14 - 34*i.
(i - 1)*(i + 14)*(3*i - 2)/2
Let v(a) be the second derivative of a**6/70 - 3*a**5/28 + 9*a**4/28 - a**3/2 + 3*a**2/7 + 42*a. Determine q, given that v(q) = 0.
1, 2
Let g(n) = -n. Let z(i) = i**2. Let q be (1 - 0)/(1/(-3)). Let t(o) = q*g(o) + 6*z(o). Factor t(x).
3*x*(2*x + 1)
Let j(r) = -r**4 + r**3 + r**2 + 11*r + 2. Let y(i) = 2*i**4 - 4*i**3 - 3*i**2 - 26*i - 4. Let v(c) = 5*j(c) + 2*y(c). Solve v(u) = 0 for u.
-2, -1, 1
Let t(d) be the second derivative of -d**6/30 + 3*d**5 - 177*d**4/2 + 810*d**3 - 6561*d**2/2 + 3*d - 4. Factor t(v).
-(v - 27)**2*(v - 3)**2
Let r be ((-20)/3)/(-5)*6. Suppose -47 = -5*b + r. Factor -b*t + 3*t**5 + 14*t + 0*t**4 - 6*t**3 + 0*t**4.
3*t*(t - 1)**2*(t + 1)**2
Solve 40841*d + 88*d**3 - 20842*d + 22593*d + 2904*d**2 + d**4 + 234256 = 0 for d.
-22
Let v(n) = 8*n**4 - 15*n**3 - 5*n**2 + 15*n - 3. Let y(u) = 15*u**4 - 30*u**3 - 10*u**2 + 30*u - 5. Let a(m) = 5*v(m) - 3*y(m). Factor a(h).
-5*h*(h - 3)*(h - 1)*(h + 1)
Factor 0*m**3 + 12/5*m**2 - 4/5*m**4 + 0 - 8/5*m.
-4*m*(m - 1)**2*(m + 2)/5
Let h = 186 + -186. Suppose h + 1/3*i**3 + 0*i**2 + 1/3*i**5 + 0*i + 2/3*i**4 = 0. What is i?
-1, 0
Suppose 3*z - 2*s - 35 = 0, -3 + 23 = 3*z - 5*s. Factor -3*m**2 + z*m**3 - 6*m**4 + 6*m**4 - 12*m**2 + 5*m - 5*m**4.
-5*m*(m - 1)**3
Let c(a) = -a**2 - 15*a - 24. Let w be c(-13). Let l(m) be the first derivative of 1/4*m + 1/12*m**3 - 10 + 1/4*m**w. Factor l(s).
(s + 1)**2/4
Let b be (5 - 3)*(1 - 0). Let s be 736/96 - (-7)/(-1). Suppose 1/6*t**3 + 5/6*t + s*t**b + 1/3 = 0. Calculate t.
-2, -1
Factor -92*v**5 - 9*v**4 + 169*v**3 - 4*v**2 + 4*v**2 - 17*v**4 + 93*v**5.
v**3*(v - 13)**2
Let m(a) be the third derivative of -1/240*a**6 + 4/3*a**3 + 0 - 1/6*a**4 - 9*a**2 + 0*a - 7/120*a**5. Factor m(g).
-(g - 1)*(g + 4)**2/2
Let q be ((1485/(-75))/(-11))/(-2 + 54/20). Factor 3*g**4 - q*g**2 + 0 - 33/7*g**3 + 0*g.
3*g**2*(g - 2)*(7*g + 3)/7
Let l(m) be the first derivative of 2*m - 2/9*m**3 + 2/3*m**2 - 6. Factor l(p).
-2*(p - 3)*(p + 1)/3
Suppose 0*s - 5*s = 150. Let i be -2 - ((-55)/s - 4). Suppose -i*m**3 - 5/6*m + 1/3 + 2/3*m**2 = 0. Calculate m.
1, 2
Let n = -1/25 - -27/50. Let k(x) be the third derivative of 0*x + 2*x**3 + 0 + 9*x**2 + 1/20*x**5 - n*x**4. Solve k(h) = 0 for h.
2
Factor -80/9*f**2 + 2/9*f**5 + 50/9*f + 20/3*f**3 - 4/3 - 20/9*f**4.
2*(f - 6)*(f - 1)**4/9
Let f(d) be the second derivative of d**6/6 + 33*d**5/2 + 1455*d**4/4 - 5940*d**3 + 29160*d**2 - 654*d. Factor f(y).
5*(y - 3)**2*(y + 36)**2
Let d(k) = 3*k + 25. Let f be d(-6). Find u such that 0*u**2 - 37*u - 12 - 28 - f*u - 4*u**2 = 0.
-10, -1
Suppose -3*s = -16 + 1. Let d be 1/s + (-87)/(-15). Factor 9*q + 79*q**2 - 3*q**3 - 79*q**2 - d.
