 3278181/2 - 95481/2*a = 0?
103
Let s(y) = -y**4 + 47*y**3 + 309*y**2 + 753*y + 489. Let q(v) = 4*v**4 - 234*v**3 - 1546*v**2 - 3766*v - 2444. Let l(k) = -6*q(k) - 28*s(k). Factor l(j).
4*(j + 1)*(j + 3)*(j + 9)**2
Let u(v) be the third derivative of v**6/8 - 5*v**5/6 + 5*v**4/24 + 5*v**3 + 3*v**2 - 3*v. Factor u(h).
5*(h - 3)*(h - 1)*(3*h + 2)
Let f be (-4)/3*(-144)/(-480)*3*-1. Factor 0*b**2 + 0*b - f*b**3 - 3/5*b**4 + 0.
-3*b**3*(b + 2)/5
Let b(r) = -r**5 - r - 1. Let s(g) = 3*g**5 + 4*g**4 - 28*g**3 - 28*g**2 - g + 3. Let h(u) = -5*b(u) + s(u). Factor h(q).
4*(q - 2)*(q + 1)**3*(2*q - 1)
Let b = 226 + -221. Let p(y) be the first derivative of 6*y - 15/2*y**2 + 15/4*y**4 - 2*y**3 - b. Suppose p(x) = 0. Calculate x.
-1, 2/5, 1
Let c be 1/(-5) - -2*6870/1200. Find y such that 5/4*y**2 + c*y**4 + 5/2 + 45/4*y - 105/4*y**3 = 0.
-1/3, 1, 2
Let b(x) be the third derivative of -x**9/20160 - x**8/6720 - x**5/4 - 9*x**2. Let k(m) be the third derivative of b(m). Determine h, given that k(h) = 0.
-1, 0
Solve -3/2*y + 96*y**2 - 63/2*y**3 - 9 = 0 for y.
-2/7, 1/3, 3
Factor 0*w - 2*w**3 + 1/3*w**2 + 0.
-w**2*(6*w - 1)/3
Let i(j) = j**3 + 8*j**2 - 11*j - 13. Let k be i(-9). Suppose f + 30 = k*m, -4*f = m + 4*m - 5. What is g in 6*g**2 - 3 + 3*g**2 - m*g**2 - 1 = 0?
-1, 1
Let r(z) = 4*z**4 + 16*z**3 + 10*z**2 + 8*z + 10. Let h(b) = b**2 - 1. Let l(o) = 10*h(o) + r(o). Factor l(s).
4*s*(s + 1)**2*(s + 2)
Let v be 3/(-20) - (-3)/4. Suppose 5*c - 3*m - 7 = 12, 4*m + 16 = 2*c. Factor -b - v + 2/5*b**c.
(b - 3)*(2*b + 1)/5
Let u(d) be the first derivative of -1/9*d**2 + 0*d + 9 - 2/27*d**3. Suppose u(f) = 0. What is f?
-1, 0
Let v(w) be the first derivative of w**4/22 - 2*w**3/11 - 6*w**2/11 + 16*w/11 + 104. Find d such that v(d) = 0.
-2, 1, 4
Suppose -90*f + 32 = -82*f. Let b(j) be the second derivative of -17/18*j**3 + 5/36*j**f + 0 - 5*j + j**2. Suppose b(u) = 0. What is u?
2/5, 3
Let b(c) be the second derivative of c**7/168 - c**6/60 - 3*c**5/16 - 142*c. Determine j, given that b(j) = 0.
-3, 0, 5
Let t = 113/202 + -6/101. Factor s**2 - 1/2*s + 0 - t*s**3.
-s*(s - 1)**2/2
Let t(k) be the third derivative of k**5/20 - 223*k**4/8 + 111*k**3 + k**2 - 199. Factor t(n).
3*(n - 222)*(n - 1)
Find g, given that -1/3*g**3 + 0 + 1/3*g**5 - 1/3*g**2 + 1/3*g**4 + 0*g = 0.
-1, 0, 1
Let s(p) be the first derivative of 3*p**3 - 17 - 1/4*p**4 + 4*p - 1/5*p**5 - 11/2*p**2. Find o, given that s(o) = 0.
-4, 1
Suppose 14*j - 21*j - 40*j = 0. Let 1/5*x**2 + 6/5*x + j = 0. Calculate x.
-6, 0
Let g(k) be the first derivative of 1/4*k**2 - 30 - 1/16*k**4 - 1/12*k**3 + 0*k. Factor g(j).
-j*(j - 1)*(j + 2)/4
Suppose m - 4 - 2 = 3*r, -3*m = -2*r - 18. Let o be m/(3 - 6*1/(-4)). Factor 2/3*t**2 + 2/3 - o*t.
2*(t - 1)**2/3
Let y(h) be the third derivative of 1/180*h**6 - 1/75*h**5 + 0 + 15*h**2 + 0*h + 2/45*h**3 - 1/20*h**4. Suppose y(z) = 0. Calculate z.
-1, 1/5, 2
Let n = -1938 - -1938. Factor 13/3*x**2 - 4/3*x**3 - x + n.
-x*(x - 3)*(4*x - 1)/3
Let i = -46 - -51. Suppose -39 = i*v - 39. Solve v*z**2 + 1/4*z**4 - 1/4*z**3 + 0*z + 0 = 0.
0, 1
Let h(i) be the third derivative of i**7/2100 + i**6/180 + 2*i**5/75 + i**4/15 - 7*i**3/6 + 8*i**2. Let d(n) be the first derivative of h(n). Factor d(g).
2*(g + 1)*(g + 2)**2/5
Let j(v) = 7*v**3 + 9*v**2 + 23*v + 15. Let s(i) = -30*i**3 - 36*i**2 - 93*i - 61. Let x(h) = 26*j(h) + 6*s(h). Factor x(m).
2*(m + 1)*(m + 2)*(m + 6)
Let l(x) be the third derivative of x**6/60 - 4*x**5/15 + x**4 + 114*x**2. Let l(u) = 0. What is u?
0, 2, 6
Let c(z) = -2*z**5 - 19*z**4 - 30*z**3 - 18*z**2 - 5*z + 5. Let v(y) = -y**4 + 339*y**3 + 1 - 339*y**3 - y. Let i(k) = -c(k) + 5*v(k). Factor i(s).
2*s**2*(s + 1)*(s + 3)**2
Let t(v) be the first derivative of -v**6/3 + 8*v**5 - 26*v**4 - 320*v**3 - 576*v**2 + 165. Find y such that t(y) = 0.
-2, 0, 12
Let f = -29 - -28. Let i = 3 + f. Factor -4/9 - 2/9*h**i + 2/3*h.
-2*(h - 2)*(h - 1)/9
Suppose -2*m - 5*b - 17 = -41, -3*m + b = -2. Factor 8*t - 63*t*