. Let y(m) = -9*m**2 - 13*m + 5. Let t(g) = a*u(g) + 4*y(g). Determine f, given that t(f) = 0.
-2, 0
Let h(i) be the third derivative of i**9/9072 + i**8/1344 + i**7/504 + i**6/432 + 3*i**4/8 - 4*i**2. Let n(f) be the second derivative of h(f). Factor n(x).
5*x*(x + 1)**3/3
Suppose -8*g - 7 + 55 = 0. Let o be (24 - 23)/(g/4). Factor -o*p + 0 - 1/3*p**2.
-p*(p + 2)/3
Let v(u) be the second derivative of 245*u**4/6 + 14*u**3 + 9*u**2/5 - 165*u. Factor v(d).
2*(35*d + 3)**2/5
Let -12*r - 40*r**2 - 92*r**3 + 32*r**5 - 5*r**4 + 152*r**3 + 125*r**4 = 0. Calculate r.
-3, -1, -1/4, 0, 1/2
Determine u so that -9*u**4 + 34*u**2 + 3*u**5 - 14*u**2 - 3*u**3 + 16*u**2 - 9*u**3 = 0.
-2, 0, 2, 3
Let a(p) be the third derivative of 17*p**5/12 + 15*p**4/2 + 10*p**3/3 - 18*p**2. Factor a(v).
5*(v + 2)*(17*v + 2)
Suppose -3*n - 2*s - 4 = 2*s, -5*n = 4*s - 4. Suppose 13 + 7 = n*w. Solve u**2 + 0*u**3 - 1 + 3*u**4 - u + 1 + w*u**3 = 0.
-1, 0, 1/3
Let s(n) = -n**2 + n. Let o(a) = -a**2 + 1. Let q(v) = 3*o(v) - 2*s(v). Factor q(c).
-(c - 1)*(c + 3)
Let m(q) be the first derivative of -3*q**5/20 + q**3/4 + 21. Factor m(g).
-3*g**2*(g - 1)*(g + 1)/4
Let f = 49 + -24. Let 10*k**4 - 2*k**2 - 4*k**2 + f*k**4 + 10*k**3 + k**2 + 20*k**5 = 0. Calculate k.
-1, 0, 1/4
Factor 34/15*l - 2/15*l**2 - 32/15.
-2*(l - 16)*(l - 1)/15
Let b(j) be the second derivative of 1/6*j**3 - 1/168*j**7 + 0 - 14*j + 1/30*j**6 - 1/80*j**5 + j**2 - 5/24*j**4. Factor b(n).
-(n - 2)**3*(n + 1)**2/4
Suppose -61*r**4 - 40*r**2 + 110*r**4 - 28*r**3 + 4*r**5 - 33*r**4 = 0. What is r?
-5, -1, 0, 2
Let p be (2/6)/(22/1188). Let q be (p/10 + -1)*(-1)/(-2). Solve q*h**2 - 6/5*h + 4/5 = 0 for h.
1, 2
Suppose 2*o - 347 = -0*o + 3*b, 5*b = -2*o + 371. Let f = -886/5 + o. Suppose f*j**2 - 6/5*j**5 + 16/5*j**4 + 0*j + 0 - 14/5*j**3 = 0. What is j?
0, 2/3, 1
Let k(g) = -g**3 + 7*g**2 + 4*g + 4. Let z be k(8). Let o be z*(0 - 1/4) + -5. Factor 2/3 + 2/3*h**o + 5/3*h.
(h + 2)*(2*h + 1)/3
Let i(t) be the third derivative of -2*t**7/525 + 7*t**6/150 + t**5/15 - 5*t**4/2 - 4*t**2 - 40*t. Let i(k) = 0. Calculate k.
-3, 0, 5
Let u(n) = -5*n**2 + 7. Let b(w) = 135*w**2 - 117 + 38 - 111. Let f(l) = -2*b(l) - 55*u(l). Determine j, given that f(j) = 0.
-1, 1
Factor -10/9*y**2 - 61/9*y + 1/9*y**3 + 70/9.
(y - 14)*(y - 1)*(y + 5)/9
Suppose -14*m - 5 = -15*m - 5*a, 3 = 3*a. What is f in -2/3*f**4 - 2/3*f**2 - 4/3*f**3 + m*f + 0 = 0?
-1, 0
Let x(o) = o**4 - o**3 - o**2 + 1. Let z(p) = 7*p**4 - 7*p**3 - 5*p**2 + 8. Let m(u) = -10*x(u) + 2*z(u). Let r(j) = -1. Let a(v) = m(v) + 6*r(v). Factor a(b).
4*b**3*(b - 1)
Let z(h) be the third derivative of -h**10/226800 - h**9/90720 + 19*h**5/60 - 7*h**2. Let j(b) be the third derivative of z(b). Factor j(i).