-3*(q - 1)**2*(q + 2)
Let h(n) = -5*n**2 - 8*n + 16. Let k(a) = 2*a**2 - 2*a + 1. Let i be k(2). Let y(q) = 4*q**2 + 8*q - 16. Let r(p) = i*h(p) + 6*y(p). Let r(v) = 0. Calculate v.
4
Let i = -3009 + 1854. Let x be 3 + (i/(-5))/3. What is v in 6*v**2 - 3*v**2 + 2*v**2 + x - 40*v = 0?
4
Let b(y) = 33*y**3 + 183*y**2 - 186*y - 15. Let o(r) = 2*r**3 - r**2 + r - 1. Let f(i) = b(i) - 15*o(i). Determine n so that f(n) = 0.
-67, 0, 1
Let b(s) be the third derivative of s**10/226800 - s**8/15120 + s**6/1080 + 11*s**5/60 - 8*s**2. Let o(w) be the third derivative of b(w). Factor o(i).
2*(i - 1)**2*(i + 1)**2/3
Let z(f) = 6*f**2 - 17*f - 2. Let t(n) = -12*n**2 + 33*n + 4. Suppose -4*v = -1 + 25. Let a(w) = v*t(w) - 11*z(w). Factor a(c).
(c - 2)*(6*c + 1)
Let c(k) be the first derivative of -12 - 8/19*k + 5/19*k**2 - 2/57*k**3. Suppose c(w) = 0. What is w?
1, 4
Let g(f) be the second derivative of -1/12*f**3 - 1/24*f**4 + 0*f**2 + 0 + 1/40*f**5 + 17*f + 1/60*f**6. Find z, given that g(z) = 0.
-1, 0, 1
Suppose -3675/2*p**2 + 210*p - 6 = 0. Calculate p.
2/35
Let m(l) = 2*l**2 - 49*l - 25. Let x be m(25). Suppose x = -3*h - 7*h. Factor -1/2*r + 1/4*r**4 + h*r**3 - 3/4*r**2 + 0.
r*(r - 2)*(r + 1)**2/4
Let t(u) be the second derivative of 44*u**7/63 - 74*u**6/45 + 17*u**5/15 - 2*u**4/9 - 41*u. Solve t(r) = 0 for r.
0, 2/11, 1/2, 1
Let t(s) be the third derivative of s**6/120 - s**5/30 - 5*s**4/24 + s**3 - 101*s**2 + 2. Determine o so that t(o) = 0.
-2, 1, 3
Let r be -3*1*(-4 - -3). Factor 3*y**3 + 2*y - r*y - y**3 + 2*y**2 - 3*y.
2*y*(y - 1)*(y + 2)
Let -3*p**3 + 6/5*p**4 + 0*p + 9/5*p**2 + 0 = 0. What is p?
0, 1, 3/2
Let j be -9 + (-9 + 7)*-10. Let p(t) be the second derivative of 0*t**2 + 0 - 2/3*t**3 + 1/3*t**4 + j*t. Factor p(c).
4*c*(c - 1)
Let p(a) = 3*a**3 + 126*a**2 - 395*a + 277. Let t(v) = v**3 + 32*v**2 - 99*v + 69. Let h(j) = -6*p(j) + 22*t(j). Factor h(n).
4*(n - 6)**2*(n - 1)
Let w(n) = -n**2. Let c be (-12)/8*8/(-6). Let g(m) = -8*m**3 - 23*m**2 - 4*m + 2. Let i(z) = c*g(z) - 18*w(z). Suppose i(d) = 0. Calculate d.
-1, 1/4
Suppose 1/3*l**4 + 0 + 8/3*l - 1/3*l**2 - 8/3*l**3 = 0. What is l?
-1, 0, 1, 8
Let x(n) = -n**2 - 4*n - 1. Let o be x(-3). Suppose -15 + 11 = -o*l. Determine j, given that -j + 2*j**2 + 4*j**4 - j**3 + 4*j**5 - 5*j**l - j**4 - 2*j**5 = 0.
-1, -1/2, 0, 1
Let w = 47 - 44. Factor 3*b**3 - 3*b**3 - w*b**3 - 2*b**3.
-5*b**3
Let k be (-49)/392*16/(-6). Factor 3/2*n**3 - 5/6*n**4 + 0 + 1/6*n**5 + k*n - 7/6*n**2.
n*(n - 2)*(n - 1)**3/6
Find o such that -36/5 + 1/5*o**2 + 7*o = 0.
-36, 1
Let m(z) = z**2 - 19*z + 34. Let a be m(17). Solve -2*p**2 + 3*p**2 - 5*p**2 - 12*p + a*p**2 - 8 = 0.
