.
(s - 2)*(s + 1)*(7*s - 2)**2/4
Let h(n) be the second derivative of n**7/147 - n**6/35 + n**5/35 + n**4/21 - n**3/7 + n**2/7 + 8*n. Determine y, given that h(y) = 0.
-1, 1
Let b(k) = -k**2 + 2*k - 9. Let m be b(-4). Let l = m + 33. Solve l*x + 1/2*x**2 - 1/2 = 0 for x.
-1, 1
Let y = -15 + 17. Suppose 0 = 3*w - 4 - y. What is m in m**w - 2*m + 4*m - 3*m = 0?
0, 1
Factor -16/11*i**2 - 2/11*i**3 + 38/11*i - 20/11.
-2*(i - 1)**2*(i + 10)/11
Let d(t) = t**3 - 58*t**2 - 62*t + 180. Let o be d(59). Let i(s) be the first derivative of -3/4*s**4 + 0*s + s**o + 0*s**2 + 2. Suppose i(a) = 0. Calculate a.
0, 1
Determine s so that 2/9*s**2 + 10/3*s - 32/9 = 0.
-16, 1
Let j = -2/5017 - -20078/25085. Find p such that -24/5*p**3 + 0 + 8/5*p**2 + 0*p - j*p**5 + 18/5*p**4 = 0.
0, 1/2, 2
Let m = 13659 + -13657. Factor f + 1/2*f**3 + 3/2*f**m + 0.
f*(f + 1)*(f + 2)/2
Let k(g) = g**5 - g**2 - g + 1. Let r(c) = 3*c**5 + 7*c**4 - 3*c**3 - 9*c**2 - 4*c + 6. Let f = -9 + 8. Let v(b) = f*r(b) + 6*k(b). Factor v(a).
a*(a - 1)**3*(3*a + 2)
Let w(f) be the second derivative of f**6/120 + 11*f**5/80 + 5*f**4/24 + 454*f. Find g, given that w(g) = 0.
-10, -1, 0
Let b = 5 + -2. Suppose 4*z - 3 = b*j, -3*z + z + 18 = 4*j. Factor 0 + 0*u**z + 4/5*u**2 - 4/5*u**4 + 2/5*u**5 - 2/5*u.
2*u*(u - 1)**3*(u + 1)/5
Suppose 0*d - 14 = -4*d + r, 0 = 5*r - 10. Suppose -4*y + 5 = -9*y, -4*l = y - 7. Factor -d + 8*c**3 + 42*c - c**l + 4*c**4 + c**2 - 50*c.
4*(c - 1)*(c + 1)**3
Let w(c) = 2*c**3 - 1. Let r(p) = 5*p**4 - 104*p**3 + 270*p**2 - 260*p + 87. Let h(x) = r(x) + 2*w(x). Factor h(m).
5*(m - 17)*(m - 1)**3
Let f be 186/63 + (64/112)/(-2). Let c(t) be the third derivative of 0 - 11*t**2 + 0*t - f*t**3 + 1/15*t**5 - 1/3*t**4 + 1/60*t**6. Solve c(z) = 0 for z.
-2, 2
Let o(b) be the second derivative of -b**4/6 - 14*b**3/15 + 3*b**2/5 + 51*b. Factor o(v).
-2*(v + 3)*(5*v - 1)/5
Let m(o) be the third derivative of o**5/90 - o**4/12 + 2*o**3/9 + 128*o**2. Factor m(z).
2*(z - 2)*(z - 1)/3
Let t(f) be the third derivative of -f**8/1176 - 4*f**7/245 - 8*f**6/105 + f**5/3 + 75*f**4/28 - 250*f**3/21 - 94*f**2. Find m, given that t(m) = 0.
-5, 1, 2
Suppose -v = -5*f + 21, 27*f - 30*f = -5*v + 5. Find i such that -9*i - 3 + 9/4*i**4 + 3/4*i**f - 33/4*i**2 - 3/4*i**3 = 0.
-2, -1, 2
Let u(n) be the second derivative of -n**8/224 + n**7/70 + n**6/80 - n**5/20 + 5*n**2/2 - 12*n. Let d(w) be the first derivative of u(w). Solve d(l) = 0 for l.
-1, 0, 1, 2
Let a(s) be the third derivative of 1/120*s**6 + 0 + 0*s - 1/20*s**5 - 6*s**2 + 2*s**3 + 0*s**4. Let d(u) be the first derivative of a(u). Factor d(k).
3*k*(k - 2)
Let z(o) be the second derivative of 9*o + 1/15*o**5 + 7/9*o**4 - 2/15*o**6 + 0*o**3 - 8/3*o**2 - 2/63*o**7 + 0. Let z(y) = 0. Calculate y.
-2, -1, 1
Solve 175*m**5 + 218*m**5 - 60*m**4 - 397*m**5 = 0.
