1. Let h(k) = q*v(k) + 4*c(k). What is w in h(w) = 0?
-1, 1
Suppose 25 = -3674*i + 3679*i. Let q(y) be the first derivative of -4 + 0*y**i + 0*y + 8/3*y**3 + 0*y**2 - 3*y**4 + 2/3*y**6. Find t such that q(t) = 0.
-2, 0, 1
Let b be 17/4 - (-2)/(-8). Let j be (b/(-7))/(8/(-28)). Factor 0*q - 1/5*q**j + 1/5.
-(q - 1)*(q + 1)/5
What is a in -3*a**4 + 6*a + 6*a**3 + 300 + 91*a**2 - 1425 - 156*a + 29*a**2 = 0?
-5, -3, 5
Factor 3/4 - 3/2*w + 3/4*w**2.
3*(w - 1)**2/4
Let v(o) be the first derivative of -1/6*o**2 - 19 - 1/6*o - 1/18*o**3. Determine p, given that v(p) = 0.
-1
Let m(a) be the third derivative of -1/56*a**4 + 1/280*a**6 + 0 - 1/70*a**5 + 1/7*a**3 + 0*a + 25*a**2. Determine w, given that m(w) = 0.
-1, 1, 2
Let k(i) be the second derivative of -i**6/15 + i**5/6 + i**4/9 + 51*i. Factor k(v).
-2*v**2*(v - 2)*(3*v + 1)/3
Suppose 8 = 2*p + d, -5*d + 7 = 4*p + 3. Let v(q) = -14*q**2 - 3*q - 23. Let n(m) = -5*m**2 - m - 8. Let r(x) = p*v(x) - 17*n(x). Factor r(o).
(o - 2)*(o + 1)
Let a(x) be the second derivative of -x**7/63 + x**6/45 + x**5/15 + 3*x - 27. Factor a(f).
-2*f**3*(f - 2)*(f + 1)/3
Let 5618/11 - 2/11*x**5 + 218/11*x**4 - 6260/11*x**3 - 17066/11*x + 17492/11*x**2 = 0. Calculate x.
1, 53
Let z(v) be the first derivative of v**6/360 + v**5/20 + 3*v**4/8 - 13*v**3/3 - 8. Let r(d) be the third derivative of z(d). Factor r(x).
(x + 3)**2
Let w(p) = 7*p**2 + p - 5. Let q(g) = g**2 - g + 1. Let i(r) = 3*q(r) - w(r). Let v(m) = m - 1. Let c(x) = i(x) + 8*v(x). Factor c(t).
-4*t*(t - 1)
Let n(v) be the third derivative of v**6/120 - v**5/40 - 3*v**4/4 + 8*v**3/3 + 10*v**2. Let s(a) be the first derivative of n(a). Factor s(u).
3*(u - 3)*(u + 2)
Let n = 359/1068 - 1/356. Let a(w) be the second derivative of n*w**3 + 1/36*w**4 + 4*w + 0 + 3/2*w**2. Solve a(s) = 0.
-3
Factor 42 - 93 + 501*j**3 + 70*j - 63*j**4 - 18*j**4 + 957*j**3 - 1404*j**2 + 392*j.
-3*(j - 17)*(3*j - 1)**3
Let c = 16732/7 + -83646/35. Suppose -2*l - 6/5 + 2/5*l**3 - c*l**2 = 0. Calculate l.
-1, 3
Let w(m) be the third derivative of -m**9/37800 - m**8/16800 + m**5/60 - 5*m**4/12 - 2*m**2 - 7*m. Let z(t) be the third derivative of w(t). Factor z(f).
-2*f**2*(4*f + 3)/5
Suppose 0*v + 1/7*v**3 + 0 - 9/7*v**2 = 0. What is v?
0, 9
Let f be (-5008)/(-240) - 21 - (-32)/90. Let c(j) be the first derivative of f*j**3 + 4/15*j**5 - 1/18*j**6 + 0*j**2 + 7 - 5/12*j**4 + 0*j. Factor c(x).
-x**2*(x - 2)*(x - 1)**2/3
Find v, given that 4/11*v**2 + 8/11*v**4 + 0 + 2/11*v**5 + 0*v + 10/11*v**3 = 0.
-2, -1, 0
Suppose -13*q + 1772 - 238 = 0. Let r = q - 233/2. Factor 0*z + 0 - r*z**2.
-3*z**2/2
Determine l so that -2*l**2 - 1492 - 13996 + 299*l + 53*l = 0.
88
Let l(g) be the first derivative of -12/5*g + 0*g**3 + 7/5*g**2 - 1/10*g**4 + 19. Factor l(t).
