 1)
Let r(a) be the second derivative of -343/11*a**2 - 49/11*a**3 - 1/110*a**5 - 7/22*a**4 - 6*a + 0. Determine z so that r(z) = 0.
-7
Suppose b - 4*t - 13 = 0, b - 141 = -4*b + t. Factor b*c**4 - 4*c**3 - 4*c**3 - 25*c**4.
4*c**3*(c - 2)
Let z be (12/(-24))/((-1)/6). Suppose 12 = -z*b, -l - 17 = -6*l + 3*b. What is g in -1/2*g**4 + l - 3/2*g**3 + 3/2*g - 1/2*g**2 = 0?
-2, -1, 1
Let l(w) be the third derivative of -11*w**2 + 0*w - 1/15*w**5 + 0*w**3 + 2/105*w**7 + 1/84*w**8 + 0*w**4 + 0 - 1/30*w**6. Factor l(m).
4*m**2*(m - 1)*(m + 1)**2
Let k(r) be the first derivative of r**9/10584 + r**8/2940 + r**7/2940 + 38*r**3/3 - r**2 + 14. Let g(w) be the third derivative of k(w). Factor g(i).
2*i**3*(i + 1)**2/7
Let d(p) be the first derivative of p**6/5 - 3*p**5/25 - 9*p**4/5 + 22*p**3/5 - 21*p**2/5 + 9*p/5 - 109. Solve d(t) = 0 for t.
-3, 1/2, 1
Let k = 2187 - 2187. Let 2/7*b**3 + k*b + 0*b**2 + 0 = 0. Calculate b.
0
Let r(k) = 2*k + 283. Let m be r(0). Let 48*c**3 + 15*c**5 + m*c - 283*c + 12*c**2 + 51*c**4 = 0. Calculate c.
-2, -1, -2/5, 0
Solve -18*c - 2/7*c**2 - 124/7 = 0 for c.
-62, -1
Suppose -2*w + 18 = 4*w. Suppose -7*g + 30*g**2 + 18*g**4 - 2*g - w*g**5 + 0*g**4 - 36*g**3 = 0. What is g?
0, 1, 3
Let a(t) be the third derivative of -t**7/315 - 7*t**6/90 - 4*t**5/5 - 40*t**4/9 - 128*t**3/9 - 86*t**2. Factor a(i).
-2*(i + 2)*(i + 4)**3/3
Suppose 7*p**2 + 14*p - 6*p**2 + 196 - 42*p = 0. Calculate p.
14
Let h(m) be the second derivative of -3/10*m**6 + 0*m**4 - 1/10*m**5 + 0*m**3 + 0 + 0*m**2 - 1/6*m**7 - 7*m. Factor h(s).
-s**3*(s + 1)*(7*s + 2)
Let i = -5749832/5 - -1156295. Let o = -6309 + i. Find g, given that -154/5*g**3 - 16/5 - 132/5*g**2 + o*g**4 + 104/5*g = 0.
-1, 2/7, 2
Suppose -2*g + 7*g = 15. Find u such that 2*u**3 + 1 + g*u**2 - 8*u + 3 - 2 + 2 - u**4 = 0.
-2, 1, 2
Let i be ((-36)/(-54))/((-105)/(-45)). Factor 3/7 - 1/7*g**2 - i*g.
-(g - 1)*(g + 3)/7
Let m(g) be the third derivative of g**7/5460 - g**6/780 - g**5/195 - 2*g**3/3 + 3*g**2. Let v(a) be the first derivative of m(a). Factor v(s).
2*s*(s - 4)*(s + 1)/13
Let d(j) be the third derivative of -j**6/900 + j**5/150 - 4*j**3/45 - 2*j**2 - 25*j. Suppose d(z) = 0. What is z?
-1, 2
Let z be 20/3*(0 + (-9)/(-6)). Let o be z/4 - ((-6)/(-4) + -2). Suppose 0*t + 2/5*t**4 + 2/5*t**o + 0 + 0*t**2 = 0. Calculate t.
-1, 0
Find r such that 0 + 0*r + 6*r**3 - 40/3*r**4 - 2/3*r**2 = 0.
0, 1/5, 1/4
Factor 3*b**3 + 10*b**2 - 4*b**3 - 9*b**2 + 6*b - 2*b**2.
-b*(b - 2)*(b + 3)
Let g(k) be the third derivative of k**6/420 + 4*k**5/21 + 13*k**4/28 - 19*k**2. What is d in g(d) = 0?
-39, -1, 0
Let f(k) = 24*k**4 + 20*k**3 - 32*k**2 - 12*k. Let m(j) = -j**4 - j**3 + j**2 + j. Let g be -1 - ((0/(-3) - -1) + -1). Let q(w) = g*f(w) - 20*m(w). Factor q(i).
