, 1, 5
Let b be ((-18)/(-39))/(-3)*156/(-48). Factor -6*c - 4 - b*c**3 - 3*c**2.
-(c + 2)**3/2
Let n = -74 + 76. Let l be n/6 - 10/(-30). Factor 2/3*m**3 - l*m**2 - m + 1/3*m**5 - 1/3 + m**4.
(m - 1)*(m + 1)**4/3
Solve 341*l - 89 + 245 + 189 + 11*l + 3 + 4*l**2 = 0 for l.
-87, -1
Suppose 0 = 2*z - f - 8, 5*z = f - 2*f + 6. Let h be 564/252 - (-4)/(-7). Find v such that h*v - 2/3 + 2/3*v**z - 5/3*v**3 = 0.
-1, 2/5, 1
Find o, given that 129/4*o**2 + 67/4*o**3 + 3*o**4 + 24*o + 5 = 0.
-2, -5/4, -1/3
Let d(j) = j**2 - 10*j - 229. Let v be d(21). Factor -4/5*b + 2/5*b**v - 6/5.
2*(b - 3)*(b + 1)/5
Let i(w) be the third derivative of -1/210*w**7 - 13/60*w**5 - 2/3*w**3 + 0 - 6*w**2 + 1/2*w**4 + 1/20*w**6 + 0*w. Let i(m) = 0. What is m?
1, 2
Let d(o) be the second derivative of -1/10*o**4 + 0 + 23/10*o**3 + 18/5*o**2 + 2*o. Factor d(h).
-3*(h - 12)*(2*h + 1)/5
Let i(v) = 7*v**5 + 14*v**4 - 3*v**3 - 12*v**2 + 2*v. Let s(d) = -29*d**5 - 58*d**4 + 11*d**3 + 49*d**2 - 9*d. Let z(j) = 9*i(j) + 2*s(j). Factor z(x).
5*x**2*(x - 1)*(x + 1)*(x + 2)
Let c(d) be the second derivative of -d**6/60 - 9*d**5/20 - 25*d**4/24 + 9*d**3 - 16*d**2 - 640*d. Factor c(k).
-(k - 1)**2*(k + 4)*(k + 16)/2
Let s(v) be the first derivative of 5*v**6/16 - 21*v**5/40 - 39*v**4/32 + 11*v**3/8 + 3*v**2/2 - 3*v/2 - 205. Suppose s(b) = 0. What is b?
-1, 2/5, 1, 2
Let a(h) = -h**3 - 5*h**2 + h + 1. Let z(j) = -7*j**3 - 836*j**2 - 28139*j + 44101. Let s(k) = a(k) - z(k). Factor s(w).
3*(w + 70)**2*(2*w - 3)
Find t such that -516*t**2 + 135*t**5 + 22*t**3 - 328*t**3 - 24*t + 234*t**5 + 633*t**4 - 156*t**3 = 0.
-2, -2/3, -2/41, 0, 1
Suppose 9 = -4*o + 7*o, -2*o = 3*u - 12. Determine j, given that 5 + 0*j**2 + 4*j**2 - 9*j**u + 15*j**3 - 15*j = 0.
-1, 1/3, 1
Let c(r) be the third derivative of -12/5*r**3 + 0 + 0*r + 14*r**2 - 1/5*r**4 - 1/150*r**5. Solve c(n) = 0.
-6
Let q(h) be the third derivative of h**5/12 - 125*h**4/12 + 3125*h**3/6 + 3*h**2 + 10. Find k, given that q(k) = 0.
25
Factor 1286*j**4 + 1293*j**4 - 116*j**2 - 2575*j**4 + 112*j**3.
4*j**2*(j - 1)*(j + 29)
Let r(o) be the third derivative of o**5/180 + 13*o**4/36 - 28*o**3/9 - 165*o**2. Factor r(m).
(m - 2)*(m + 28)/3
Factor 10*b - 34/7 - 4/7*b**2.
-2*(b - 17)*(2*b - 1)/7
Let h(l) be the second derivative of -l**9/720 + l**8/1120 + l**7/120 - l**6/120 + l**4 - 15*l. Let c(y) be the third derivative of h(y). Factor c(a).
-3*a*(a - 1)*(a + 1)*(7*a - 2)
Let h(d) = -d**2 + 13*d - 9. Let b be h(12). Suppose b*w + 3 = 9. Determine n so that 6*n**4 + 0*n**5 + 4*n**3 + 7*n + w*n**5 - 7*n = 0.
-2, -1, 0
Let p(k) be the second derivative of k**7/126 + k**6/45 - k**5/20 - 2*k**4/9 - 2*k**3/9 - 153*k. Find m, given that p(m) = 0.
-2, -1, 0, 2
Let -165*c**3 - 15*c**3 - 81*c**2 - 8 - 16 - 37*c**4 + 24 - 2*c**5 = 0. What is c?