-2*(t - 2)*(t - 1)*(t + 3)/5
Let n(r) be the third derivative of r**6/60 - 7*r**5/10 + 33*r**4/4 - 45*r**3 + 712*r**2. Suppose n(v) = 0. What is v?
3, 15
Let x = 69887143/224 + -311997. Let h = 1/32 - x. Factor -h*a - 10/7*a**2 + 4/7.
-2*(a + 1)*(5*a - 2)/7
Suppose 3*o = -2*o + 10. Let u(g) = -g**3 - 2*g**2 + g + 2. Let b(s) = 3*s**3 + 5*s**2 - 3*s - 5. Let h(x) = o*b(x) + 5*u(x). Factor h(f).
f*(f - 1)*(f + 1)
Let k(f) be the third derivative of -f**8/6720 + f**7/504 - f**6/90 + f**5/30 + f**4/3 + 5*f**2. Let q(w) be the second derivative of k(w). Factor q(v).
-(v - 2)**2*(v - 1)
Let i(h) = h**3 - h**2 - h. Let r be i(2). Suppose 27*n**2 + 46*n + 49*n**r + 16 - 34*n**2 + 10*n**3 - 2*n**4 = 0. What is n?
-1, 8
Factor 1250/3 + 4052/3*l**2 - 1556/3*l**3 - 2/3*l**5 - 3850/3*l + 106/3*l**4.
-2*(l - 25)**2*(l - 1)**3/3
Let r(h) be the third derivative of -3*h**8/560 - h**7/70 - 7*h**6/600 - h**5/300 + 937*h**2. Factor r(b).
-b**2*(b + 1)*(3*b + 1)**2/5
Suppose -5 + 9 = 2*c. Let d be (32/(-22) + c)*1. Factor d*v**2 + 14/11*v - 12/11.
2*(v + 3)*(3*v - 2)/11
Solve 171/8*p**3 - 63/4 - 531/8*p**2 + 501/8*p - 15/8*p**4 = 0 for p.
2/5, 1, 3, 7
Let g(f) be the first derivative of -f**4/10 + 2*f**3/3 - 4*f**2/5 + 120. Let g(j) = 0. Calculate j.
0, 1, 4
Let -852 + 425 - 25*k**3 - 5*k**4 + 40*k**2 + 60*k + 427 = 0. What is k?
-6, -1, 0, 2
Suppose -446*f = 102*f - 2192. Factor 0*s**f + 0*s**3 + 0*s**2 + 0 - 1/3*s**5 + 0*s.
-s**5/3
Let y = -3650/3 - -1218. Factor y*v**2 + 20/3*v - 8.
4*(v - 1)*(v + 6)/3
Let v(u) be the first derivative of -u**7/420 - u**6/90 + u**5/60 + u**4/6 - 3*u**3 + 7. Let b(d) be the third derivative of v(d). Factor b(r).
-2*(r - 1)*(r + 1)*(r + 2)
Find o, given that -1/5*o**3 + 125 - 135*o + 51/5*o**2 = 0.
1, 25
Suppose 3*v = 7*v + 5*c - 35, -4*c + 28 = 0. Let x be ((-2)/(-4))/(2/8). Suppose v*n**x + 3/8*n**3 + 0*n + 0 + 1/8*n**4 = 0. Calculate n.
-3, 0
Let f = 50 - 48. Suppose -t + f*p + 20 = 6, -t + 4*p = -24. Find q, given that 0*q + 1/3*q**3 + 0 - 1/6*q**2 - 1/6*q**t = 0.
0, 1
Factor -82*h**2 + 27*h**2 + 2*h**4 + 29*h**2 + 22*h**2 + 2*h**3.
2*h**2*(h - 1)*(h + 2)
Let k(q) = q**3 - 3*q**2 + 6*q - 2. Let l(w) = 7*w**3 - 18*w**2 + 37*w - 13. Let a(x) = -39*k(x) + 6*l(x). Find v such that a(v) = 0.
-4, 0, 1
Let t(a) be the second derivative of a**8/320 + 3*a**7/280 + a**6/120 + 19*a**4/12 + 43*a. Let k(r) be the third derivative of t(r). Find f such that k(f) = 0.
-1, -2/7, 0
Let o be ((-32)/(-88) - 126/165)*(-5 + 0). Factor -18/5 - 1/5*k**3 - 8/5*k**o - 21/5*k.
-(k + 2)*(k + 3)**2/5
Let l(g) = g**5 + g**4 + 2*g**3 + g**2. Let j(r) = 7*r**5 - 20*r**4 + 71*r**3 - 62*r**2 + 24*r. Let d(o) = -j(o) + 4*l(o). What is q in d(q) = 0?
0, 1, 2, 4
Let b(p) be the second derivative of 7*p**5/100 + 3*p**4/20 - 2*p**3/5 - 2*p**2/5 + 38*p + 1. Factor b(n).
