he third derivative of t**7/210 + 19*t**6/120 - 41*t**5/60 + 7*t**4/8 + 26*t**2. Solve a(q) = 0 for q.
-21, 0, 1
Let j(s) = s**4 - 64*s**3 + 120*s**2 - 72*s + 5. Let b(h) = 33*h**3 - 60*h**2 + 36*h - 3. Let d(u) = -5*b(u) - 3*j(u). Factor d(r).
-3*r*(r - 6)*(r - 2)*(r - 1)
Suppose -5*n = 3 + 7. Let h be 2/4 + (-1)/n. Find j such that 8 - j**2 - 4 - 2*j**2 - h - 3*j + 3*j**3 = 0.
-1, 1
Let d(m) be the first derivative of 2*m**3/21 - 4*m**2/7 - 6*m + 105. Suppose d(x) = 0. What is x?
-3, 7
Factor 208 - 416*r**3 - 2417*r**5 + r**2 + 7*r**2 + 2413*r**5 + 420*r - 216*r**4.
-4*(r - 1)*(r + 1)**3*(r + 52)
Let s = 124 + -116. Suppose -4*c - 4 = 2*r, 4*r = 10*c - s*c + 22. Solve 1/3 - 2/3*f**2 + 1/3*f**5 + 1/3*f**r - 2/3*f**3 + 1/3*f = 0.
-1, 1
Factor 48/5*t**2 - 4/5*t**3 - 84/5*t + 8.
-4*(t - 10)*(t - 1)**2/5
Factor 1651*s + 170*s**2 - 1651*s + 5*s**4 + 0*s**4 - 175*s**3.
5*s**2*(s - 34)*(s - 1)
Let t(n) = -12*n**2 - 75*n + 3. Let a(r) = 15*r**2 + 75*r - 4. Let i(v) = -3*a(v) - 4*t(v). Find h such that i(h) = 0.
-25, 0
Suppose 27*w = 3*l + 31*w - 26, w = 5*l - 5. Let k(r) be the first derivative of 6 - 2/21*r**3 + 0*r - 1/7*r**l. Factor k(f).
-2*f*(f + 1)/7
Let l(n) be the first derivative of -n**6/240 - n**5/80 + n**4/8 + 4*n**3 - 4. Let q(b) be the third derivative of l(b). Factor q(h).
-3*(h - 1)*(h + 2)/2
Suppose 18 + 22 = 2*z. Determine t so that 4*t + 37*t**2 - 22*t**2 - z*t**2 = 0.
0, 4/5
Let k(v) be the third derivative of v**6/30 - v**5/3 - 25*v**4/3 + 6*v**2 - 81*v. Find c such that k(c) = 0.
-5, 0, 10
Let a be ((-52)/(-4) - 2)/(-1). Let s = a - -13. Factor -4*k**2 - 2*k**4 + 2*k**3 - 2*k**5 + k**s + 5*k**2.
-2*k**2*(k - 1)*(k + 1)**2
Let c be 1/4 - (-660)/176. Let i(j) be the second derivative of 0*j**2 + 1/18*j**3 + 2*j - 1/90*j**6 + 0 - 1/60*j**5 + 1/36*j**c. Solve i(d) = 0 for d.
-1, 0, 1
Let c = 10 + -9. Let n(s) = -s**2 - s + 2. Let o be n(c). Factor 1/4*b**4 + 0 + b**2 + o*b + b**3.
b**2*(b + 2)**2/4
Suppose 17*z - 13*z = 0. Suppose 3*t - 12 = -t + 3*c, 0 = -3*t + 2*c + 8. Find f, given that z + t*f + 1/3*f**2 = 0.
0
Let f(t) = -3*t**2 + t + 3 + 2*t**2 + 2*t**2 - 1. Let c be f(-2). Factor 4*z**3 - 2*z**5 + 4*z**3 - c*z**3 - 2*z**3.
-2*z**3*(z - 1)*(z + 1)
Let h = 558 - 558. Let p(a) be the third derivative of 1/840*a**7 + 7*a**2 + 0*a**3 + 0*a**5 + 0*a + 0 - 1/480*a**6 + h*a**4. Let p(q) = 0. What is q?
0, 1
Suppose -3*z - 5*x = -17, -z + 4 = z - 4*x. Factor 8*s**2 - 54*s + 54*s - z*s**2.
4*s**2
Let q(o) be the first derivative of o**6/9 + 14*o**5/15 + 8*o**4/3 + 16*o**3/9 - 16*o**2/3 - 32*o/3 + 182. Determine v so that q(v) = 0.
-2, 1
Let g(a) be the first derivative of a**4/18 - 140*a**3/27 + 538. Factor g(z).
2*z**2*(z - 70)/9
Let a be 2/9 - (-10)/(-45). Let w be (a - 1)/(-7 - -5). Factor 0*z**2 - 1/2 - z + w*z**4 + z**3.
