)**3
Let v be 58/667*115 - (-102)/(-11). Suppose -48/11*p + 78/11*p**2 - 28/11*p**3 + v = 0. What is p?
2/7, 1/2, 2
Let f(a) = -3*a + 51. Let y be f(15). Factor 3*g**3 - 6*g**3 - 2*g**2 - y + 2 - 7*g + 4*g**3.
(g - 4)*(g + 1)**2
Let m be (-10)/(-36) - 12/72. Let g(x) be the first derivative of 1/3*x**2 - x + 3 + m*x**3. Factor g(d).
(d - 1)*(d + 3)/3
Let l(x) = 3*x + 15. Let f be l(-2). Let m(i) = i**3 - 10*i**2 + 14*i - 13. Let c be m(f). Find j such that -1/2 - c*j**2 - 8*j = 0.
-1/8
Factor 1 + 13/6*n - 11/2*n**2.
-(3*n - 2)*(11*n + 3)/6
Let l(n) be the first derivative of -4*n**5/5 - 7*n**4 - 56*n**3/3 - 16*n**2 + 80. What is m in l(m) = 0?
-4, -2, -1, 0
Let x be (91/14)/((-2)/(-4)). Let u = -9 + x. Let 1/2*r + 7/4*r**4 + u*r**3 + 11/4*r**2 + 0 = 0. Calculate r.
-1, -2/7, 0
Let k(s) = 12*s**2 + 249*s - 2409. Let q(w) = 7*w**2 + 125*w - 1205. Let n(g) = 5*k(g) - 9*q(g). Factor n(t).
-3*(t - 20)**2
Let o(i) = -i**2 + 2*i + 1. Let v be o(1). Factor -1181*k**v + 19*k + k + 1116*k**2 - 35*k**4 + 5*k**5 + 75*k**3.
5*k*(k - 4)*(k - 1)**3
Let p = -20904 - -83617/4. Determine a, given that -15/4*a - 11/4*a**5 - 35/2*a**3 - 25/2*a**2 - p - 45/4*a**4 = 0.
-1, -1/11
Let q = -68 + 74. Solve -z - z + 2*z**2 - q*z**2 + 2*z**2 = 0.
-1, 0
Factor -7/2*d**4 - 50/3*d**2 + 0*d + 0 + 1/6*d**5 + 20*d**3.
d**2*(d - 10)**2*(d - 1)/6
Suppose 24 = 5*a + 3*z - 13, -3*a - 5*z = -35. Suppose 25 = -0*x + a*x. Factor -6*b**2 - 3*b**3 - 12*b**x - 3*b**5 + 49*b**4 - 25*b**4.
-3*b**2*(b - 1)**2*(5*b + 2)
Let n(y) = -y**2 + 16*y + 3. Let o be n(16). Let s be (o*(-1)/2)/(-6). Factor -1/4*l**4 + s*l + 1/4*l**2 - 1/4*l**3 + 0.
-l*(l - 1)*(l + 1)**2/4
Let f be -2 - -2 - (4 + -6). Suppose -2*h + 3*q + 5 = 12, 0 = f*h + q - 13. Factor 4*b + 2*b**3 + 0*b**2 - 2*b + h*b**2.
2*b*(b + 1)**2
Factor 14*q + 4*q**4 + 4*q**3 - 4*q**2 - 34*q + 7*q + 13*q - 4*q**5.
-4*q**2*(q - 1)**2*(q + 1)
Let p(u) be the first derivative of -58/3*u**3 + 10*u**5 - 25/3*u**6 + 29/2*u**4 + 2 - 4*u**2 + 8*u. Let p(m) = 0. Calculate m.
-1, -2/5, 2/5, 1
Let w(h) be the second derivative of h**5/40 - 15*h**4/8 + 29*h**3/4 - 43*h**2/4 + 3*h - 229. Factor w(k).
(k - 43)*(k - 1)**2/2
Suppose -22/7*a**2 + 6/7*a**4 - 32/7*a - 8/7 + 8/7*a**3 = 0. What is a?
-2, -1, -1/3, 2
Let f be (-116)/1160*(-2 + -2). Factor -1/5*j**3 + 2/5 + 1/5*j - f*j**2.
-(j - 1)*(j + 1)*(j + 2)/5
Let k(x) = -4*x**2 + x - 7. Let v(w) = 5*w**2 - 1. Let y(a) = 4*a**2 - 1. Let q(c) = -5*v(c) + 6*y(c). Let o(s) = -k(s) + 5*q(s). Determine i so that o(i) = 0.
-2, 1
Let a(z) be the third derivative of z**5/20 + 5*z**4/24 - z**3/3 - 25*z**2. Let t be a(-2). Solve 3/2*f + t + 2*f**2 = 0.
-3/4, 0
Let k(j) be the third derivative of j**5/105 + 2*j**4/7 - 8*j**3/3 - 44*j**2. Factor k(g).
