1
Let z = -5441 - -21775/4. Factor -16*x + z*x**4 + 4*x**2 + 9*x**3 + 0 + 1/4*x**5.
x*(x - 1)*(x + 4)**3/4
Factor 38 - 22 + 20*z**2 - 15*z**3 - 16 - 5*z**4.
-5*z**2*(z - 1)*(z + 4)
Let f(b) be the second derivative of 0 + 35/36*b**4 - 40/63*b**7 + 5/18*b**3 - b + 0*b**2 + b**5 - 2/9*b**6. Determine p, given that f(p) = 0.
-1/2, -1/4, 0, 1
Let g(v) be the third derivative of v**6/20 + 29*v**5/30 - 43*v**4/12 + 11*v**3/3 - 30*v**2 + v. Factor g(l).
2*(l - 1)*(l + 11)*(3*l - 1)
Suppose 0*y - 28 = -7*y. Let p be 1*(0 + (1 - 1)/y). Solve 0 + 2/13*w**3 - 2/13*w + p*w**2 = 0.
-1, 0, 1
Suppose -9 = -6*d + 3*d. Find k such that -d*k**5 - k - k**3 + 2*k**5 + 5*k**3 - 2*k**3 = 0.
-1, 0, 1
Let t(x) = 589*x**2 + 371*x + 65. Let o(c) = 0 + 149*c**2 + 186*c + 33 + 145*c**2. Let p(m) = 11*o(m) - 6*t(m). Factor p(k).
-3*(10*k + 3)**2
Suppose -16 = -h - 2*m, 7*h = 4*h + m + 27. Suppose -t + 13 - h = 0. Suppose 4/3*u**t + 4*u**4 - 7/3*u**5 - 14/3*u**2 + u + 2/3 = 0. What is u?
-1, -2/7, 1
Suppose 7500 + 174*u + 3*u**2 - 125*u + 251*u = 0. What is u?
-50
Suppose 0 = g - 4*y + 12, 46*g - 48*g + 5*y = 12. Solve 0 + 9/2*d - 15*d**g - 9/2*d**5 + 0*d**3 + 15*d**2 = 0 for d.
-3, -1, -1/3, 0, 1
Let j be 6 - 30/25*60/24. Let 3*g**2 + 1/2*g**4 + 1/2 - 2*g - 2*g**j = 0. Calculate g.
1
Let j(g) = -6*g**3 + 20*g**2 - 68*g + 60. Let n(h) = -h**3 - h - 1. Let y(b) = j(b) - 4*n(b). Factor y(r).
-2*(r - 4)**2*(r - 2)
Let p = 2114/1581 - 2/527. Factor p*z**2 - 2/3 + 7/3*z.
(z + 2)*(4*z - 1)/3
Suppose 5*r = -5*o + 30, 1652*r + 12 = 1651*r + 5*o. Let 0*l + 3/4*l**3 - 9/4*l**2 + r = 0. Calculate l.
-1, 2
Let v(t) be the first derivative of t**3/5 + 21*t**2/10 + 73. Factor v(w).
3*w*(w + 7)/5
Let i(x) be the second derivative of 0*x**2 + 1/48*x**4 + 0*x**3 + 0 - 19*x. Factor i(f).
f**2/4
Let u(v) = -v**2 + 7*v + 5. Let j be u(8). Let x be (-7)/j - (-16)/(-48). Factor -6*a + x*a**3 - 3*a**2 - 3*a**4 + 4 + 2*a + 4*a**4.
(a - 1)**2*(a + 2)**2
Solve 15/4*g + 0 + 3/8*g**3 - 21/8*g**2 = 0 for g.
0, 2, 5
Let v(x) be the second derivative of 69*x**5/80 + x**4/24 + 46*x. Factor v(n).
n**2*(69*n + 2)/4
Let a(l) = 5*l**2 + 40*l - 20. Let s(i) be the second derivative of i**4/12 + 5*i**3/3 - 5*i**2/2 + 16*i. Let q(r) = 6*a(r) - 25*s(r). Factor q(o).
5*(o - 1)**2
Let d(c) be the third derivative of 6*c**2 + 1/2*c**3 - 1/40*c**5 + 0 - 1/16*c**4 + 0*c. Factor d(a).
-3*(a - 1)*(a + 2)/2
Let o(u) be the first derivative of -3*u**5/25 - 9*u**4/10 + 48*u**2/5 - 6. Solve o(x) = 0.
-4, 0, 2
What is d in -13520 + 367*d - 1056*d + 169*d - 5*d**2 = 0?
-52
Let r = 203 + -134. Suppose r*n + 2 = 70*n. Factor -3/4*i + 0 - 3/4*i**n.