(z - 1)*(z + 1)**3/2
Let y be 1 - 136/(-12)*3/(-35). Let j(t) be the third derivative of 0*t + 0*t**4 + 0*t**3 + y*t**7 + 0 + 0*t**5 + 1/30*t**6 + 5*t**2. Factor j(w).
2*w**3*(3*w + 2)
Let x be 620/(-80) - (0 + -8). Factor 0*l - x*l**2 + 0 + 0*l**3 + 1/4*l**4.
l**2*(l - 1)*(l + 1)/4
Let y(d) = d - 10. Let z be y(10). Suppose l + 2*x - x - 4 = z, 8 = 2*l + x. Suppose -2*u + 3*u + 2*u**l + 2*u**5 - 3*u**5 - 2*u**2 = 0. What is u?
-1, 0, 1
Let u(i) be the first derivative of 4*i**3/3 - i**2 - 2*i + 3. Let v be u(-1). Factor 7*p**2 + v*p - 2 - 6*p - 3*p.
(p - 1)*(7*p + 2)
Let o(v) be the first derivative of v**4/16 + 2*v**3 + 45*v**2/8 + 11*v/2 + 327. Determine z so that o(z) = 0.
-22, -1
Let i(y) be the second derivative of 4*y**6/75 - 9*y**5/25 - 47*y**4/120 + 3*y**3/5 - y**2/4 - 96*y. Find l, given that i(l) = 0.
-1, 1/4, 5
Let f(x) = x**5 - x**3 + x - 1. Let i(r) = 62*r**5 - 112*r**4 + 62*r**3 - 13*r**2 - r + 2. Let m(d) = -10*f(d) - 5*i(d). Factor m(t).
-5*t*(t - 1)*(4*t - 1)**3
Let y = 873 - 870. Let -5/4*o**5 + 7/4*o - 1/2*o**y + 5/2*o**2 + 1/4 - 11/4*o**4 = 0. Calculate o.
-1, -1/5, 1
Let r(h) = -18*h**4 - 58*h**3 - 178*h**2 - 182*h - 60. Let g(i) = 2*i**4 - i**3 - i**2. Let s(n) = -8*g(n) - r(n). Factor s(p).
2*(p + 1)**3*(p + 30)
Let d(v) be the third derivative of v**7/210 - 47*v**6/480 + 7*v**5/10 - 57*v**4/32 - 9*v**3/4 - 24*v**2 + 2. Determine j, given that d(j) = 0.
-1/4, 3, 6
Let y(o) be the third derivative of -o**5/50 - 19*o**4/5 - 1444*o**3/5 + 5*o**2 + o. Factor y(j).
-6*(j + 38)**2/5
Let r(s) = -6*s**2 - 3*s - 5. Let q(y) = 8*y**2 + 5*y + 7. Let o(z) = -5*q(z) - 7*r(z). What is j in o(j) = 0?
0, 2
Suppose -4*y + 184 - 48 = 0. Let x = -29 + y. Determine d so that 15*d**x + 8*d**4 - 18*d**5 + 8*d**5 + 15*d**5 = 0.
-2/5, 0
Suppose -5*a - 31 = -4*r, a = -r - r + 5. Factor 6*q**3 + 9*q**2 - 6*q - r*q - 9*q**3 + 4*q.
-3*q*(q - 2)*(q - 1)
Let k = 116 + -72. Let z = k + -42. Let -1/5 + 1/5*v**z + 0*v = 0. What is v?
-1, 1
Let b(w) be the first derivative of -w**3/9 - 2*w**2 - 11*w/3 - 122. Let b(h) = 0. What is h?
-11, -1
Let k(m) be the third derivative of 0*m**3 + 0 + 0*m + 1/48*m**4 + 1/120*m**5 - 8*m**2 + 1/960*m**6. Factor k(t).
t*(t + 2)**2/8
Suppose 2 + 4 = 2*n. Determine x so that -2*x + 3*x**2 - 3*x**5 - n*x - x + 9*x**3 + 0*x**5 - 3*x**4 = 0.
-2, -1, 0, 1
Let p(y) be the second derivative of -1/90*y**6 + 1/5*y**5 + 0 - y**4 + 0*y**2 + 21*y + 0*y**3. Factor p(i).
-i**2*(i - 6)**2/3
Let a(d) be the second derivative of -d**7/42 - d**6/30 + d**5/10 + d**4/6 - d**3/6 - d**2/2 + d - 192. Factor a(k).
-(k - 1)**2*(k + 1)**3
Let q(h) be the second derivative of 11*h + 0 + 1/165*h**6 + 0*h**3 + 1/22*h**4 - 1/231*h**7 + 1/22*h**5 + 0*h**2. Factor q(v).