-2*i**3*(i + 1)/3
Factor 2/5*o**2 + 208/5*o - 42.
2*(o - 1)*(o + 105)/5
Let p = -32303 - -32305. Factor 8/3 + 1/3*a**p - 3*a.
(a - 8)*(a - 1)/3
Solve -10*o - 16*o - 96 + 17*o**3 + 14*o - 11*o**3 + 24*o**2 - 3*o**3 = 0.
-8, -2, 2
Let x = -281/5 + 5059/90. Let f(z) be the second derivative of -1/15*z**5 + 1/2*z**2 - 1/18*z**4 + 7*z + 2/9*z**3 + 0 - x*z**6. Factor f(v).
-(v - 1)*(v + 1)**2*(v + 3)/3
Let s(a) = -a**3 - 2*a**2 - a - 3. Let q(w) = w**3 + 2*w**2 + w + 4. Let x(k) = 3*q(k) + 4*s(k). What is o in x(o) = 0?
-1, 0
Let j(z) = -17*z**2 - 163*z - 2021. Let i(u) = -12*u**2 - 109*u - 1347. Let g(c) = -7*i(c) + 5*j(c). Let g(d) = 0. Calculate d.
-26
Let w(x) be the second derivative of -605*x**4/12 - 55*x**3/3 - 5*x**2/2 + 19*x. Factor w(y).
-5*(11*y + 1)**2
Let f = 8065/32 - 252. Let d(w) be the third derivative of 1/12*w**3 + 0*w + 1/240*w**5 - 8*w**2 + f*w**4 + 0. Factor d(c).
(c + 1)*(c + 2)/4
Let d(t) be the second derivative of -t**7/350 + t**6/100 + t**5/100 - t**4/20 - t**2/2 + t. Let i(x) be the first derivative of d(x). Factor i(u).
-3*u*(u - 2)*(u - 1)*(u + 1)/5
Let b = -5013/5 + 1003. Factor b*o**3 + 0 + 2/3*o**2 + 4/15*o.
2*o*(o + 1)*(3*o + 2)/15
Factor 6400/3 + 1/3*s**2 - 160/3*s.
(s - 80)**2/3
Let f(y) be the second derivative of -y**7/27720 + y**6/3960 - y**5/1320 - 4*y**4/3 - y. Let a(r) be the third derivative of f(r). Factor a(i).
-(i - 1)**2/11
Suppose 27/2*d**5 + 48*d**2 + 24*d - 12*d**3 - 36*d**4 + 0 = 0. What is d?
-2/3, 0, 2
Let b be (18 + -2)/((-13)/(234/(-45))). Let j = -2189/5 + 441. Determine o, given that -2/5*o**2 - b - j*o = 0.
-4
Let h(q) be the first derivative of -q**4 - 4*q**3/3 + 2*q**2 + 4*q - 39. Factor h(l).
-4*(l - 1)*(l + 1)**2
Suppose -5*f - 5*v + 7 + 8 = 0, 5*f = -4*v + 12. Suppose -5*t + k = -6, f = -3*t + k - 0*k + 2. Factor -7*s**t - 3*s - 2 + 2 + 4*s**2.
-3*s*(s + 1)
Suppose -4*k - 114 = 5*v, -3*k - 24 + 109 = -4*v. Let z be (4 - (-119)/(-28))*(v + 2). Factor -2/5*h**2 + 0*h - 6/5*h**3 + 0 - 2/5*h**z - 6/5*h**4.
-2*h**2*(h + 1)**3/5
Let o(r) be the second derivative of 2/9*r**3 - 1/36*r**4 + 0*r**2 + 0 + 6*r. Factor o(j).
-j*(j - 4)/3
Let v be -2 + 3 + (9 - -38). Suppose z - 5 = v. Solve 3*t**5 + 4*t**4 - t**3 + 53*t - z*t - 2*t**2 = 0.
-1, 0, 2/3
Let m be -4*5/(-40)*0. Find b, given that -66*b - b**2 + 68*b + m - 1 = 0.
1
Suppose 0 - 5*m + 7/2*m**2 + 19/2*m**3 - 19/2*m**4 + 3/2*m**5 = 0. What is m?
-2/3, 0, 1, 5
Let o(d) = -d - 2. Let f be o(-5). Suppose 0 = p - 0*n - n - 1, -4*n + 41 = 5*p. Factor -2*z**p + 3*z**2 + z**f + 2*z**4 - z**2 + z**3 - 4*z**4.
-2*z**2*(z - 1)*(z + 1)**2
Suppose 4*f - 95*f = -273. Determine k, given that -9/2*k**f + 6*k + 0 - 3/2*k**4 + 0*k**2 = 0.
