(-2)/a). Factor r - 2/9*q + 2/9*q**2.
2*q*(q - 1)/9
Let h(s) be the first derivative of s**4/4 + 4*s**3/3 - 3*s**2 - s + 11. Let y be h(-5). Factor -n**5 - 2*n**2 + 3*n**3 - y*n**2 + 4*n**2.
-n**2*(n - 1)**2*(n + 2)
Let s(q) be the third derivative of q**7/1400 - q**3/6 + 10*q**2. Let m(o) be the first derivative of s(o). Factor m(x).
3*x**3/5
Let v be (-24)/12*(-3)/((-3)/(-1)). Let c(r) be the first derivative of -5 - 1/2*r - 5/6*r**3 + r**v + 1/4*r**4. Suppose c(d) = 0. What is d?
1/2, 1
Suppose 0 = -20*x - 6*x. Let m(n) be the second derivative of -2/21*n**4 + 8*n - 1/70*n**5 - 4/21*n**3 + 0 + x*n**2. Factor m(z).
-2*z*(z + 2)**2/7
Let m(c) = c**5 - c**4 - 2*c**3 - c**2 - 1. Let k(j) = -8*j**5 - 2*j**4 + 30*j**3 + 38*j**2 - 40*j + 6. Let l(a) = -k(a) - 6*m(a). What is w in l(w) = 0?
-5, -2, 0, 1, 2
Let m(u) be the third derivative of -2*u**2 + 0*u**3 - 1/2184*u**8 + 2/1365*u**7 + 0*u - 1/195*u**5 + 1/156*u**4 + 0*u**6 + 0. Factor m(x).
-2*x*(x - 1)**3*(x + 1)/13
Let v be (((-3825)/60)/5 - -13)*(-16)/(-6). Factor 0 - 1/3*u**2 - 1/3*u**4 + v*u**3 + 0*u.
-u**2*(u - 1)**2/3
Let q = 17124 + -17124. Factor 10/3*h**2 + 2/3*h**4 + q + 0*h + 4*h**3.
2*h**2*(h + 1)*(h + 5)/3
Suppose 28 = 16*k - 20. Suppose -k*y + 14 = 4*y. Find p, given that 2/3*p**y + 0*p + 0 + 1/3*p**3 = 0.
-2, 0
Solve -9 + 26/3*s + 1/3*s**2 = 0 for s.
-27, 1
Let c(o) be the second derivative of -9*o - 1/25*o**5 + 0 + 2/15*o**3 + 1/5*o**4 - 6/5*o**2. Factor c(t).
-4*(t - 3)*(t - 1)*(t + 1)/5
Suppose 0 = -12*i + 58 + 14. Let p(z) be the first derivative of -i*z**2 + 1/2*z**3 + 9/8*z**4 + 6*z - 2. What is q in p(q) = 0?
-2, 2/3, 1
Let a(j) be the second derivative of -j**4/8 + 3*j**3/4 - 12*j - 9. Factor a(t).
-3*t*(t - 3)/2
Let s be (-1 - 0/1) + -4 + 78. Let h = -44 - -100. Factor 86*a**2 - 30*a**2 + 8 - h*a - 31*a**2 + s*a**2.
2*(7*a - 2)**2
Suppose 5*l - 4 - 6 = 0. Let k be 24/(-216) + 14/18. Factor k + 5/3*d + d**l.
(d + 1)*(3*d + 2)/3
Let w be 136/22 + (-16)/88. Let j(a) = a**4 + a**3 - a - 1. Let s(z) = 2*z**4 + 6*z**3 - 16*z**2 - 6*z + 14. Let r(p) = w*j(p) + s(p). Solve r(i) = 0.
-2, -1, 1/2, 1
Let -1/8*v**2 + 7 - 1/8*v = 0. What is v?
-8, 7
Suppose 21/2 - 1/2*s**2 + 2*s = 0. Calculate s.
-3, 7
Let k = 26 + -56. Let m be (-2)/10 + (-126)/k. Factor 6/5*t**2 - 4/5*t**3 + 1/5 + 1/5*t**m - 4/5*t.
(t - 1)**4/5
Suppose -t - 6 = -2*i - 4*t, 5*i - 4*t - 15 = 0. Let r(n) be the second derivative of -1/36*n**4 + 0*n**i + 0*n**2 + 0 + 7*n. Suppose r(l) = 0. Calculate l.
0
Determine s so that 0 - 646/7*s**3 - 2/7*s**5 - 578/7*s**2 + 0*s - 10*s**4 = 0.
-17, -1, 0
Let m(i) be the second derivative of -i**7/126 - i**6/90 + i**5/30 + i**4/18 - i**3/18 - i**2/6 + 2*i - 14. Solve m(d) = 0.
