*p + 5*p = -2*y + 6, 2*y - 6 = p. Factor -6/5*j**2 + p - 4/5*j - h*j**3.
-2*j*(j + 1)*(j + 2)/5
What is q in 14*q - 2*q**2 + 15*q + 18*q - 43*q - 2 = 0?
1
Let b(d) = -70*d**3 - 220*d**2 - 175*d - 50. Let u(k) = -17*k**3 - 55*k**2 - 44*k - 12. Let r(s) = 6*b(s) - 25*u(s). Factor r(i).
5*i*(i + 1)*(i + 10)
Find r, given that 255*r - 1110*r**2 + 968 - 84*r - 2*r**4 - 88*r**3 - 83*r + 144*r**2 = 0.
-22, -1, 1
Factor -10/3*l**2 + 23/3*l - 14/3 + 1/3*l**3.
(l - 7)*(l - 2)*(l - 1)/3
Let r be 88/(-22) + (3 - -5). Let b(l) be the third derivative of 1/210*l**5 + l**2 + 0 + 0*l**3 + 0*l - 1/84*l**r. Factor b(u).
2*u*(u - 1)/7
Suppose 23*r = 21*r + 8. Let 4*x**2 + 141*x**3 - 2*x**5 - 147*x**3 + r*x**5 = 0. What is x?
-2, 0, 1
Let 10*i - 2*i - 8 - 2*i**3 + i**4 + 4 - 165*i**2 + 162*i**2 = 0. Calculate i.
-2, 1, 2
Solve 48/7 + 2/7*o**2 + 4*o = 0.
-12, -2
Let s(x) = -x**2 - 12*x + 2. Let m be s(-12). Let 20*q**3 - 10*q**2 + 10*q**4 - 16*q**5 - q**5 + m*q**5 + 4*q - 9*q = 0. What is q?
-1, -1/3, 0, 1
Let q(a) = 7*a**2 - 119*a - 130. Let k(p) = -15*p**2 + 237*p + 261. Let c(b) = -4*k(b) - 9*q(b). Find t, given that c(t) = 0.
-1, 42
Let s(w) be the second derivative of 5*w**7/42 + w**6/3 - 3*w**5 - 95*w**4/6 - 185*w**3/6 - 30*w**2 - 2*w + 35. Factor s(f).
5*(f - 4)*(f + 1)**3*(f + 3)
Let q(j) = 10*j**3 + 2*j**2 - 4*j + 2. Let a be q(1). Solve -a*r**4 + 13*r**4 - 4*r**4 = 0.
0
Let x(v) be the third derivative of v**5/12 + 25*v**4/24 - 5*v**3 + 29*v**2. Find h, given that x(h) = 0.
-6, 1
Let p(d) be the second derivative of d**4/8 - 125*d**3/2 + 46875*d**2/4 - 95*d. Solve p(i) = 0.
125
Let p(d) be the second derivative of 2*d**6/75 + 3*d**5/5 + 5*d**4 + 50*d**3/3 - 5*d + 1. Solve p(k) = 0.
-5, 0
Let n be (16/(-48))/(50/(-54)). Let d(a) be the second derivative of n*a**5 - 1/2*a**3 + a - 1/5*a**4 + 0 + 3/5*a**2. Factor d(o).
3*(2*o - 1)**2*(3*o + 2)/5
Let a(y) be the third derivative of y**6/40 - 3*y**5/10 + 5*y**4/8 + 6*y**3 - y**2 - 13. Find i, given that a(i) = 0.
-1, 3, 4
Let d(c) be the first derivative of 8/3*c - 10/3*c**2 + 16/9*c**3 + 43 - 1/3*c**4. Factor d(q).
-4*(q - 2)*(q - 1)**2/3
Let x(l) be the first derivative of l**7/483 - 2*l**6/345 + l**4/69 - l**3/69 - 35*l + 31. Let b(f) be the first derivative of x(f). Solve b(h) = 0.
-1, 0, 1
Solve 0*o - 55/4*o**3 + 13/4*o**4 + 3*o**2 + 0 = 0.
0, 3/13, 4
Factor 7 + 9/2*a + 1/2*a**2.
(a + 2)*(a + 7)/2
Let r(v) = 8*v**4 + 78*v**3 + 211*v**2 + 190*v + 64. Let a(z) = 9*z**4 + 78*z**3 + 210*z**2 + 186*z + 63. Let s(p) = 5*a(p) - 6*r(p). Let s(f) = 0. Calculate f.
-23, -1
Let k(m) = -m**4 - m**2. Let x(z) be the third derivative of z**8/112 + 3*z**7/70 - z**6/8 + z**5/4 + 20*z**2. Let p(u) = -6*k(u) - x(u). Factor p(n).
-3*n**2*(n - 1)**2*(n + 3)
Determine g so that 26 - 4*g + 2/13*g**2 = 0.
