- 2/3*y**w - 2*y.
-2*(y + 1)*(y + 2)/3
Let i = 25977/2 - 12988. Suppose 0*d - 4*d + 20 = 0. Factor d*t**2 + 6*t**3 + 3/2*t + i*t**5 + 0 + 3*t**4.
t*(t + 1)**3*(t + 3)/2
Let p = 8923 - 8920. Let h(s) be the first derivative of 6 + 1/7*s**p + 6/7*s + 9/14*s**2. Factor h(f).
3*(f + 1)*(f + 2)/7
Let a(r) = r**4 + r**3 + r**2 - r - 2. Let c(u) = 7*u**4 - 7*u**3 - 33*u**2 - 53*u - 34. Let h = -438 - -440. Let p(w) = h*c(w) - 18*a(w). Factor p(m).
-4*(m + 1)**2*(m + 2)*(m + 4)
Let m = 1115 - 1124. Let n be -5 - (-19 + (-81)/m). Suppose 0*l**4 + 0 + 6/5*l**3 + 0*l + 4/5*l**2 - 2/5*l**n = 0. What is l?
-1, 0, 2
Let p(q) = -12*q**2 - 78*q. Let d = -841 - -839. Let g(f) = 2*f**2. Let s(o) = d*p(o) - 14*g(o). Solve s(w) = 0.
0, 39
Let a(x) = 4*x**5 - 35*x**4 - 1202*x**3 + 1189*x**2 - 11*x. Let b(p) = -p**5 + 9*p**4 + 301*p**3 - 297*p**2 + 3*p. Let h(t) = 3*a(t) + 11*b(t). Factor h(o).
o**2*(o - 20)*(o - 1)*(o + 15)
Let h(q) be the first derivative of -1/8*q**3 + 5/32*q**4 - 1/8*q + 88 - 5/16*q**2 + 1/10*q**5. Solve h(b) = 0 for b.
-1, -1/4, 1
Let f(o) = -o**2 - 8*o - 8. Let p be f(-6). Let q be -3 + 204/p - -2. Determine n so that 1 + 8 - 1 + 18*n**3 - q*n**2 + 24*n = 0.
-2/9, 1, 2
Let b(h) be the first derivative of -29*h**4/28 + 38*h**3/7 + 153*h**2/14 + 10*h/7 - 1562. Factor b(x).
-(x - 5)*(x + 1)*(29*x + 2)/7
Let f(s) be the second derivative of 74*s - 23/14*s**3 + 0 - 1/10*s**6 + 1/28*s**4 + 69/140*s**5 + 9/7*s**2. Suppose f(b) = 0. Calculate b.
-1, 2/7, 1, 3
Let l(v) be the third derivative of v**5/135 - 25*v**4/27 - 34*v**3/9 - 60*v**2 + 3*v. Factor l(p).
4*(p - 51)*(p + 1)/9
Let u(k) be the third derivative of -k**6/180 - 7*k**5/30 - 95*k**4/36 + 13*k**3 + 135*k**2 - 13. Determine p, given that u(p) = 0.
-13, -9, 1
Let 227*w**3 - 263*w**3 + 0 + 4 - 4 - 84*w**2 + 3*w**4 = 0. What is w?
-2, 0, 14
Let x(m) be the second derivative of m**6/840 + 3*m**5/28 + 225*m**4/56 - 5*m**3/6 - 7*m**2/2 + 6*m + 2. Let c(t) be the second derivative of x(t). Factor c(z).
3*(z + 15)**2/7
Let n = -1599613/85 - -18819. Let j(o) be the first derivative of n*o**5 + 0*o - 27 - 5/34*o**4 + 5/17*o**2 - 2/51*o**3. Factor j(c).
2*c*(c - 5)*(c - 1)*(c + 1)/17
Suppose -t + 11 = -3. Let z be (8/(-6))/(t/(-21)). Factor -g**2 + 4 + 9*g**2 + 2*g + 0*g**3 + 8*g + z*g**3.
2*(g + 1)**2*(g + 2)
Determine m so that -355*m + 138*m**3 + 4*m**5 - 65*m + 1582*m**2 + 24*m**4 - 710*m**2 - 618*m**3 = 0.
-15, 0, 1, 7
Let p be ((-2)/18)/((-975)/(-27) + -37). Let p*b**2 + 1 + 9/8*b = 0. What is b?
-8, -1
Let f = 1111 + -1814. Let k = 703 + f. Factor -1/3*q + 0 + k*q**2 + 1/3*q**3.
q*(q - 1)*(q + 1)/3
Let l be 157157/308 - ((-3)/(-4))/3. Solve 4*r**2 - l + 4*r**3 - 11*r + 516 - 3*r**3 = 0 for r.