-1, 1
Let o be ((-10)/(-20))/(2/7). Find s, given that -o*s**3 - 1/4*s**5 + 1/4*s**2 + 1 + 2*s - 5/4*s**4 = 0.
-2, -1, 1
Suppose 0 = 2*w + 6, -5*f + 40 = -8*w + 3*w. Suppose 30*z + 80*z**3 - f + 22*z**4 - 70*z**2 - 83*z**4 + 18*z**5 - 8*z**5 + 16*z**4 = 0. Calculate z.
1/2, 1
Let v(i) be the second derivative of 1/10*i**6 + 1/12*i**4 + 0*i**2 + 0*i**3 + 0 - 2*i - 3/14*i**7 + 1/4*i**5. Factor v(u).
-u**2*(u - 1)*(3*u + 1)**2
Let z(b) be the first derivative of -b**4/6 + 2*b**3/3 - b**2 - 3*b + 5. Let m(r) be the first derivative of z(r). Solve m(j) = 0 for j.
1
Let a(s) = -4*s**2 + 25*s - 34. Let o be a(4). Find p, given that -1/2*p**3 + 1 + 3/2*p + 0*p**o = 0.
-1, 2
Let b(s) be the third derivative of 0*s - 13/50*s**5 + 0 + 20/3*s**3 - 3*s**4 + 17*s**2 - 1/150*s**6. Determine f, given that b(f) = 0.
-10, 1/2
Let i = -2017/2 - -1009. Suppose -v**3 + v + i*v**4 - 1/2 + 0*v**2 = 0. What is v?
-1, 1
Factor 73 - 4 - 141*w + 21 + w**3 + 54*w**2 - 4*w**3.
-3*(w - 15)*(w - 2)*(w - 1)
Suppose 1 = 4*t + 17, -31 = -3*a + 4*t. Suppose -4*g + 11 = q, -4 - 1 = 5*g - a*q. Determine l so that -2 + 2*l**g + 1 - 1 = 0.
-1, 1
Let s(g) be the third derivative of g**6/200 + 23*g**5/600 + 7*g**4/120 - g**3/20 + 24*g**2. Determine k so that s(k) = 0.
-3, -1, 1/6
Suppose 2*r + 2*c = 3 + 7, 5*c + 7 = 3*r. Suppose 30 = 8*i + 14. Solve -o**i + o**2 + 10*o - r*o - 5*o**2 - 1 = 0.
1/5, 1
Let r(b) = 5*b**2 - 12*b - 17. Let u(k) = 11*k**2 - 14*k - 1. Let l(o) = 4*o**2 - 5*o. Let s(z) = 8*l(z) - 3*u(z). Let c(m) = 6*r(m) + 34*s(m). Solve c(j) = 0.
-1, 0
Let -4*r**2 - 7*r + 56 - 7*r + 3*r - 9*r = 0. What is r?
-7, 2
Let h(p) be the second derivative of p**9/108 + 3*p**8/140 + p**7/105 - 14*p**3/3 - 7*p. Let f(g) be the second derivative of h(g). Factor f(j).
4*j**3*(j + 1)*(7*j + 2)
Let u(d) = d**3 + 10*d**2 + 26*d + 38. Let l be u(-7). Factor -10/17*q**l + 14/17*q**2 - 4/17*q + 0.
-2*q*(q - 1)*(5*q - 2)/17
Let z(d) = d**2 - 8*d - 6. Let t be z(9). Factor 5*v**3 - 4*v**3 + t*v**2 + 2*v**3.
3*v**2*(v + 1)
Suppose 4*r + 111 = -129. Let m be r/(-8) + -3 - (-2 + 6). Factor -h + m*h**2 + 0.
h*(h - 2)/2
Let p(a) be the second derivative of a**7/11340 + a**6/135 + 4*a**5/15 - 37*a**4/12 + 7*a. Let y(t) be the third derivative of p(t). Factor y(s).
2*(s + 12)**2/9
Factor 52/7 + 54/7*c + 2/7*c**2.
2*(c + 1)*(c + 26)/7
Let t(h) be the second derivative of 13*h - 3/100*h**5 + 0*h**2 + 2/35*h**7 + 1 - 3/50*h**6 + 0*h**3 + 0*h**4. Let t(k) = 0. Calculate k.
-1/4, 0, 1
Factor 171/7*y + 15/7*y**3 - 96/7*y**2 - 54/7.
3*(y - 3)**2*(5*y - 2)/7
Let j(u) be the second derivative of -u**6/20 + 9*u**5/4 - 57*u**4/8 + 7*u**3 - 202*u. What is k in j(k) = 0?