-3*i*(i + 1)/4
Let s(f) = f**5 - 3*f**4 - 21*f**3 + 19*f**2 - 4. Let t(u) = 3*u**5 - 9*u**4 - 61*u**3 + 56*u**2 - 11. Let i(x) = 11*s(x) - 4*t(x). Factor i(k).
-k**2*(k - 5)*(k - 1)*(k + 3)
Factor 1/6*s**4 - 2/3*s - 1/2*s**2 + 1/3*s**3 + 2/3.
(s - 1)**2*(s + 2)**2/6
Let g be 376/(-32) - (-1)/(-4). Let d be -2 + 8/g + 3. Factor 0*i + d*i**2 - 1/3.
(i - 1)*(i + 1)/3
Let n(v) be the second derivative of v**6/90 + v**5/30 - 23*v**4/36 - 4*v**3/3 + 24*v**2 + 47*v. Factor n(z).
(z - 3)**2*(z + 4)**2/3
Determine l, given that -12*l - 21*l**3 + 26*l**3 - 26*l**2 + 2*l**4 - 2*l - 15*l**3 = 0.
-1, 0, 7
Let c(b) be the second derivative of -5*b**7/14 - 9*b**6/10 - 9*b**5/20 + b**4/4 + 9*b + 1. Factor c(a).
-3*a**2*(a + 1)**2*(5*a - 1)
Let a(h) = -49*h**3 - 108*h**2 - 72*h - 7. Let d(k) = 98*k**3 + 215*k**2 + 144*k + 17. Let r(s) = 5*a(s) + 3*d(s). Find v, given that r(v) = 0.
-1, -4/7
Let w(l) be the third derivative of l**6/180 - l**5/15 - 7*l**4/36 + 45*l**2 - 1. Factor w(s).
2*s*(s - 7)*(s + 1)/3
Let b(a) be the first derivative of a**7/210 - a**6/45 + a**5/30 - 17*a**3/3 + 6. Let u(k) be the third derivative of b(k). Factor u(f).
4*f*(f - 1)**2
Let b = -134 + 136. Factor -1372*n - n**3 - 12*n**b + 1372*n.
-n**2*(n + 12)
Let c(h) be the second derivative of h**4/6 - 30*h**3 + 136*h. Let c(q) = 0. Calculate q.
0, 90
Let z(y) be the second derivative of y**6/50 - 7*y**5/100 - 7*y**4/60 + y**3/10 + 4*y + 52. Determine h so that z(h) = 0.
-1, 0, 1/3, 3
Suppose -5*i - 30 = -2*i. Let b = i + 13. Factor 5 - 3*l**b + l + 2*l - 5.
-3*l*(l - 1)*(l + 1)
What is t in 35/4 + 10*t + 5/4*t**2 = 0?
-7, -1
Suppose -p = -4*p + 9. Let d(z) = -2*z**3 - 6*z**2 + 3*z + 9. Let s be d(-3). Suppose 4/5*v**2 - 4/5*v**p + s*v + 0 = 0. Calculate v.
0, 1
Let g(a) be the first derivative of -2*a**3/39 + 10*a**2/13 - 50*a/13 + 112. Factor g(l).
-2*(l - 5)**2/13
Find j such that -12*j + 5*j**3 + 8 + 14*j - 6*j**3 - 5*j**2 + 2*j**3 = 0.
-1, 2, 4
Suppose 0 = -3*h + 1 + 5. Factor 16*s**2 - 50 + s - 20*s**h - 66*s + 19*s**2.
5*(s - 5)*(3*s + 2)
Let m(h) be the second derivative of -h**2/2 - h. Let v(t) = -75 - 70 + t + t**2 + 149. Let q(z) = 12*m(z) + 3*v(z). Determine l so that q(l) = 0.
-1, 0
Let z(g) be the first derivative of 4 - 1/40*g**6 - 1/8*g**4 - 1/10*g**5 + 0*g**3 + 0*g + 3*g**2. Let r(b) be the second derivative of z(b). Factor r(a).
-3*a*(a + 1)**2
Let h(v) be the first derivative of 11 + 1/17*v**2 + 2/51*v**3 + 0*v. Factor h(o).
2*o*(o + 1)/17
Factor -72/5 - 6*a**2 - 2/5*a**3 + 104/5*a.
-2*(a - 2)*(a - 1)*(a + 18)/5
Let i(b) = -b**3 - 8*b**2 - b + 1. Let w be i(-8). Factor -2*d - w*d + 2*d + 25 - d + d**2.
(d - 5)**2
Let s(t) = -10*t**4 - 792*t**3 - 15176*t**2 + 792*t + 15198. Let p(h) = 4*h**4 + 317*h**3 + 6070*h**2 - 317*h - 6079. Let q(z) = -12*p(z) - 5*s(z). Factor q(o).