4*(g - 2)*(g + 14)/7
Factor -17/5*s + s**2 - 21/5 + 1/5*s**3.
(s - 3)*(s + 1)*(s + 7)/5
Let r(q) be the first derivative of 13 - 1/10*q**5 - 29/6*q**3 + 9/8*q**4 + 39/4*q**2 - 9*q. Factor r(c).
-(c - 3)**2*(c - 2)*(c - 1)/2
Suppose 3*q + r = 2*r + 19, -5*q - 5*r + 25 = 0. Suppose c - 2 = z - 4*z, q = 3*c + 3*z. Factor 2/5*f**c + 4/5*f - 2/5*f**3 + 0.
-2*f*(f - 2)*(f + 1)/5
Let f(l) = -l**3 - l + 10. Let o be f(2). Suppose 0 = 4*s - 3*s. Let 2/9*g**4 - 2/3*g**2 - 4/9*g + o*g**3 + s = 0. Calculate g.
-1, 0, 2
Let p be (3 - 440/144)*(54/(-6) - 1). Factor p*d + 1/9*d**2 + 2/3.
(d + 2)*(d + 3)/9
Let h(j) be the first derivative of -50*j**6 - 176*j**5/5 + 104*j**4 + 56*j**3 - 58*j**2 + 8*j - 43. Let h(q) = 0. What is q?
-1, 2/25, 1/3, 1
Let l(b) be the first derivative of -1/30*b**6 - 11 - 2/25*b**5 + 0*b + 0*b**2 - 1/20*b**4 + 0*b**3. Factor l(r).
-r**3*(r + 1)**2/5
Let n(o) be the third derivative of -o**5/80 + 17*o**4/16 - 289*o**3/8 + 29*o**2. Factor n(v).
-3*(v - 17)**2/4
Factor 56/3*c - 26/3*c**2 - 8/3.
-2*(c - 2)*(13*c - 2)/3
Factor 803*s**4 - 33*s - s**5 - 815*s**4 - 2*s**5 - 8*s**2 + 2*s**2 + 18 + 36*s**3.
-3*(s - 1)**3*(s + 1)*(s + 6)
Determine z so that 32/5*z**3 - 32/5*z + 14/5*z**4 - 8/5 - 6/5*z**2 = 0.
-2, -1, -2/7, 1
Let i(o) be the second derivative of -o**4/12 - 4*o**3/3 - 7*o**2/2 + 119*o. Solve i(w) = 0 for w.
-7, -1
Factor 10/11*a + 0 + 6/11*a**3 - 18/11*a**2 + 2/11*a**4.
2*a*(a - 1)**2*(a + 5)/11
Determine i so that 7 - 116*i + 31*i**3 + 1 + 2 - 2 - 108*i**4 + 100*i**2 + 85*i**3 = 0.
-1, 2/27, 1
Factor 0 + 1/4*a**2 + 1/2*a.
a*(a + 2)/4
Let d be ((-12)/7)/((-2)/14). Suppose d*u = 11*u + 10. What is h in -4*h**2 + 0*h**2 - 11 - u*h - 2*h + 3 = 0?
-2, -1
Let k be 6/(-138) - 11/(-253). Factor 3/7*r**3 + k*r - 6/7*r**2 + 0 + 3/7*r**4.
3*r**2*(r - 1)*(r + 2)/7
Let a(g) be the first derivative of g**4/20 - 41*g**3/15 + 44*g**2 - 80*g - 628. Let a(k) = 0. What is k?
1, 20
Suppose -2*c - 4 = 2*y, -2*c + 1 = 2*c - 5*y. Let l be c*-1*(10 - -1). Suppose -l*s - 3*s**2 - 9*s - s**2 - 12 + 4*s**3 = 0. What is s?
-1, 3
Let m = -6541 + 6544. Determine l, given that -2/9*l**4 - 2/9*l**5 + 0*l + 0*l**2 + 0 + 4/9*l**m = 0.
-2, 0, 1
Let c(i) be the first derivative of -3*i**5/5 - 21*i**4 - 270*i**3 - 1458*i**2 - 2187*i - 12. Find h, given that c(h) = 0.
-9, -1
Suppose -8*y - 4*v + 4 = -4*y, -5*y + v = -11. Let k(t) be the second derivative of 0 - 1/7*t**3 + 0*t**y + 3/140*t**5 - 1/28*t**4 - 11*t. Solve k(s) = 0 for s.
-1, 0, 2
Let p = 149 - 147. Factor -2*b**3 - 5*b**3 + 58*b**2 - 77*b**p + 3*b + 3*b.
-b*(b + 3)*(7*b - 2)
Let j = -60 + 41. Let a = 23 + j. What is v in 0 - 3*v**3 + 0*v**2 + 3/2*v**5 + 3/2*v + 0*v**a = 0?