-2, -1
Suppose -16 - 24*n + 6*n + 2*n**2 + 3*n - 3*n**2 + 7*n = 0. Calculate n.
-4
Let u(p) be the second derivative of p**6/45 - p**4/9 + p**2/3 - 21*p. Suppose u(r) = 0. What is r?
-1, 1
Let m(l) = 5*l**3 - 11*l**2 - 15*l + 11. Let b be m(3). Suppose 0 + y**5 - 1/4*y**3 + 0*y**b + 0*y + 3/4*y**4 = 0. What is y?
-1, 0, 1/4
Suppose h + 2*h - 6 = 0. Solve p**2 + 24*p - 3*p**h - 26*p = 0 for p.
-1, 0
Let j(a) be the third derivative of 0*a**4 + 0 + 0*a**5 - 1/1848*a**8 - 1/660*a**6 + 0*a + 0*a**3 + 2/1155*a**7 + 13*a**2. What is z in j(z) = 0?
0, 1
Factor 8/3*m**4 - 13*m**3 - 1/6*m**5 - 49/6*m + 56/3*m**2 + 0.
-m*(m - 7)**2*(m - 1)**2/6
Let v(a) be the second derivative of -5*a**4/21 + 794*a**3/21 - 316*a**2/7 + 92*a. Let v(o) = 0. Calculate o.
2/5, 79
Let j be 1242/(-184) + (-16)/(-56) + 94/14. Suppose -j*u**2 + 0 + 1/4*u + 1/4*u**4 - 1/4*u**3 = 0. Calculate u.
-1, 0, 1
Let n be -10*(-8)/(-16) - 2*(3 - 6). Let f be ((-21)/6 - -2)/(-3). Determine y so that f*y**2 - n + 1/2*y = 0.
-2, 1
Let x(m) = m**3 - 15*m**2 + 84*m + 96. Let c(b) = b**3 - 14*b**2 + 85*b + 95. Let o(l) = -4*c(l) + 5*x(l). Factor o(n).
(n - 10)**2*(n + 1)
Let m(t) be the first derivative of t**5/20 - 15*t**4/8 + 7*t**3 - 41*t**2/4 + 27*t/4 - 173. Factor m(q).
(q - 27)*(q - 1)**3/4
Let p(s) be the second derivative of 0*s**2 + 2/7*s**3 - 5/21*s**4 + 0 + 2/35*s**5 - 3*s. Find z such that p(z) = 0.
0, 1, 3/2
Let b(r) = 3*r**3 - 324*r**2 + 5425*r - 9610. Let n(p) = 20*p**3 - 2270*p**2 + 37975*p - 67270. Let s(j) = 15*b(j) - 2*n(j). Let s(h) = 0. What is h?
2, 31
Let r(z) = -194*z**2 + 140*z - 23. Let q(l) = -2133*l**2 + 1540*l - 252. Let h(w) = 6*q(w) - 69*r(w). Find n, given that h(n) = 0.
5/14
Let t(j) be the first derivative of -3*j**4/2 + j**3 + 3*j**2 - 3*j + 15. Determine f so that t(f) = 0.
-1, 1/2, 1
Factor -62/3*l**3 + 32/3*l**2 + 0 + 0*l + 2/3*l**5 + 28/3*l**4.
2*l**2*(l - 1)**2*(l + 16)/3
Suppose a - 3 = -1. Factor -2*d**4 - a*d**2 - 3*d**3 + 6*d**5 - 7*d**5 - 2*d**4 - 2*d**3.
-d**2*(d + 1)**2*(d + 2)
Let f(q) be the second derivative of 10*q + 0 + 1/16*q**3 + 1/32*q**4 + 0*q**2. Factor f(t).
3*t*(t + 1)/8
Let m(w) be the first derivative of -w**6/120 - w**5/40 + w**3/12 + w**2/8 + 7*w - 20. Let q(j) be the first derivative of m(j). Find f such that q(f) = 0.
-1, 1
Let s(f) be the third derivative of f**7/560 - f**6/320 - 3*f**5/160 + 5*f**4/64 - f**3/8 + 154*f**2. What is c in s(c) = 0?
-2, 1
Let v(r) be the second derivative of r**5/140 + 2*r**4/3 + 56*r**3/3 - 11*r - 1. Let v(g) = 0. Calculate g.
-28, 0
Let k(z) be the first derivative of 3*z**5/20 - 123*z**4/4 + 1681*z**3 - 43. Find a, given that k(a) = 0.
0, 82
Let h(y) be the third derivative of -y**6/24 + 19*y**5/12 - 65*y**4/3 + 440*y**3/3 + 44*y**2. Determine n so that h(n) = 0.
4, 11
Let n(b) be the first derivative of b**3/7 + 3*b**2 + 21*b - 171. Factor n(k).
3*(k + 7)**2/7
Suppose 1