13
Let a(o) be the second derivative of o**7/168 + o**6/120 - o**5/80 - o**4/48 - o - 7. Factor a(u).
u**2*(u - 1)*(u + 1)**2/4
Let w = 1156504/7 - 165499. Let g = -277 - w. Suppose -g*q**2 - 40/7*q - 8/7 = 0. What is q?
-2/5
Suppose 15 = 5*w, 5*n - w + 6 = w. Suppose 4*q = -n + 12. Let p**5 - 2*p**3 + 0*p**q + 3*p**3 - 2*p**3 = 0. Calculate p.
-1, 0, 1
Let j(w) = -w**3 - 11*w**2 - 5*w + 19. Let q(c) = 3*c**3 + 19*c**2 + 12*c - 39. Let k(z) = 5*j(z) + 2*q(z). Factor k(m).
(m - 17)*(m - 1)*(m + 1)
Suppose 2*b - 14 = w, -2*b + 6*b + 3*w = 8. Suppose b*l = -2*s + 30, -2*l - 2*s - 2 = -20. Let -1/2*a + 1/2*a**3 + 1/4*a**l - 1/4 + 0*a**2 = 0. Calculate a.
-1, 1
Let r be (0/2 - -11) + -1. Suppose -3*k + 5*k = r. Suppose -s**5 - 12*s**2 - 7*s**k - 2*s + 2*s**5 - 20*s**4 - 22*s**3 - 2*s**3 = 0. What is s?
-1, -1/3, 0
Let f(b) = 1. Let d(k) = -2*k**4 - 5*k**3 - 4*k**2 - k - 11. Let x = 4 + 2. Let s = -16 - x. Let y(v) = s*f(v) - 2*d(v). Factor y(m).
2*m*(m + 1)**2*(2*m + 1)
Let l(y) be the third derivative of -3/200*y**5 + 0*y**3 + 0 + 0*y + 1/120*y**4 + 2*y**2. Factor l(j).
-j*(9*j - 2)/10
Let g(u) be the first derivative of -u**3/15 - 7*u**2/10 + 8*u/5 - 35. Solve g(a) = 0.
-8, 1
Let z = 23 + -19. Let g(q) be the first derivative of 1/6*q**3 + 1/10*q**5 - 3 + 0*q**2 + 1/4*q**z + 0*q. What is h in g(h) = 0?
-1, 0
Factor -1/4*v**2 + 1/4 + 0*v.
-(v - 1)*(v + 1)/4
Let l(i) be the second derivative of 5*i**4/72 - 5*i**3/12 + 68*i. Solve l(w) = 0.
0, 3
Let u(p) = 16*p**4 - 11*p - 224 - 41*p**3 + 11*p**2 + 224. Let g(k) = -3*k**4 + 8*k**3 - 2*k**2 + 2*k. Let n(z) = 11*g(z) + 2*u(z). Factor n(i).
-i**3*(i - 6)
Let s(g) = 4*g**3 + 60*g**2 + 212*g - 236. Let y(m) = 2*m**3 + 20*m**2 + 71*m - 78. Let p(h) = 3*s(h) - 8*y(h). Let p(t) = 0. What is t?
-3, 1, 7
Factor 9/2*j**3 - 93*j**2 + 0 - 63/2*j.
3*j*(j - 21)*(3*j + 1)/2
Let z be (1240/6696)/((4/(-36))/(2/(-30))). Factor z*t**3 + 4/9*t**4 - 2/3*t**2 + 0*t + 1/9*t**5 + 0.
t**2*(t - 1)*(t + 2)*(t + 3)/9
Let x be (-98)/(-36) + 2 + 2/(-9). Suppose 0 = 2*o - 2*u, -o - 3*u = 3 - 15. Find l such that x*l + o + 3/2*l**2 = 0.
-2, -1
Let d(b) = 12*b**3 - 57*b**2 - 55*b - 17. Let k(c) = 6*c**3 - 28*c**2 - 27*c - 8. Let i(q) = -6*d(q) + 14*k(q). Factor i(u).
2*(u - 5)*(2*u + 1)*(3*u + 1)
Let 58/9*s - 2*s**3 + 2/9*s**4 - 2/3*s**2 - 4 = 0. Calculate s.
-2, 1, 9
Let u be (-4)/120*(52/(-6) - -7). Let y(o) be the second derivative of 1/15*o**2 - u*o**4 + o + 0 + 4/45*o**3. Factor y(q).
-2*(q - 1)*(5*q + 1)/15
Factor -260/3*n**2 - 2/3*n**3 + 526/3*n - 88.
-2*(n - 1)**2*(n + 132)/3
Let d(w) be the second derivative of 4*w**3 - 18*w**2 + 15*w + 0 - 1/3*w**4. What is l in d(l) = 0?