-2*v**2*(v - 3)*(v + 1)**2/11
Suppose 11*w - 10*w - 4 = 0. Let -3*m - m - 69*m**3 + 35*m**3 - 4*m**4 + w*m**2 + 38*m**3 = 0. What is m?
-1, 0, 1
Factor 16/3*x + 2/3*x**2 + 14/3.
2*(x + 1)*(x + 7)/3
Let c(z) = -z**2 - 6*z - 4. Let r be c(-5). Let j = r - -5. Factor -5*o**3 + j*o**2 - 6*o**3 + 6*o**4 + 2*o**3 - 2*o**3 - o.
o*(o - 1)*(2*o - 1)*(3*o - 1)
Factor 326*s - 7*s**2 - 8*s**2 + 14*s**2 - s**2.
-2*s*(s - 163)
Let d(n) = 2*n**2 + n - 2. Let m be d(-10). Factor m*r**4 + 4*r**5 + r**2 - 192*r**4 + 3*r**2 - 4*r**3.
4*r**2*(r - 1)**2*(r + 1)
Suppose f = 0, 5*r - 30 = -f - 0*f. Factor -r*g**3 - 4 + 11*g**3 - 10*g**2 + 4.
5*g**2*(g - 2)
Suppose 0 = -38*m + 41*m + 2*v, -2*v = 0. Suppose m*s + 0 + 0*s**2 - 1/5*s**3 + 0*s**4 + 1/5*s**5 = 0. What is s?
-1, 0, 1
Let o = 3 + -3. Suppose o*a - 3 = -a. Find z such that 9*z + a + 0 + 3 - 15*z**2 = 0.
-2/5, 1
Let u(w) be the second derivative of -1/273*w**7 + 686/39*w**4 - 11*w - 2401/39*w**3 + 2 - 147/65*w**5 + 28/195*w**6 + 0*w**2. Suppose u(c) = 0. Calculate c.
0, 7
Suppose -9 + 12 = -k. Let z be 3/(k/(-2))*1. Let 44*o**3 + 64*o + 119 + 130 - 4*o**4 + 7 - 65*o**z - 79*o**2 = 0. What is o?
-1, 4
Let u(q) = 5*q**5 + 9*q**4 - 20*q**3 - 41*q**2 - 2*q + 1. Let n(d) = d**4 + d**2 + 2*d - 1. Let v(o) = -n(o) - u(o). Factor v(f).
-5*f**2*(f - 2)*(f + 2)**2
Factor 16/7*i**2 + 0*i + 4/7*i**5 + 0 + 36/7*i**3 + 24/7*i**4.
4*i**2*(i + 1)**2*(i + 4)/7
Let r(u) = -u**2 + u + 1. Let p = 8 - 2. Suppose 3 = -12*m + 9*m. Let t(f) = -4*f**2 + 12*f + 10. Let l(g) = m*t(g) + p*r(g). Suppose l(o) = 0. What is o?
-2, -1
Let l(b) be the third derivative of -b**6/200 - b**5/10 - 4*b**4/5 - 16*b**3/5 - 3*b**2 - 4*b. Determine x so that l(x) = 0.
-4, -2
Suppose -1/2*o**2 - 7 - 9/2*o = 0. What is o?
-7, -2
Let p(m) = m**2 - 1. Let c be p(1). Factor c*f**2 + 2*f + 3*f**2 + f.
3*f*(f + 1)
Let f(z) be the third derivative of -z**8/1176 - z**7/735 + z**6/140 + z**5/210 - z**4/42 - 46*z**2 + z. Solve f(s) = 0 for s.
-2, -1, 0, 1
Suppose -5*x + 15 = 5. Let b be 12/(-18)*(-15)/x. Solve -5*z**5 - b*z**5 + 7*z**5 = 0.
0
Let 124*m**4 - 56*m**4 - 66*m**4 - 53*m**4 - 6*m**3 = 0. What is m?
-2/17, 0
Let l = 31 - 29. Let r be 1*(-2 - -1) - -3. Factor 5*d**2 - 2*d**r - 2*d**l + 3*d.
d*(d + 3)
Let n = -9 - -11. Suppose -n*v + 0*v = 0. Find m, given that -m + 1 - m**2 + 20*m**3 - 19*m**3 + v*m**2 = 0.
-1, 1
Factor 32 - 8*k - 937*k**2 + 1874*k**2 - 941*k**2.
-4*(k - 2)*(k + 4)
Suppose -441 = 4*h - 21. Let o be (-98)/h*12/14. Find p, given that -2/5*p**3 - o*p**2 + 0 + 0*p + 6/5*p**4 = 0.
-2/3, 0, 1
Let f = 18 - 16. Factor -8*i + 2 - f + 4*i**2 - 6*i**2.
-2*i*(i + 4)
Let j(o) be the first derivative of -o**4/5 + 32*o**3/15 - 42*o**2/5 + 72*o/5 + 18. Factor j