2/4
Suppose -q = -4*k - 0*q + 12, 5*k - 15 = -5*q. Find z such that 3*z + 0*z + z**5 - 313*z**3 + 309*z**k + 2*z**2 - 2 = 0.
-2, -1, 1
Suppose -2*g = 4*k - 26, 0 = 3*g + 2*k + 3*k - 38. Solve 16*x**4 + 4*x**3 + 4*x**5 - 80*x - 42*x**2 - 32 + 7*x**2 + g*x**2 - 32*x**2 = 0.
-2, -1, 2
Let s be ((-1)/(-2))/(102/(-36) - -3). Factor -9/7 - 22/7*k**2 - 1/7*k**4 - 8/7*k**s - 24/7*k.
-(k + 1)**2*(k + 3)**2/7
Let c(j) be the third derivative of 0*j**3 + 1/30*j**4 - 1/50*j**5 + 0*j + 1/300*j**6 + 23*j**2 + 0. Factor c(q).
2*q*(q - 2)*(q - 1)/5
Let q(j) be the second derivative of j**7/21 + 18*j**6/35 + 15*j**5/14 + 8*j**4/21 - 4*j**3/7 - 23*j - 1. Solve q(a) = 0.
-6, -1, 0, 2/7
Let f = 22 + -5. Find o, given that 5*o**2 + 30*o - 27*o + f*o + 4 + 11 = 0.
-3, -1
Let n(y) = -y - 4. Let h(z) = z**2 - 69*z + 1229. Let c(v) = -h(v) - n(v). Factor c(p).
-(p - 35)**2
Find f, given that 40/11*f + 16/11 - 2/11*f**5 - 8/11*f**4 + 28/11*f**2 - 2/11*f**3 = 0.
-2, -1, 2
Let a(g) be the second derivative of -5*g**4/72 + 5*g**3/36 + 25*g**2/3 - 160*g. Factor a(n).
-5*(n - 5)*(n + 4)/6
Let r(m) be the first derivative of 3*m**4/4 - 87*m**3 + 7569*m**2/2 - 73167*m + 99. Determine h, given that r(h) = 0.
29
Let h be 1/(-4) - (-381)/(-12). Let s = h + 42. Factor -2 - 3*b**2 - 1 - 16*b + s*b.
-3*(b + 1)**2
Find w, given that 236/3*w + 2/9*w**2 + 6962 = 0.
-177
Factor -34*q**2 + 13*q**4 - 8*q**4 - 2*q**4 + 20*q - 44*q**3 + 7*q**4.
2*q*(q - 5)*(q + 1)*(5*q - 2)
Let 8/5 - 22/5*v + 14/5*v**2 = 0. Calculate v.
4/7, 1
Suppose 4*u - 5*l + 3*l = 12, -9 = 3*u + 3*l. Suppose 0 = -g - u + 3. Solve -1/3*v + 1/6*v**g + 0 = 0 for v.
0, 2
Let r = -24 + 26. Factor 1/6*p**r + 1/3*p + 0 - 1/6*p**3.
-p*(p - 2)*(p + 1)/6
Factor 405*c**3 - 2*c**4 + 43930*c**2 + 5*c**4 + 13467*c - 30061*c**2.
3*c*(c + 1)*(c + 67)**2
Find u, given that 33*u - 83*u + 5*u**2 - 50*u + 0*u**2 = 0.
0, 20
Let o(u) be the first derivative of -2*u**5/65 - 16*u**4/13 - 16*u**3 - 896*u**2/13 - 1568*u/13 - 99. Factor o(a).
-2*(a + 2)**2*(a + 14)**2/13
Let x(a) = -a + 13. Suppose 4*o = -3*h + 31, -54 = -5*h + 4*o - 13. Let k be x(h). Factor -3*r + 8*r**3 - 4*r**5 + 4*r - r - k*r.
-4*r*(r - 1)**2*(r + 1)**2
Let r(n) = n**3 - 10*n**2 + 10*n - 18. Let h be r(9). Let u be -2*h/12 + 5/(-5). Factor u*s + 1/8 + 3/4*s**2 + 1/2*s**3 + 1/8*s**4.
(s + 1)**4/8
Let p be (-172)/(-301) - -2*(-4)/14. Let w(n) be the second derivative of 0 + 1/70*n**5 + p*n**4 - 1/7*n**3 - 9*n - 2/7*n**2. Factor w(d).
2*(d - 2)*(d + 1)**2/7
Let h(d) = -25*d**3 + 240*d**2 - 145*d + 35. Let x(a) = -2*a**3 + 20*a**2 - 12*a + 3. Let t(c) = 3*h(c) - 35*x(c). Let t(r) = 0. What is r?
0, 1, 3
Let f be (6/8)/((-1 - -2)/(-4)). Let t be (-46)/(-24) - f/(-18). Find q such that 5/4*q + 1/2 - t*q**2 = 0.