-2, 0, 1
Solve 209*r + 28*r**3 + 12*r**2 + 49*r**2 + 31*r - 29*r**2 + 112*r**2 + 128 = 0 for r.
-2, -8/7
Let i(y) = 4*y + 132. Let x be i(-33). Let s(g) be the third derivative of 0*g + 4*g**2 - 1/16*g**4 + 1/6*g**3 + 1/120*g**5 + x. Factor s(t).
(t - 2)*(t - 1)/2
Let j = 743 + -8915/12. Let f(i) be the second derivative of j*i**4 - 8*i + 0 - i**2 + 1/6*i**3. Factor f(m).
(m - 1)*(m + 2)
Let t(u) be the third derivative of 3*u**7/980 - u**6/180 - u**5/210 + 2*u**3 + 11*u**2. Let z(p) be the first derivative of t(p). Factor z(q).
2*q*(q - 1)*(9*q + 2)/7
Let i(b) be the third derivative of 0 + 1/15*b**5 + 0*b - 1/4*b**4 - 2/3*b**3 - 1/168*b**8 + 1/15*b**6 + 0*b**7 + 11*b**2. Determine y so that i(y) = 0.
-1, 1, 2
Suppose -3*m + k = -13, -2*k = -3*m + k + 21. Solve -20 + 6*d - 29*d**2 + 24*d**2 - 23*d - m*d = 0.
-2
Let p = 11899/6 - 3965/2. Find b, given that -16/3 - p*b**3 - 8*b - 4*b**2 = 0.
-2
Let x(b) be the second derivative of -b**5/5 - 11*b**4/3 - 26*b**3 - 90*b**2 + 30*b + 3. Solve x(t) = 0.
-5, -3
Factor -23/4*t**2 + 25/2*t + 3/4*t**3 - 6.
(t - 4)*(t - 3)*(3*t - 2)/4
Let r be (-2 - 3*-2) + 0. Let t(q) = q + 5 - 2*q**3 + 3*q**3 - q**2 - r - 2*q. Let h(k) = 4*k**3 - 6*k**2 - 4*k + 6. Let s(u) = -h(u) + 5*t(u). Solve s(b) = 0.
-1, 1
Let p = -3358 + 10088/3. Find i such that 2/3*i**3 - 4/3*i**2 - 8/3 - p*i = 0.
-1, 4
Let g be ((16 - 16)*(-1 + 0))/2. Let w(c) be the third derivative of 5*c**2 - 1/44*c**4 + 1/660*c**6 + 0*c**5 - 2/33*c**3 + g*c + 0. Factor w(a).
2*(a - 2)*(a + 1)**2/11
Suppose 0 = 9*s - 5*s - 16. Let m(t) be the first derivative of 4/7*t - 6/7*t**3 + t**2 + s. Factor m(v).
-2*(v - 1)*(9*v + 2)/7
Let v(r) be the third derivative of r**7/420 - r**6/60 + r**5/120 + r**4/8 + 5*r**2 + 9*r. Suppose v(z) = 0. Calculate z.
-1, 0, 2, 3
Factor 162/19*n**2 + 0 - 216/19*n - 10/19*n**4 - 18/19*n**3 + 2/19*n**5.
2*n*(n - 3)**3*(n + 4)/19
Let z(s) be the third derivative of s**7/630 + 4*s**6/45 + 64*s**5/45 + 3*s**2 - 1. Factor z(h).
h**2*(h + 16)**2/3
Let p(f) = -f**3 - 3*f**2 + 4*f + 3. Let y be p(-5). Solve 640*s - 900*s**4 + 180 - 176*s**2 + 109 - y - 1440*s**3 = 0 for s.
-4/5, -2/3, 2/3
Let f = 755 + -753. Let i(p) be the second derivative of 0 - 4/3*p**3 - 6*p + 1/12*p**4 + 8*p**f. Factor i(r).
(r - 4)**2
Let m(f) be the third derivative of -19*f**6/80 - 14*f**5/15 + f**4/12 + 39*f**2 + 1. Determine i, given that m(i) = 0.
-2, 0, 2/57
Factor 18*b**2 - 19678 - 108*b**2 - 5*b**3 + 19578 + 195*b.
-5*(b - 1)**2*(b + 20)
Let b be (-3)/2*((-24)/(-9))/(-1). Let u(h) be the first derivative of -3*h**2 - 4/3*h**3 + 3/2*h**4 + b*h - 2. Factor u(q).
2*(q - 1)*(q + 1)*(3*q - 2)
Let p(y) be the second derivative of y**6/105 + 4*y**5/35 + 5*y**4/14 - 4*y**3/21 - 20*y**2/7 - y - 10. Determine x, given that p(x) = 0.
-5, -2, 1
What is k in -1/2*k**2 + 0 - k = 0?
-2, 0