-15, 0
Suppose 0*q - 4*s - 52 = -q, -5*q + 4*s = -308. Suppose -q = -55*g + 23*g. Factor 1/5*b + 1/5 - 1/5*b**g - 1/5*b**3.
-(b - 1)*(b + 1)**2/5
Let d(b) be the first derivative of -2*b**2 - 7 + 4/3*b**3 + 0*b. Factor d(k).
4*k*(k - 1)
Let n(w) be the third derivative of w**11/3160080 - w**10/1436400 - w**5/5 - 2*w**2. Let y(r) be the third derivative of n(r). Find z such that y(z) = 0.
0, 1
Let y be 1608/(-16)*(-28)/6. Find x, given that 5*x**2 - 5*x - 474*x**3 + y*x**3 + 5*x**2 = 0.
0, 1
Let q be 1 - 1 - (-5 + 3). Suppose 22 - q = 4*p. What is c in 15*c**2 + 9 + 21*c + 0 - 2*c**3 + p*c**3 = 0?
-3, -1
Let a(s) be the second derivative of -1/30*s**6 + 13*s + 0*s**2 + 0*s**4 + 0*s**3 + 0 + 1/20*s**5. Solve a(u) = 0.
0, 1
Let q be (354/(-84) + 4)/(36/(-7)). Let n(w) be the second derivative of 1/24*w**4 + 10*w + q*w**3 - 1/80*w**5 + 0 - 1/4*w**2. Factor n(s).
-(s - 2)*(s - 1)*(s + 1)/4
Solve 23*q - 183*q**3 + 362*q**3 - q - 53*q**2 - 184*q**3 = 0 for q.
-11, 0, 2/5
Suppose -7*a = -a - 12. Solve 6*q + 11*q**4 - 5*q**4 + 10*q**3 - 3*q**4 - 14*q**a - 5*q**4 = 0 for q.
0, 1, 3
Suppose 2*j - 3*v = -8, -5*v + 16 = -2*j - 0*v. Suppose j*u - 3*h + 9 = 0, -4*u + 3*u = -4*h + 12. Factor u - r**3 + 5/3*r**2 - 2/3*r.
-r*(r - 1)*(3*r - 2)/3
Let s(p) be the second derivative of -p**6/30 - p**5/4 - p**4/6 + 4*p**3/3 - 3*p. What is y in s(y) = 0?
-4, -2, 0, 1
Let j = 62 - 62. Let o(r) = 3*r**2 - 2*r + 2. Let u be o(1). Suppose -1/4*f**4 + 0*f**2 + j*f + 1/4*f**u + 0 = 0. What is f?
0, 1
Let d(w) = -2*w**5 - 7*w**4 - w**3 + 4*w**2 + 3*w - 3. Let t(b) = -b**5 - b**4 + b - 1. Let u(n) = -d(n) + 3*t(n). Let u(s) = 0. Calculate s.
-1, 0, 1, 4
Let w(j) be the second derivative of j**6/60 + j**5/10 - 4*j**3/3 - 4*j**2 + 23*j. Determine k so that w(k) = 0.
-2, 2
Factor -4/3 + 2/3*g**2 + 2/3*g.
2*(g - 1)*(g + 2)/3
Let h(x) be the first derivative of -x**3/9 + 5*x**2/2 - 18*x + 8. Factor h(u).
-(u - 9)*(u - 6)/3
Let d(n) be the first derivative of n**6/2160 - n**5/720 - n**4/72 + 2*n**3/3 + 18. Let u(a) be the third derivative of d(a). Determine c so that u(c) = 0.
-1, 2
Let n(m) be the second derivative of m**7/210 - m**6/30 - 3*m**5/50 - m + 100. Factor n(c).
c**3*(c - 6)*(c + 1)/5
Suppose -21 = -u - 4*w, -u - 2*w + 13 = -0*w. Suppose -4*o + v + 0*v = -21, u*o + 4*v = 0. Factor -4*h**2 - 1 + 1 - 221*h**o + 225*h**4.
4*h**2*(h - 1)*(h + 1)
Let p be (20/28)/(((-55)/2)/(-11)). Factor p*k**3 - 6/7*k**2 + 0 + 0*k.
2*k**2*(k - 3)/7
Let x(t) = t**2 + 27*t + 185. Let b be x(-15). Let 0 + 7/2*r**4 + 0*r + 0*r**3 - 2*r**2 + 3/2*r**b = 0. What is r?
-2, -1, 0, 2/3
Find n, given that 0*n**2 - 3/2*n**4 - 1/3*n**5 - 2/3*n**3 + 0*n + 0 = 0.
-4, -1/2, 0
Let q(c) be the second derivative of -c**6/15 + 11*c**5/25 - 4*c**4/15 + 110*c. Factor q(j).