0, 1, 28
Suppose -2*y = -5*p + 2*p - 5, -2*p = -2. Suppose 6*u - 5*u + 5 = 5*v, -y*v - 3*u = -23. Suppose 8 - 16*x**v + 6*x + 6*x - 4*x**3 + 16*x**2 = 0. Calculate x.
-1, 2
Determine p, given that 24 + 16 + 30*p - 14*p**2 - 32*p - 134*p = 0.
-10, 2/7
Let t(i) be the second derivative of -i**6/30 + i**5/10 + i**4 - 4*i**3/3 - 16*i**2 + 20*i - 12. Determine l, given that t(l) = 0.
-2, 2, 4
Suppose -2*o - 3*o - 2*v = -661, 4*o - 515 = 3*v. Let k = o - 128. Determine d, given that 1/2 - 1/2*d**4 + 0*d**2 + d**k - d = 0.
-1, 1
Suppose 4*d + 11 - 19 = 0. Let r(w) be the first derivative of d - w**2 + 4/3*w**3 - 1/2*w**4 + 0*w. Factor r(g).
-2*g*(g - 1)**2
Find r such that 11*r + 21*r**2 + 10 - 4*r - 20*r**2 = 0.
-5, -2
Let p(s) = -s**2 - 7*s - 2. Let o(w) = -6*w**2 - 35*w - 11. Let i(k) = 2*o(k) - 11*p(k). Let i(m) = 0. Calculate m.
0, 7
Let g be 37 + 9 + -4 + -2. Let p be g/22 + (-16)/(-88). Factor 28*t**p - 5*t - 5*t**5 - 23*t**3 + 20*t**4 - 8*t**2 - 7*t**3.
-5*t*(t - 1)**4
Let r(d) be the second derivative of -d**9/3024 + d**8/672 - d**6/72 + d**5/24 + 9*d**4/2 + 56*d. Let q(g) be the third derivative of r(g). Factor q(h).
-5*(h - 1)**3*(h + 1)
Suppose -6*h - 3*h + 18 = 0. Factor 4*s**3 - 2*s**3 - 7*s + s - 4*s**h.
2*s*(s - 3)*(s + 1)
Let r(p) be the second derivative of p**6/720 - p**5/240 - p**4/8 + 41*p**3/6 - 44*p. Let i(c) be the second derivative of r(c). Find w, given that i(w) = 0.
-2, 3
Let c = -120 - -120. Let h(d) be the third derivative of 0*d**3 + 0*d**5 + c*d + 0*d**4 + 0 - 3*d**2 - 1/660*d**6. Factor h(v).
-2*v**3/11
Let v(d) be the third derivative of d**6/180 - d**5/18 - 13*d**4/36 - 7*d**3/9 - 2*d**2 - 41*d. Factor v(u).
2*(u - 7)*(u + 1)**2/3
Let 0 + 65/7*t**3 + 3/7*t**4 - 44/7*t - 24/7*t**2 = 0. Calculate t.
-22, -2/3, 0, 1
Let o(p) = -8*p**5 - 8*p**4 + 15*p**3 + 15*p**2 - 7*p + 7. Let h(q) = -3*q**5 - 3*q**4 + 5*q**3 + 5*q**2 - 2*q + 2. Let c(g) = -7*h(g) + 2*o(g). Factor c(t).
5*t**2*(t - 1)*(t + 1)**2
Let c(f) be the third derivative of -f**5/360 + 257*f**4/72 - 66049*f**3/36 - 158*f**2 - 3*f. Factor c(k).
-(k - 257)**2/6
Let i(l) = -5*l**4 + 9*l**3 + 21*l**2 + 31*l + 6. Let m(x) = x**3 - x**2 + x. Let y be (-80)/15 + (-4)/6. Let u(v) = y*m(v) + i(v). What is n in u(n) = 0?
-1, -2/5, 3
Let w(x) be the second derivative of 3*x**5/40 - 13*x**4/24 - 8*x**3/3 + 3*x**2 + 220*x. Factor w(u).
(u - 6)*(u + 2)*(3*u - 1)/2
Let b(p) be the second derivative of -p**6/45 - 13*p**5/10 + 28*p**4/3 - 172*p**3/9 + 143*p. Factor b(f).
-2*f*(f - 2)**2*(f + 43)/3
Let f(t) = -3*t**2 + 16*t - 5. Let d be f(5). Let u(a) be the second derivative of d + 2*a**2 + 2*a - a**3 + 1/6*a**4. Let u(l) = 0. Calculate l.
1, 2
Let b(p) = -6*p**2 + 394*p - 19608. Let l(z) = -8*z**2 + 393*z - 19611. Let d(r) = -6*b(r) + 4*l(r). What is u in d(u) = 0?
99
Let r(n) be the first derivative of -n**4/12 + 2*n**3/9 + n**2/6 - 2*n/