-9, -1/2, 0
Let v(h) be the second derivative of -10*h - 4 - 5/12*h**2 - 5/18*h**3 - 5/72*h**4. Factor v(g).
-5*(g + 1)**2/6
Let a = 11077/4 + -2767. Factor -1/4*l**2 - a - 3/2*l.
-(l + 3)**2/4
Factor 3*n**3 + 1/2*n**4 + 2*n**2 - 3*n - 5/2.
(n - 1)*(n + 1)**2*(n + 5)/2
Let c(k) be the second derivative of k**4/20 - 26*k**3/5 - 159*k**2/10 + 4*k + 23. Determine u, given that c(u) = 0.
-1, 53
Factor 136*k - 137*k**2 + 208 - 128 + 10*k**4 + 14*k**3 - 19*k**2.
2*(k - 2)**2*(k + 5)*(5*k + 2)
Let d(r) = -r - 4. Let y be d(-6). Let m = 0 + y. Factor -29*l**2 + m*l**4 + 0*l**5 - 2*l**3 + 2*l**5 + 27*l**2 + 0*l**4.
2*l**2*(l - 1)*(l + 1)**2
Let s = 22 - 20. Factor 5*n**2 - 13*n - n**2 - 7*n + n**s.
5*n*(n - 4)
Factor -121 - 1/4*b**2 + 11*b.
-(b - 22)**2/4
Suppose 5*t - s = 8, -5*t + 20 = -0*t - 5*s. Suppose l - 1 = t. Solve l*y**2 - 2*y**4 - 3*y**5 + 6*y - 7*y + 4*y**5 = 0 for y.
-1, 0, 1
Let x be 28/(-14) + -5 - (1 + -14 + 3). Factor 4/3*q**2 + 4/3*q + 0 + 1/3*q**x.
q*(q + 2)**2/3
Let z(r) = -r - 4. Let u(l) = l**2 + l + 1. Suppose -9*w + 5 = -8*w. Let p(y) = w*z(y) + 15*u(y). Factor p(c).
5*(c + 1)*(3*c - 1)
Solve -2/23*w**3 + 2/23*w + 2/23*w**4 + 12/23 - 14/23*w**2 = 0.
-2, -1, 1, 3
Let i(x) = 2*x. Let j be i(5). Suppose -d - 14 = -3*z, 4*z - j - 10 = d. Factor 5*b - b - 3*b**5 + 6*b**2 + 6*b - 7*b - z*b**4.
-3*b*(b - 1)*(b + 1)**3
Let p(l) be the third derivative of 0 + 2/3*l**3 + 0*l - 4*l**2 - 1/15*l**5 - 1/60*l**6 + 1/12*l**4. Solve p(g) = 0.
-2, -1, 1
Let p(a) be the third derivative of 0*a + 0 - 1/420*a**5 + 6*a**2 - 1/168*a**4 + 0*a**3. Factor p(h).
-h*(h + 1)/7
Let r(t) be the second derivative of t**4/3 - 6*t**3 - 20*t**2 + 4*t + 1. Factor r(d).
4*(d - 10)*(d + 1)
Let n be 4 - ((-3)/12 + 2). Factor -n*i - 1/2 - 7/4*i**2.
-(i + 1)*(7*i + 2)/4
Let b = 5729/4 + -1430. Let w(f) be the first derivative of -3/4*f**2 - b*f**4 + 9 + 0*f + 2*f**3 + 6/5*f**5 - 1/4*f**6. Solve w(c) = 0 for c.
0, 1
Let a(w) be the second derivative of -w**4/12 + w**3 - 2*w**2 + 32*w. Let j(f) = -1. Let n(v) = 4*a(v) - 44*j(v). Factor n(k).
-4*(k - 7)*(k + 1)
Factor 0 + 1/2*d**3 - 1/2*d**2 - 3*d.
d*(d - 3)*(d + 2)/2
Let x(o) be the first derivative of 1 + 2/15*o**3 + 3/5*o**2 + 0*o. Find h, given that x(h) = 0.
-3, 0
Let f(i) be the third derivative of 0 + 1/15*i**3 - 2*i**2 + 0*i**4 - 1/75*i**5 + 0*i**6 + 1/525*i**7 + 0*i. Factor f(w).
2*(w - 1)**2*(w + 1)**2/5
Let g(q) = -q**3 + 13*q**2 - 46*q + 51. Let x be g(3). Factor x*s - 3/5*s**2 - 12/5.
-3*(s - 4)*(s - 1)/5
Let k(f) be the third derivative of 2*f**7/105 - f**6/5 - 356*f**2. Factor k(p).
4*p**3*(p - 6)
Let z be 2 - (32/4)/(-4) - (14 + -12). Determine m, given that 1/4*m**4 - 1/4*m**z + 0 + 1/4*m - 1/4*m**3 = 0.