3
Suppose 10*i - 82 - 58 + 19*i**2 + 57*i + 11*i**2 - 152*i = 0. Calculate i.
-7/6, 4
Let d be 4/(-2)*(-21)/(-14) + 32. Let 3*q - 3 + 3*q**3 - q**3 - d + 13*q + 14*q**2 = 0. Calculate q.
-4, 1
Let w(t) be the third derivative of -1/40*t**6 + 0*t**4 + 0*t + 1/120*t**5 - 1/168*t**8 + 0 + 3/140*t**7 + 6*t**2 + 0*t**3. Find v, given that w(v) = 0.
0, 1/4, 1
Let g be (-1)/(15/(-2)) + (-43)/(-645). Factor g*b**3 + 0*b - 2/5*b**2 + 0 + 1/5*b**4.
b**2*(b - 1)*(b + 2)/5
Let c(j) be the third derivative of -j**7/280 - j**6/32 - 9*j**5/80 - 7*j**4/32 - j**3/4 - 91*j**2. Solve c(d) = 0.
-2, -1
What is q in 5*q**3 + 2*q - 8 - 2*q**4 + 14*q**2 - 6*q + 4*q**2 - 11*q**5 + 8*q**5 - 6*q**4 = 0?
-2, -2/3, 1
Let g(l) be the second derivative of 2*l**5/25 + 3*l**4/10 + 2*l**3/5 + l**2/5 + 25*l - 2. Solve g(v) = 0 for v.
-1, -1/4
Factor -18 - 20*u**2 - 2*u**5 - 2*u**3 + 14*u**3 - 42*u - 23*u**4 + 29*u**4.
-2*(u - 3)**2*(u + 1)**3
Find l such that -105*l**2 - 365*l + 189 + 521 + 110*l**2 = 0.
2, 71
Let c(y) be the third derivative of -2*y**5/15 + y**4/6 + 2*y**3/3 + 93*y**2. Find d, given that c(d) = 0.
-1/2, 1
Let t = 40/143 + 7030/429. Find b, given that -5/3*b**4 + 0 + t*b - 20/3*b**3 + 35/3*b**2 = 0.
-5, -1, 0, 2
Let y = -402 + 405. Let b(i) be the second derivative of -1/7*i**2 + 1/42*i**4 - 4/21*i**y + 0 + 2/35*i**5 - 5*i. Factor b(a).
2*(a - 1)*(a + 1)*(4*a + 1)/7
Let l(j) = 10*j. Let m be l(-3). Let u be -6*(63/m - -2). Factor 3/5*n**2 - u + 3/5*n**3 - 3/5*n.
3*(n - 1)*(n + 1)**2/5
Let a = 2082 + -2082. Let b(y) be the second derivative of 1/315*y**6 + 1/63*y**3 + 0 - 1/126*y**4 - 1/210*y**5 + a*y**2 - 8*y. Factor b(p).
2*p*(p - 1)**2*(p + 1)/21
Let f(i) be the first derivative of -7*i**6/1440 - 3*i**5/160 - i**4/48 + 11*i**3/3 - 14. Let o(u) be the third derivative of f(u). Factor o(n).
-(n + 1)*(7*n + 2)/4
Factor 1/4*m**5 + 4*m**3 + 0*m**2 - 2*m**4 + 0 + 0*m.
m**3*(m - 4)**2/4
Let h(w) be the third derivative of w**6/1020 - 8*w**5/255 - 189*w**2. Let h(k) = 0. Calculate k.
0, 16
Let s = 28/141 - 3/94. Suppose 0 - 5/6*c**2 + s*c + 7/6*c**3 - 1/2*c**4 = 0. Calculate c.
0, 1/3, 1
Factor 117/4 - 235/8*r + 1/8*r**2.
(r - 234)*(r - 1)/8
Let z(v) = v**2 - 3*v. Let b(r) = r**2 + 1. Let k(h) = -2*b(h) + z(h). Determine y, given that k(y) = 0.
-2, -1
Let m(y) = -7*y**2 - 286*y - 3926. Let s(o) = -15*o**2 - 575*o - 7855. Let x(c) = -5*m(c) + 2*s(c). Suppose x(j) = 0. Calculate j.
-28
Let w(s) = -s**3 + 51*s**2 + 55*s - 154. Let j be w(52). Factor 0*v + 1/3*v**3 + 0 + 1/3*v**j.
v**2*(v + 1)/3
Let l(q) = -12*q + 329. Let k be l(27). Let a(s) be the third derivative of 1/56*s**4 - 1/21*s**3 + 0*s - 1/420*s**k - 6*s**2 + 0. Factor a(u).
-(u - 2)*(u - 1)/7
Let q(o) be the third derivative of 6*o**2 - 1/40*o**6 + 1/10*o**5 + 0*o + 0*o**3 + 0*o**4 + 0. Factor q(f