-6, 1
Let m(c) be the first derivative of -5*c**6/6 - 8*c**5 + 5*c**4/2 + 80*c**3/3 - 5*c**2/2 - 40*c - 4480. Find v such that m(v) = 0.
-8, -1, 1
Let u = 694579/132300 + -1/33075. Let u*s + s**3 - 21/4*s**2 - 1 = 0. What is s?
1/4, 1, 4
Let i(c) be the second derivative of -c**6/30 - c**5 + 39*c**4/4 - 98*c**3/3 + 50*c**2 + 23*c + 37. Determine r, given that i(r) = 0.
-25, 1, 2
Find w such that -55*w + 350 + 12*w**3 - 35*w - 6*w**2 - 10*w**3 = 0.
-7, 5
Let a(i) be the first derivative of i**5/3 + 665*i**4/2 + 88445*i**3 - 6985. Solve a(u) = 0.
-399, 0
Suppose j = 51 - 47. Factor 426*x**3 - j*x**2 - 2*x**4 - 422*x**3 + 6*x**4 - 4*x.
4*x*(x - 1)*(x + 1)**2
Let g(b) = -3*b + 203. Let n be g(67). Let h(a) be the second derivative of 0*a**4 - 2/15*a**6 + 0 + 0*a**n + 3/5*a**5 - 8/3*a**3 + 11*a. Factor h(z).
-4*z*(z - 2)**2*(z + 1)
Let n be (3 - -15)*(-5)/(-10). Determine i so that -4*i**2 - 5*i**4 - 10*i**2 + 23*i + 38*i**2 - 50 - 25*i**3 - n*i**2 + 42*i = 0.
-5, -2, 1
Let q(x) be the second derivative of x**4/54 + 79*x**3/9 + 78*x**2 - 6524*x. Factor q(l).
2*(l + 3)*(l + 234)/9
Let a(b) be the second derivative of 813/80*b**5 + 1/8*b**7 + 0 - 273/16*b**4 - 49/4*b**3 + 93/40*b**6 + 28*b + 0*b**2. Suppose a(u) = 0. What is u?
-7, -2/7, 0, 1
Let f(m) be the second derivative of m**7/252 + 7*m**6/180 + 7*m**5/60 + m**4/9 + 279*m - 1. Find r, given that f(r) = 0.
-4, -2, -1, 0
Suppose k = -3*k + 5*a + 16, 5*k + 5*a - 20 = 0. Let r(j) be the first derivative of 1/10*j**5 - 7/8*j**2 + 1/16*j**k + 16 - 1/2*j - 1/2*j**3. Factor r(i).
(i - 2)*(i + 1)**2*(2*i + 1)/4
Let x(p) = 3*p**3 + 31*p**2 + 81*p + 8. Let w be x(-5). Let a(u) be the first derivative of 39 + 0*u - 5/3*u**w - 10*u**2. Solve a(s) = 0.
-4, 0
What is o in 15*o**3 - 4*o - 278*o**5 - 136*o + 283*o**5 + 90*o**3 + 50*o**4 - 20*o**2 = 0?
-7, -2, 0, 1
Let n(f) be the second derivative of f**4/4 - 148*f**3 + 2637*f**2/2 + 2*f + 1850. Find b, given that n(b) = 0.
3, 293
Let c = -5173529/11 - -470321. Determine a so that -10/11*a**3 - 14/11*a**2 + 0 - 6/11*a - c*a**4 = 0.
-3, -1, 0
Let z(f) be the second derivative of -f**4/42 - 31*f**3/21 + 66*f**2/7 + 6568*f. Factor z(c).
-2*(c - 2)*(c + 33)/7
Solve 1974*c - 1764 + 305/2*c**3 - 14*c**4 + 1/2*c**5 - 799*c**2 = 0 for c.
2, 6, 7
Suppose 3406*z = 3416*z - 20. Find x, given that 384 + 48*x + 3/2*x**z = 0.
-16
Let n = -1382 + 1151. Let u be (-1056)/n - (-6)/(1 + -3). Find g such that -1/7*g**4 + 9/7*g**2 - 1/7*g**3 - u*g + 4/7 = 0.
-4, 1
Let v = -4529/26 + 2271/13. Let i(g) be the first derivative of 1/4*g**6 + v*g**3 + 0*g + 9/8*g**4 - 33 + 9/10*g**5 + 0*g**2. Factor i(f).
3*f**2*(f + 1)**3/2
Let n(w) be the first derivative of -8*w**3/3 + 13*w**2/2 + 16*w - 374. Let z(o) = -8 - 3*o**2 + 5*o**2 - 6*o + 2*o**2. Let j(t) = 2*n(t) + 5*z(t). Factor j(b).