-4*i*(i - 1)**2*(i + 2)
Let a(j) be the first derivative of 22 + 0*j + 57/25*j**5 - 3/2*j**6 - 3/5*j**2 + 3/4*j**4 - 7/5*j**3. Solve a(k) = 0 for k.
-2/5, -1/3, 0, 1
Let a(v) = -5 - 22*v + v**2 + 5*v**4 + 4*v**2 - 15*v**3 + 79*v - 37*v. Let t(n) = 5*n**4 - 15*n**3 + 6*n**2 + 20*n - 6. Let b(g) = 6*a(g) - 5*t(g). Factor b(s).
5*s*(s - 2)**2*(s + 1)
Let q(n) be the second derivative of 1/5*n**2 + 0 + 13*n - 1/30*n**4 - 1/15*n**3 + 1/50*n**5. Determine k, given that q(k) = 0.
-1, 1
Let p = 16040/3 - 5345. Factor p*b**2 + 320/3 - 80/3*b.
5*(b - 8)**2/3
Let m(o) be the second derivative of 3*o**5/140 - 2*o**3/7 + 113*o. Solve m(j) = 0.
-2, 0, 2
Factor 2/9*s**5 + 0*s - 26/9*s**3 + 14/9*s**2 + 0 + 10/9*s**4.
2*s**2*(s - 1)**2*(s + 7)/9
Let c(s) be the second derivative of s - 1/6*s**3 + 5/48*s**4 + 0 + 0*s**2 - 1/80*s**5. Factor c(r).
-r*(r - 4)*(r - 1)/4
Let o(m) be the second derivative of m**7/10 + 33*m**6/50 + 24*m**5/25 - 3*m**4/5 + m - 11. Suppose o(t) = 0. Calculate t.
-3, -2, 0, 2/7
Let o(f) = -3*f**2 - 4*f + 27. Let m be o(6). Let g = 737/7 + m. Let 0 - g*c**2 + 4/7*c = 0. Calculate c.
0, 2
Factor 64/5*l + 0 + 2/5*l**2.
2*l*(l + 32)/5
Let s = 2078 - 6232/3. Factor -2/3*l**2 + s - l.
-(l + 2)*(2*l - 1)/3
Let z(n) = -n**2 + n + 2. Let o be z(2). Suppose -3*w + t + 3 = o, -w - t = 4*t - 17. Find k such that -4*k**w + k + k - 14*k - 10 + 2 = 0.
-2, -1
Let g = 10 + -7. Let y(q) = -q**3 - 7*q**2 + 4*q + 4. Let r be y(-8). Determine n so that 2 - 46*n - 2*n**g + 8*n**2 + 2 + r*n = 0.
1, 2
Let z(m) be the first derivative of -14*m**6/3 - 104*m**5/5 - 27*m**4 - 16*m**3/3 + 8*m**2 + 147. Solve z(l) = 0.
-2, -1, 0, 2/7
Let n(d) be the first derivative of -5*d**6/6 - 15*d**5 - 90*d**4 - 180*d**3 - 4. Factor n(m).
-5*m**2*(m + 3)*(m + 6)**2
Let s(t) be the first derivative of t**6/105 - t**5/35 + 2*t**3/21 - t**2/7 + 17*t + 19. Let d(k) be the first derivative of s(k). Factor d(a).
2*(a - 1)**3*(a + 1)/7
Let v be (-6)/(-15) + (-1 - 136/(-10)). Let p be (-2)/((-2)/v - (-5)/(-390)). Determine r, given that 6*r - 3/4*r**2 - p = 0.
4
Let h(g) = 10*g + 362. Let p be h(-36). Let -17*u**4 + 27/2*u**3 - 21/2*u**5 + 0 + 12*u**2 + p*u = 0. Calculate u.
-2, -1/3, -2/7, 0, 1
Suppose 5*c - 8*c - 12 = 0. Let j be (32 + -33)/(c - 1). Suppose -2/5*w - j - 1/5*w**2 = 0. What is w?
-1
Let a(b) be the second derivative of -b**7/280 - b**6/120 + b**5/20 + 2*b**3/3 + 2*b. Let x(w) be the second derivative of a(w). Factor x(k).
-3*k*(k - 1)*(k + 2)
Let l be 14/4*(-56)/(-98). Factor -2*a - 4*a**l - 14 + 6*a + 14.
-4*a*(a - 1)
Let s(d) be the third derivative of -d**9/252 - d**8/112 - d**7/280 + 5*d**3/3 + 5*d**2. Let t(f) be the first derivative of s(f). Factor t(h).
-3*h**3*(h + 1)*(4*h + 1)
Suppose 31*o**2 + 3*o**3 - 11*o**2 - o**3 + o**3 + 2*o**3 = 0. What is o?