-1, 0, 1
Let j be 61/(-122)*(1 + 4/((-28)/39)). Let -2/7*x**4 - j*x**3 + 80/7*x - 12/7*x**2 - 50/7 = 0. What is x?
-5, 1
Let k(v) be the first derivative of -v**6/72 + 13*v**5/24 - 5*v**4/2 + 16*v**3 - 12. Let l(a) be the third derivative of k(a). Factor l(f).
-5*(f - 12)*(f - 1)
Let h be 1523/(-7)*2*2/(-4). Let a = h - 217. Suppose 0 + 0*y + a*y**2 + 2/7*y**4 + 6/7*y**3 = 0. Calculate y.
-2, -1, 0
Let m(r) be the second derivative of 7/27*r**3 + 0 + 0*r**2 - 1/54*r**4 - 23*r. Find q such that m(q) = 0.
0, 7
Let q be (-63)/6*28/6. Let g = q + 51. What is k in 1/6*k**g + 0*k + 0 = 0?
0
Let d(r) be the first derivative of r**8/1344 - r**7/280 + r**5/60 - r**2/2 - 35. Let m(c) be the second derivative of d(c). Let m(f) = 0. What is f?
-1, 0, 2
Suppose 3*a + t = -82, 4*t + 49 + 71 = -4*a. Let b be 3/(4 + a/8). Factor 3*w - 3*w**2 - 6*w + 18*w**b - 19*w**4 + 2*w - 3*w**3.
-w*(w + 1)**3
Let o(w) be the first derivative of 35*w**4/4 - 5*w**3/3 - 70*w**2 + 20*w - 433. What is c in o(c) = 0?
-2, 1/7, 2
Let p = 480 - 17279/36. Let n(r) be the second derivative of 0*r**2 + 0*r**3 + 1/90*r**6 + 0 + 1/30*r**5 + p*r**4 - 7*r. Suppose n(b) = 0. What is b?
-1, 0
Let l(u) = -3*u**2 - 51*u - 13. Let f be l(-16). Let o be 25/f*(-12)/(-20). Factor 2/7*v - 1/7*v**2 + o.
-(v - 3)*(v + 1)/7
Let x(t) be the second derivative of 8/3*t**3 - 1/3*t**4 + 0 - 6*t**2 - 31*t. Factor x(w).
-4*(w - 3)*(w - 1)
Let b be (((-6)/4)/3)/((-10)/40). Solve -3/4*w**b + 0 - 3/4*w**3 + 0*w = 0 for w.
-1, 0
Let s(b) be the first derivative of 51*b**5/10 + b**4/4 - 51*b**3/2 - 27*b**2 - 2*b + 444. Let s(t) = 0. Calculate t.
-1, -2/51, 2
Suppose 3*g = -3*x - 12, -4 = 3*g + g. Let o be (x/(-2))/(15/20). Factor q**2 + 1 + q**2 - 3*q**o.
-(q - 1)*(q + 1)
Let f(v) = v**2 - 2*v - 1. Let u be f(4). Suppose -u + 1 = -3*k. Factor 5*x**2 - 3*x**k + 0*x**2 + 0*x - x**3 - x.
-x*(x - 1)**2
Let t = 204/109 - 707/436. Factor 2*a + 21/8*a**2 + t*a**4 + 11/8*a**3 + 1/2.
(a + 1)*(a + 2)**2*(2*a + 1)/8
Let s(i) be the third derivative of -i**6/60 - 2*i**5/15 - i**4/3 - 4*i**2 - 10*i. Suppose s(x) = 0. Calculate x.
-2, 0
Let c(y) = 12*y**2 - 11*y - 1. Let v be c(1). Let q(p) be the first derivative of v*p**5 + 1/2*p**6 + 0*p - 3/2*p**4 - 3 + 0*p**3 + 3/2*p**2. Factor q(f).
3*f*(f - 1)**2*(f + 1)**2
Determine w so that 4/3*w**4 - 10/3*w**2 + 0 + 8/3*w + 1/3*w**5 - w**3 = 0.
-4, -2, 0, 1
Let g = -1/3 - -19/21. Suppose 15*o - 23 - 7 = 0. Let 4/7*v**o - g*v**4 + 2/7*v**5 + 0*v**3 - 2/7*v + 0 = 0. Calculate v.
-1, 0, 1
Let t = 1/39 - -71/273. Factor -4/7*w**4 + 0 + t*w + 10/7*w**3 - 8/7*w**2.
-2*w*(w - 1)**2*(2*w - 1)/7
Factor -1/2*n**2 - 25538 - 226*n.
-(n + 226)**2/2
Factor -27*i - 71 - 5*i**2 + 107*i - 169.
-5*(i - 12)*(i - 4)
Let w(o) be th