-2/7, 1
Let s(d) be the third derivative of d**6/280 + 2*d**5/35 + 2*d**4/7 + 65*d**2. Determine z so that s(z) = 0.
-4, 0
Let w(x) be the second derivative of -x**9/5040 + x**8/3360 + 3*x**4/4 - 11*x. Let h(l) be the third derivative of w(l). Factor h(p).
-p**3*(3*p - 2)
Let q be ((-2)/(-7))/((-3)/(-105)). Factor -q*y**3 - 3*y**2 + 47*y - 44*y - 9*y**4 - 5*y**3.
-3*y*(y + 1)**2*(3*y - 1)
Let u(p) be the third derivative of p**8/420 + 4*p**7/525 - p**6/50 + p**2 + 35*p. Factor u(o).
4*o**3*(o - 1)*(o + 3)/5
Suppose w - 4*g = 3860, -w + 3865 = -7*g + 2*g. Suppose 836*s**2 + w*s + 60*s**4 + 812 + 1084*s**2 + 3*s**5 + 2260 + 480*s**3 = 0. What is s?
-4
Let c(q) = -4*q. Let x(h) = h**2 + 15*h - 26. Let p(i) = c(i) + x(i). Factor p(g).
(g - 2)*(g + 13)
Suppose 0 = -4*s + 3*k - 12, -s - 3*k + k = -8. Let t(a) be the second derivative of -1/6*a**4 + s - 1/6*a**3 - 1/20*a**5 + 0*a**2 + 3*a. Factor t(i).
-i*(i + 1)**2
Let v(a) be the second derivative of 3*a**6/50 + 27*a**5/100 - a**4/60 - a**3/10 + 81*a. Let v(b) = 0. What is b?
-3, -1/3, 0, 1/3
Factor -27/7*u**3 + 3/7 + 45/7*u**2 - 3*u.
-3*(u - 1)*(3*u - 1)**2/7
Factor -10/3*j**4 + 4/3*j**3 + 0 + 0*j + 0*j**2.
-2*j**3*(5*j - 2)/3
Let v(y) be the first derivative of 4*y**3/3 + 8*y**2 - 20*y + 29. Solve v(k) = 0.
-5, 1
Suppose -3*r = 3*i, -4*i - 29 = -2*r - 11. Suppose -r*l = -l - 10. Suppose -5 - 1 + 9*x**3 + 4 + 16*x**2 + l*x = 0. What is x?
-1, 2/9
Suppose 10 = -2*w + 3*o - 1, 4*o + 12 = -4*w. Let a(y) = -y**2 - 5*y - 2. Let q be a(w). Find u, given that 1 - 1 + 6 - 9*u + 3*u**q = 0.
1, 2
Let x(w) = -w**3 - 4*w**2 + 2. Let a be x(-4). Suppose -1 = -q - 0, -k + 6 = a*q. What is m in 0 + 1 + k - 4 - m**2 = 0?
-1, 1
Solve 50*m**4 - 428*m**2 - 166*m**3 + 134 + 28 + 369*m + 16*m**2 - 3*m**5 = 0 for m.
-2, -1/3, 1, 9
Let x(j) = j**4 + j**3 + j**2 + j. Let a(u) = 5*u**4 - 10*u**3 + 14*u**2 + 2*u. Let n(q) = -a(q) + 2*x(q). What is y in n(y) = 0?
0, 2
Suppose 0 = -4*c - l + 2204, -4*c - 3*l + 2030 + 182 = 0. Determine d, given that -8*d - 293*d**2 + c*d**2 - 293*d**2 + 16*d**4 - 12*d**3 = 0.
-1, -1/4, 0, 2
Let a(v) be the second derivative of v**8/192 - 2*v**7/63 + v**6/36 - v**4 + 7*v. Let s(f) be the third derivative of a(f). Let s(h) = 0. What is h?
0, 2/7, 2
Let v be 2 + -18*5/50. Let r(y) be the third derivative of 1/60*y**6 + 0 - 5*y**2 + y**4 + 8/3*y**3 + 0*y + v*y**5. Factor r(n).
2*(n + 2)**3
Solve 3/2*u**3 + 0*u + 7/4*u**2 + 0 - 1/4*u**4 = 0.
-1, 0, 7
Let r(m) be the second derivative of -10/3*m**3 - 5/12*m**4 + 0 - 10*m + 10*m**2 + 1/4*m**5. Factor r(k).
5*(k - 2)*(k - 1)*(k + 2)
Let i(m) be the first derivative of -m**4/8 - 4*m**3/3 - 5*m**2/4 + 7*m - 66. Factor i(f).
-(f - 1)*(f + 2)*(f + 7)/2
Factor 1374*l - 3861*l + 328 - 1033*l**2 + 272 - 39*l**3 + 259*l**2 - 1293*l.