4*(b - 2)*(b + 1)
Let l(z) be the third derivative of 0*z + 2*z**2 + 3/70*z**7 + 123 - 2*z**3 + 1/4*z**6 + 3/20*z**5 - 3/2*z**4. Factor l(m).
3*(m - 1)*(m + 2)**2*(3*m + 1)
Find m, given that -1849 + 1/4*m**3 + 1806*m + 171/4*m**2 = 0.
-86, 1
Let v(a) = a**2 - 47*a + 144. Let t be v(44). Suppose t = -29*x + 33*x. Determine g, given that -11/5*g - 3/5 - g**2 + 3/5*g**x = 0.
-1, -1/3, 3
Let d(g) be the third derivative of 0*g + 1/30*g**5 - 1/60*g**6 - 210*g**2 + 0 + 17/12*g**4 + 5*g**3. Factor d(i).
-2*(i - 5)*(i + 1)*(i + 3)
Suppose -4*n + 42*n - 22*n = -9*n. Let h(b) be the first derivative of 22 - 1/3*b**3 + n*b**2 + 0*b. Factor h(r).
-r**2
Let n(y) be the second derivative of 1/84*y**7 + 0*y**4 + 0 + 0*y**2 + 138*y + 0*y**3 + 1/12*y**6 + 3/20*y**5. Suppose n(m) = 0. Calculate m.
-3, -2, 0
Suppose -1029 + 1095 = 11*j - 0*j. Let b(s) be the third derivative of 0*s - 21*s**2 + 0 + 1/360*s**j - 1/1260*s**7 - 1/360*s**5 + 0*s**3 + 0*s**4. Factor b(x).
-x**2*(x - 1)**2/6
Let v(x) be the third derivative of -7*x**5/480 - 587*x**4/64 + 63*x**3/4 - x**2 - 18*x + 3. Solve v(o) = 0.
-252, 3/7
Let n be 14/10*(-15)/(-1). Let -39*t**3 - 2 + n*t**4 + 42*t - 3*t**5 + 3*t**2 - 6 - 16 = 0. Calculate t.
-1, 1, 2, 4
Suppose -2*l + 2*m = -176, -276 = -3*l + 2*m - 3*m. Factor -94*h - 2*h**2 - 3*h**2 - 40 - 95*h + 250*h - l*h.
-5*(h + 2)*(h + 4)
Let g(i) = i**3 + 24*i**2 + i + 27. Let x be g(-24). Factor -x + 2674*n**2 - 2671*n**2 - 42 + 6*n.
3*(n - 3)*(n + 5)
Let i(s) be the second derivative of -34*s + 25/48*s**3 - 109/240*s**6 + 149/160*s**5 - 1/8*s**2 - 31/32*s**4 + 0 + 5/56*s**7. What is n in i(n) = 0?
2/15, 1/2, 1
Let 0 + 39/8*j**2 - 189/8*j = 0. What is j?
0, 63/13
Let f = 102616 + -102614. Determine j, given that 1/3*j**3 + 2/3*j**f + 0 - j = 0.
-3, 0, 1
Let o(p) = -p**2 - 12*p. Let w be o(-12). Let s be ((6 - 11) + 4 - -5) + w. Suppose 16/9*l + 28/9*l**2 - 4/9*l**s + 0 + 8/9*l**3 = 0. What is l?
-1, 0, 4
Let t be 330/(-60)*(-17 - (13 - 29)). Suppose -5 - 1/2*q**2 + t*q = 0. What is q?
1, 10
Factor 11/4*l**2 + 21/4 - 7/12*l**3 + 103/12*l.
-(l - 7)*(l + 1)*(7*l + 9)/12
Let l(h) be the third derivative of -h**7/105 + h**6/12 + h**5/10 - 17*h**4/12 + 10*h**3/3 - 568*h**2. Determine n so that l(n) = 0.
-2, 1, 5
Let w = -19 - -22. Let l = 25 + -23. Factor -120*y**2 - 9*y + 3*y**w + 242*y**l - 116*y**2.
3*y*(y - 1)*(y + 3)
Let h(r) = 9*r**2 - 5364*r + 1811711. Let d(i) = 17*i**2 - 10732*i + 3623423. Let f(w) = 5*d(w) - 9*h(w). Find b such that f(b) = 0.
673
Let p(b) = -2*b**3 - 10*b**2 + 9*b - 16. Let v be p(-6). Suppose -4*s**3 + 41*s**v + 9*s - 25*s**2 + 24*s**2 - 73*s = 0. Calculate s.
0, 2, 8
Let d(a) be the third derivative of -a**8/112 - 9*a**7/70 + 11*a**6/20 - a**5/10 - 21*a*