2*(o - 1)*(o + 1)*(o + 39)**2
Let b(w) be the second derivative of -w**4/12 - 4*w**3/3 + 9*w**2/2 - 3*w - 5. Determine t, given that b(t) = 0.
-9, 1
Let r(v) be the second derivative of v**6/240 + v**5/120 - v**4/48 - v**3/12 - 5*v**2 - 7*v. Let i(h) be the first derivative of r(h). Factor i(z).
(z - 1)*(z + 1)**2/2
Let f(d) be the first derivative of 19/18*d**3 - 1/6*d**2 + 0*d - 53/24*d**4 - 31 + 6/5*d**5. Solve f(x) = 0.
0, 2/9, 1/4, 1
Factor 414*h - 28566 - 3/2*h**2.
-3*(h - 138)**2/2
Let a be 9/(-12) - (-7)/4. Suppose 2 = j - a. Determine f so that -2*f + j*f + 2*f**3 - f = 0.
0
Let a(m) be the first derivative of -m**6/90 + m**4/6 + 10*m**3/3 + 2. Let g(t) be the third derivative of a(t). Factor g(u).
-4*(u - 1)*(u + 1)
Suppose -40 = 5*b - 65. Let n be (4/(-1))/(4/(-10)*b). Find y, given that 9/7*y**3 + 0*y + 3/7*y**n + 0 + 9/7*y**4 + 3/7*y**5 = 0.
-1, 0
Let x(f) = f**2 + 17*f + 18. Let z be (-5 + (2 - -1))*8. Let g be x(z). Factor -2 + d**2 + 0*d**g + 8*d - 7*d**2.
-2*(d - 1)*(3*d - 1)
Let z(i) = 2*i**4 - 8*i**2 + 4*i. Let j(k) = -4*k**4 - k**3 + 16*k**2 - 6*k. Let p(h) = 2*j(h) + 5*z(h). Factor p(d).
2*d*(d - 2)*(d - 1)*(d + 2)
Let v(r) be the first derivative of -1/3*r**2 + 4/15*r + 4 + 4/45*r**3. Factor v(l).
2*(l - 2)*(2*l - 1)/15
Let d = 15 + -11. Let 6*y**5 + 7*y**3 + 5 - 2*y**5 - 20*y - 16*y**d + 9*y**3 + 8*y**2 + 3 = 0. Calculate y.
-1, 1, 2
Let r(l) be the first derivative of -l**4/36 - 2*l**3/9 + 5*l**2/6 - 8*l + 4. Let o(h) be the first derivative of r(h). Factor o(f).
-(f - 1)*(f + 5)/3
Let j(a) be the first derivative of -2*a**7/35 + a**6/5 + 11*a**5/20 + 3*a**4/8 - a**2/2 - 5. Let s(h) be the second derivative of j(h). Factor s(n).
-3*n*(n - 3)*(2*n + 1)**2
Factor 5*b**3 + 315*b**2 - 6 + 3 + 3.
5*b**2*(b + 63)
Let l(s) be the second derivative of s**6/900 + 4*s**5/75 + 16*s**4/15 - s**3/6 + 2*s. Let r(d) be the second derivative of l(d). What is y in r(y) = 0?
-8
Suppose -5*o + 5*n + 10 = 0, 8*n = -4*o + 3*n + 35. Factor -o*z**3 + 27*z**2 + 16 + 29 - 41*z - 34*z + 8*z**2.
-5*(z - 3)**2*(z - 1)
Suppose 2/5*r**2 + 14/5*r + 0 = 0. What is r?
-7, 0
Suppose -206*h + 434 = -184. Solve 3*o**2 + 0*o**h + 0 - 3*o**4 + 3/2*o**5 - 3/2*o = 0.
-1, 0, 1
Let a be -4 + 1395/12 + -1. Let o = -111 + a. What is j in 1/2*j**4 + 0*j**3 - 1/2*j**2 + o*j + 0 - 1/4*j**5 = 0?
-1, 0, 1
Let w be (-60)/(-9)*(-9)/6. Let z be (w - -7)/((-3)/2). Factor -i - 2*i**2 + 3*i**2 + z*i - 3*i + 1.
(i - 1)**2
Suppose -154 = -14*r - 8*r. Let h(p) = 2*p**2 - 12*p - 9. Let t be h(r). Let 4/7*f**4 - 2/7*f**2 - 2/7 - 5/7*f + 4/7*f**3 + 1/7*f**t = 0. Calculate f.
-2, -1, 1
Let i(o) be the second derivative of -1/45*o**6 - 1/5*o**5 + 4/9*o**3 - 1/2*o**4 + 4*o**2 + 16*o + 0. Suppose i(s) = 0. What is s?
-3, -2, 1
Let b be ((-8)/12)/((-4)/12). Suppose -b*g = -5*g +