-3*(l + 10)**2*(13*l - 2)
Let y be 46/20 - 73/((-14235)/(-156)). Factor 0 - 3/4*u + y*u**2 - 3/4*u**3.
-3*u*(u - 1)**2/4
Let w(j) = 10*j**2 + 85*j + 110. Let v(i) = i**2 + i - 1. Let n(p) = 2*v(p) + w(p). Let l(h) = 3*h**2 + 22*h + 27. Let y(d) = -15*l(d) + 4*n(d). Factor y(r).
3*(r + 3)**2
Find x such that 141 + 328*x + 183 + 152*x**2 - 148*x**2 = 0.
-81, -1
Let y = 3 + 8. Suppose -r = -y - 12. Factor r*w - 20*w**2 + 6*w**3 - 3*w - w**3.
5*w*(w - 2)**2
Let n(k) be the third derivative of -k**7/280 - k**6/60 + 4*k**3 - 14*k**2. Let t(p) be the first derivative of n(p). Factor t(b).
-3*b**2*(b + 2)
Let l(x) be the first derivative of x**5/170 + 2*x**4/51 - x**3/51 - 4*x**2/17 - 42*x - 22. Let f(a) be the first derivative of l(a). Factor f(g).
2*(g - 1)*(g + 1)*(g + 4)/17
Suppose 12*u - 15 = 7*u. Let h(j) = j**5 - j**3 - 3*j**2 + 3*j + 3. Let t(m) = -2*m**5 + 2*m**3 + 8*m**2 - 8*m - 8. Let l(d) = u*t(d) + 8*h(d). Factor l(b).
2*b**3*(b - 1)*(b + 1)
Let q be -1*(-3 + -4)*1. Factor 6*k**3 - 10*k**2 - 4*k**4 + 2*k**3 + q*k**3 - k**4.
-5*k**2*(k - 2)*(k - 1)
Let r(o) be the second derivative of -1/20*o**3 - 18*o + 0 - 1/120*o**4 + 0*o**2. Suppose r(x) = 0. Calculate x.
-3, 0
Let y(i) = -15*i**4 - 141*i**3 - 525*i**2 + 189*i - 9. Let r(a) = 2*a**4 - a**2 + a + 3. Let c(f) = 3*r(f) + y(f). Factor c(b).
-3*b*(b + 8)**2*(3*b - 1)
Let m(l) be the second derivative of 0 + 2/135*l**6 + 0*l**2 - 1/90*l**5 + 0*l**4 - 1/189*l**7 + 0*l**3 + 8*l. Determine k so that m(k) = 0.
0, 1
Let x = -818 - -820. Factor 2/9*r**x + 0 - 10/9*r.
2*r*(r - 5)/9
Suppose 2*w - 79 = -11. Suppose 0 = 2*l + w - 42. Solve 1/3*r**l + 0 + 2/3*r**3 + 0*r + 1/3*r**2 = 0 for r.
-1, 0
Let p(a) be the third derivative of a**8/560 + a**7/35 + a**6/8 - 140*a**2 - 1. Find w, given that p(w) = 0.
-5, 0
Let h(y) = 3*y**4 + 4*y**3 - 1. Let c(x) = -x**4 + x**3 - 1. Let t(v) = -c(v) + h(v). Find n such that t(n) = 0.
-3/4, 0
Let c(m) be the third derivative of m**8/1344 + m**7/168 + m**6/240 - m**5/12 - m**4/4 - 29*m**2 + 8. Suppose c(v) = 0. What is v?
-3, -2, 0, 2
Let q be 17 + (180 + 0)/(-12). Factor -3/5*g - 3/5*g**q + 0.
-3*g*(g + 1)/5
Let i(a) be the third derivative of 0*a**5 - 1/448*a**8 + 0*a**7 - 10*a**2 + 0*a**4 + 0*a**6 + 0*a + 0 + 0*a**3. Factor i(j).
-3*j**5/4
Let w be (-144)/81 + 2 - 25/(-9). Determine z so that 1/4*z**4 - 1/4*z**2 + 0 + 0*z**w + 0*z = 0.
-1, 0, 1
Let b be (-9)/(-6)*155/(-93)*48/(-345). Solve -2/23*n**2 + 0*n + b*n**4 + 0 + 6/23*n**3 = 0 for n.
-1, 0, 1/4
Factor 1160*x**5 + 12*x**2 + 14*x**2 + 48*x**3 + 2*x**3 - 1162*x**5 + 22*x**4.
-2*x**2*(x - 13)*(x + 1)**2
Let m(y) be the second derivative of -y**5/50 + 2*y**4/15 - 59*y. Factor m(l).
-2*l**2*(l - 4)/5
Let n(y) = -y**4 - 6