(n - 1)*(n + 2)*(7*n + 2)/5
Let g = -13276 - -92934/7. Factor -2/7 + g*l**2 - 2/7*l**3 + 2/7*l.
-2*(l - 1)**2*(l + 1)/7
Suppose -6 = -5*q + 39. Suppose -6*a - 6 = -q*a. Factor -1/3*n**a + 0 - 1/3*n.
-n*(n + 1)/3
Factor -170*h - 7*h**2 - h**2 - 221 + 3*h**2 - 99 + 0.
-5*(h + 2)*(h + 32)
Let s(n) be the second derivative of n**4/72 - 25*n**3/18 - 25*n + 3. What is k in s(k) = 0?
0, 50
Let m(u) be the third derivative of u**7/630 + u**6/90 - u**4 + u**2. Let c(l) be the second derivative of m(l). Factor c(k).
4*k*(k + 2)
Let a(w) = 2*w**2 - 7*w + 6. Let f be a(3). Let b be 30/(-12) + 0 + f. Suppose 1/2 + 0*h - b*h**2 = 0. What is h?
-1, 1
Determine t so that -36/7 + 10/7*t**2 - 86/7*t = 0.
-2/5, 9
Let l be (-3243)/115 + 36 - (5 - (2 - 4)). Factor -2/5*w**3 + 0 + 6/5*w**2 - l*w.
-2*w*(w - 2)*(w - 1)/5
Let q(s) be the first derivative of s**5/110 - s**4/66 - 41*s - 33. Let i(b) be the first derivative of q(b). Determine g so that i(g) = 0.
0, 1
Factor -2/23*y + 50/23 + 2/23*y**3 - 50/23*y**2.
2*(y - 25)*(y - 1)*(y + 1)/23
Let i(c) = 2*c**3 - 2*c**2 + 1. Let a(f) = 14*f**3 + 2*f**2 - 40*f - 91. Let g(h) = a(h) - 5*i(h). Factor g(v).
4*(v - 3)*(v + 2)*(v + 4)
Let j = 4864/5 + -972. Factor 0 + 0*f**2 - j*f + 4/5*f**3.
4*f*(f - 1)*(f + 1)/5
Let t(p) = p**2 + 4*p + 6. Let q be t(-4). Suppose -7*z + 27 = -q*z. Find j, given that 4*j**4 + j**2 + z*j**5 - 5*j**2 - 25*j**5 - 2*j = 0.
-1, 0, 1
Let q = -119449/3 - -39817. Let -14/3 - q*d**2 + 16/3*d = 0. Calculate d.
1, 7
Suppose c = 3 - 1. Suppose 0 = -4*o + 16, -c*z - 4*o + o = -20. Solve -x**z - x**2 + 158*x + 2*x**3 - 158*x = 0.
0, 1
Let v(s) be the second derivative of 24*s + 0*s**2 + 0 + 2*s**3 + 1/10*s**5 - 5/6*s**4. Factor v(g).
2*g*(g - 3)*(g - 2)
Let n = -24 + 27. Factor 10*u**2 - n*u**3 - 3*u**2 + 3*u - 4*u**2 - 3.
-3*(u - 1)**2*(u + 1)
Let m(t) be the third derivative of -t**5/12 + 5*t**4/12 + 25*t**3/2 - 122*t**2. Suppose m(q) = 0. What is q?
-3, 5
Let g(i) be the first derivative of -1/6*i**2 + 1/8*i**4 + 1/30*i**5 - 1/36*i**6 + 0*i + 8 - 1/18*i**3. Determine b, given that g(b) = 0.
-1, 0, 1, 2
Let k(q) = 2*q**2 - 204*q - 197. Let p(s) = 4*s**2 - 612*s - 592. Let m(f) = 8*k(f) - 3*p(f). Factor m(w).
4*(w + 1)*(w + 50)
Let a(m) = -13*m**2 + 33*m**2 - 17*m**2 - 4 - 3*m. Let o be a(-1). Factor -1/4*r**3 - 1/2*r**o + 1/4*r**4 + 0 + 0*r.
r**2*(r - 2)*(r + 1)/4
Suppose 5*p = -h + 31, 2*h + 3*p - 32 = -p. Factor -h*t**2 + 7*t**2 + 2*t**2 - 3*t**4.
-3*t**2*(t - 1)*(t + 1)
Suppose -3 = -2*n + 4*o + 23, -4*n = -5*o - 37. Suppose 0 = -4*g + 8*g - 16. Factor -g*d - 49*d**4 + 7*d**n + 24*d**2 - 24*d**3 - 4*d**3.
-d*(d + 1)*(7*d - 2)**2
Let d(o) = 10*o + 12. Let q(