-1, 0, 1
Let m(w) be the second derivative of 10*w + 1/30*w**5 + 0 + 2/3*w**3 - 4*w**2 - 1/4*w**4. Let b(l) be the first derivative of m(l). Factor b(i).
2*(i - 2)*(i - 1)
Let l = -19102 + 19104. Find q, given that -2*q + 3*q**l - 3/4*q**4 + 0 + 1/4*q**5 - 1/2*q**3 = 0.
-2, 0, 1, 2
What is m in -64 - 24*m**2 + 128*m**3 + 56*m**2 - 15*m**4 - 16*m**5 - 256*m + 11*m**4 = 0?
-2, -1/4, 2
Let o(g) be the first derivative of -20*g**3/3 + 185*g**2/2 - 45*g + 122. Factor o(r).
-5*(r - 9)*(4*r - 1)
Let z(v) be the first derivative of -v**3/2 + 159*v**2/2 - 8427*v/2 - 184. Let z(o) = 0. Calculate o.
53
Determine t so that -8/17*t**4 + 2/17*t + 0 + 8/17*t**5 - 6/17*t**3 + 4/17*t**2 = 0.
-1/2, 0, 1
Let d be (-16)/(-30) - (-1)/(-3). Let z(j) = 2*j**2 + 42*j + 2. Let x be z(-21). Factor 1/5*q**x + d + 2/5*q.
(q + 1)**2/5
Let p(y) = y**3 - 3*y**2 - 6*y - 17. Let g be p(5). Let i = -2588/9 + 288. Factor -2/3*u + i + 2/9*u**g + 0*u**2.
2*(u - 1)**2*(u + 2)/9
Suppose -2 + 2 = -15*z. Factor 3*k**2 - 3/2*k + 9/2*k**3 + z.
3*k*(k + 1)*(3*k - 1)/2
Suppose 3*p = 3*q - 9, 3*p - 12*q + 16*q = 12. Let r(v) be the second derivative of 0*v**2 + 0*v**3 - 1/20*v**5 - 1/30*v**6 + p - 3*v + 0*v**4. Factor r(t).
-t**3*(t + 1)
Let z(k) be the third derivative of -22*k**2 + 0*k**5 + 0 + 0*k**4 + 0*k - 1/30*k**6 + 0*k**3. Suppose z(s) = 0. What is s?
0
Let w = -20339 - -40699/2. Find d such that 147/4*d + 0 + 3/4*d**3 + w*d**2 = 0.
-7, 0
Let b be 2/(84/96 + 1). Factor -8/15 + b*r - 2/5*r**2.
-2*(r - 2)*(3*r - 2)/15
Let r(k) be the third derivative of k**6/10 - 13*k**5/15 + 2*k**4/3 + 34*k**2. Determine z so that r(z) = 0.
0, 1/3, 4
Suppose 0 + 2*x**3 - 52/11*x**2 - 2/11*x**4 + 32/11*x = 0. Calculate x.
0, 1, 2, 8
Let t be 0/(((-8)/(-5))/((-64)/160)). Find h, given that 4/11*h**3 + t + 2/11*h**4 + 0*h - 6/11*h**2 = 0.
-3, 0, 1
Let m(p) = -45*p**2 + 275*p + 125. Let c(r) = -22*r**2 + 137*r + 63. Let o(d) = -5*c(d) + 3*m(d). Factor o(y).
-5*(y - 6)*(5*y + 2)
Suppose 2*o + 0*o + 2 = 0, -2*o + 484 = 3*d. Let m(w) be the first derivative of -36*w**3 + 108*w**2 - 2/5*w**5 + 6*w**4 + 4 - d*w. Factor m(v).
-2*(v - 3)**4
Let q(f) = 562*f - 2248. Let s be q(4). What is j in 0*j - 2/5*j**5 + s + 2/5*j**3 - 4/5*j**2 + 4/5*j**4 = 0?
-1, 0, 1, 2
Let h(r) = -6*r**4 - 67*r**3 - 285*r**2 - 223*r + 307. Let c(v) = -3*v**4 - 34*v**3 - 142*v**2 - 112*v + 153. Let b(k) = -7*c(k) + 3*h(k). Solve b(o) = 0 for o.
-5, -3, 2/3
Let i be ((-16)/22)/((-606)/1111). Factor -5/3*z + 1/3*z**2 + i.
(z - 4)*(z - 1)/3
Let j(g) be the first derivative of 0*g**3 + 0*g - 34 + 1/12*g**4 - 1/6*g**2. Factor j(f).
f*(f - 1)*(f + 1)/3
Factor -24/5*b**2 + 288/5*b + 3/5*b**4 - 24/5*b**3 + 432/5.
3*(b - 6)**2*(b + 2)**2/5
Let z(f) be the third derivative of f**9/151200 - f**8/16800 + f**7/6300 - 3*f**5/20 + 38*f**2. Let l(m) be the third der