-2*j**2*(j - 4)*(5*j - 2)/5
Let x be 12*4/8 + -2. Suppose 2*s + 2*k + 2 = s, -x*k - 20 = -2*s. Factor 33*v**3 + v**s + 5*v**5 + 9*v**4 - 28*v**3.
5*v**3*(v + 1)**2
Let w(d) be the second derivative of -d**4/6 - 25*d**3/4 + 19*d**2/4 + 5*d + 3. Factor w(t).
-(t + 19)*(4*t - 1)/2
Let g(l) = l**2 - 5*l + 4. Let t(o) = 4*o**2 + 5 - 31*o + 12 + 10*o. Let c(d) = 9*g(d) - 2*t(d). Factor c(z).
(z - 2)*(z - 1)
Let s(u) = -u**3 - 3*u**2 + 8*u + 11. Let c be s(-5). Determine o so that o**3 - 16*o**2 + 2*o + 2*o**3 + c*o**2 = 0.
-1, -2/3, 0
Determine y so that 33/4*y**3 + 0*y**4 - 3/4*y**5 + 18 - 21*y - 9/2*y**2 = 0.
-3, -2, 1, 2
Let b = -32561 + 553567/17. Factor -4/17*n**2 - b*n**4 + 0 + 0*n - 22/17*n**3.
-2*n**2*(3*n + 1)*(5*n + 2)/17
Let s(h) = -4*h**3 + 4*h**2 + 16*h - 28. Let q(g) = g**2 + g + 1. Let x(j) = 4*q(j) + s(j). Find n, given that x(n) = 0.
-2, 1, 3
Let 48*h**2 + 5*h**5 + 90*h**3 + 52*h**2 + 35*h**4 + 41*h + 12*h - 13*h = 0. What is h?
-2, -1, 0
Let r be -10*(-9 + 0 - 2*(-153)/36). Factor 0*z + 0 - 20/7*z**r + 0*z**2 + 0*z**3 - 12/7*z**4.
-4*z**4*(5*z + 3)/7
Let i(g) be the second derivative of -g**6/150 + 3*g**5/100 - g**4/30 + 48*g. Factor i(r).
-r**2*(r - 2)*(r - 1)/5
Suppose 2*j = -0 + 12. Let z(u) be the second derivative of 0*u**3 + 33/140*u**5 + 0*u**2 + 0 + 1/14*u**4 - 3*u + 9/70*u**j. What is y in z(y) = 0?
-1, -2/9, 0
Let g be (-4)/54*(-2)/(-3). Let q = g + 583/324. What is f in 0 - 1/2*f**2 - 3/4*f**4 - q*f**3 + 0*f = 0?
-2, -1/3, 0
Let -11*s**2 - 2*s**3 + 22*s**4 + 35*s**5 - 33*s**5 + 37*s**2 - 48*s**3 = 0. What is s?
-13, 0, 1
Let n(c) = -c**3 - c**2 - c - 4. Let i(x) = 2*x**3 - 6*x**2 + 20*x + 40. Let t(k) = i(k) + 4*n(k). Find z such that t(z) = 0.
-6, -1, 2
Let j be (7/(-2) + 0 - 1)*28. Let z be (6/5)/(j/(-140)). Factor 6*n**3 + z + 10/3*n - 32/3*n**2.
2*(n - 1)**2*(9*n + 2)/3
What is h in 24*h + 8 - 5 + 3*h**2 + 7 + 8 + 3 = 0?
-7, -1
Let q(s) be the second derivative of s**4/36 - 4*s**3 + 71*s**2/6 + 3*s + 2. Factor q(h).
(h - 71)*(h - 1)/3
Let w = 38795 + -38793. Factor 0*f + 0*f**w + 6/5*f**3 + 3/5*f**5 + 0 + 9/5*f**4.
3*f**3*(f + 1)*(f + 2)/5
Factor 75*v + 200 - 4*v**2 - 48 + 40 + 113*v.
-4*(v - 48)*(v + 1)
Let f = 1/933 - -241/65310. Let r(l) be the third derivative of -f*l**5 + 0*l + 0*l**3 + 0 + 1/84*l**4 + 2*l**2. Find x such that r(x) = 0.
0, 1
Let o be (1 + 3 - 2) + 2. Let 2 + 0 + 2*n - o*n - 8*n**2 - 4*n = 0. Calculate n.
-1, 1/4
Let n(i) = -3*i + 5. Let r = 29 + -29. Let k be n(r). Factor 3*a + 12*a + k*a**2 + 0*a.
5*a*(a + 3)
Find z, given that -4/21*z**3 + 8/21*z**2 - 4/21 - 4/21*z**4 + 2/21*z**5 + 2/21*z = 0.
-1, 1, 2
Let n(t) be the second derivative o