-4, 0
Let b be -5*(-14)/1085 - (-151)/62. Factor -b*d - 5/4*d**2 - 5/4.
-5*(d + 1)**2/4
Let p(m) = m**2 + 8*m + 16. Let t be p(-7). Factor -t*g**3 + 2*g**2 + 0*g**2 + 3*g + 4*g**2.
-3*g*(g - 1)*(3*g + 1)
Suppose 0 = -10*k + 9 + 11. Let n(y) be the second derivative of 1/30*y**4 + 0 - 1/75*y**6 - 1/50*y**5 + 0*y**k + 2*y + 1/15*y**3. Factor n(a).
-2*a*(a - 1)*(a + 1)**2/5
Let j(x) be the second derivative of x**4/12 + 13*x**3/15 - x - 176. Factor j(p).
p*(5*p + 26)/5
Suppose 210 = b + 199. Let a be (-4)/(-2) + (1 - 1). Solve q**a + 3*q**2 + 7*q - b*q - 3 - 5 = 0 for q.
-1, 2
Solve 0 + 6/7*i - 3/7*i**5 - 3/7*i**3 - 19/7*i**2 + 19/7*i**4 = 0 for i.
-1, 0, 1/3, 1, 6
Let r = 23 + -20. Factor 33*w**r + 11*w**3 + w**3 + 3*w - 10*w**2 + 27*w**4 + 31*w**2.
3*w*(w + 1)*(3*w + 1)**2
Let h(l) be the first derivative of 5*l**6/6 + 4*l**5 - 10*l**4 - 320*l**3/3 - 280*l**2 - 320*l - 107. Factor h(r).
5*(r - 4)*(r + 2)**4
Suppose -3*x + 24 = -11*x. Let i(g) = 2*g**2 - 2*g - 1. Let q(o) = -3*o**2 + 3*o + 2. Let v(k) = x*q(k) - 4*i(k). Factor v(m).
(m - 2)*(m + 1)
Let p = -7 + 17. Let y be 8/p*30/12. Factor -2/3*g**4 + 0 + 0*g**3 + 0*g + 2/3*g**y.
-2*g**2*(g - 1)*(g + 1)/3
Let c(b) = 2*b**2 - 15*b - 3. Let s(t) be the third derivative of t**5/20 - 5*t**4/8 - t**3/3 - 8*t**2. Let n(h) = 2*c(h) - 3*s(h). Factor n(v).
-5*v*(v - 3)
Let j(d) be the third derivative of d**5/120 - 11*d**4/24 + 7*d**3/4 + 160*d**2. Suppose j(x) = 0. Calculate x.
1, 21
Let a(g) be the second derivative of g**5 + 0*g**4 + 0*g**2 + 2/3*g**6 + 0 + 0*g**3 - 5*g + 5/42*g**7. Factor a(c).
5*c**3*(c + 2)**2
Factor -187*a**2 - 44 + 32 - 85*a - 16*a**5 - 171*a**3 + 12*a**5 - 61*a**4.
-(a + 1)**3*(a + 12)*(4*a + 1)
Let k = -159/19 - -496/57. Factor 8/3*c - 5/3*c**2 + k*c**3 - 4/3.
(c - 2)**2*(c - 1)/3
Suppose 4*j = 3*u - 209, 4*j = -3*u + 113 + 80. Suppose -69*x = -u*x. Suppose -2/3*i**2 + x + 2/3*i = 0. What is i?
0, 1
Determine q so that -39*q - 190*q**2 + 187*q**2 + 9*q + 33 = 0.
-11, 1
Let t(k) be the second derivative of k**8/23520 - k**6/840 - k**5/210 - 7*k**4/12 + 8*k. Let s(u) be the third derivative of t(u). Solve s(v) = 0.
-1, 2
Solve -2*i**2 + 5/4*i**3 - 1/4*i**4 + i + 0 = 0 for i.
0, 1, 2
Let j(t) be the first derivative of 2*t**3/21 - 214*t**2/7 + 22898*t/7 - 283. Factor j(o).
2*(o - 107)**2/7
Let z(u) be the third derivative of 7*u**6/150 + 44*u**5/75 + 2*u**4/5 - 8*u**2 + 4*u. Factor z(c).
4*c*(c + 6)*(7*c + 2)/5
Let q(z) = -z**2 + 12*z - 1. Let u(w) = w + 6. Let b be u(-9). Let r be b/((-12)/4)*-3. Let i(j) = -6*j. Let t(h) = r*q(h) - 5*i(h). Factor t(v).
3*(v - 1)**2
Suppose 6*h - 7*h = 4, 4*v + h - 8 = 0. Let l(z) be the second derivative of 0 + 4/3*z*