3
Suppose 4*g - s - 19 = 2, -3*g - 2*s = -2. Suppose -96*l**2 - 56*l + l**4 - 24*l**3 - 109*l + 37*l - 3*l**g = 0. Calculate l.
-4, 0
Let -91*f + 55/4*f**2 - 1/2*f**3 - 49 = 0. What is f?
-1/2, 14
Let p(j) = 2*j**3 - j**2 - 2. Let a(t) = -20*t**3 + 9*t**2 + 14*t + 30. Let b(w) = 2*a(w) + 18*p(w). Factor b(h).
-4*(h - 3)*(h + 1)*(h + 2)
Let i(a) be the third derivative of -1331*a**6/30 + 121*a**5/3 - 44*a**4/3 + 8*a**3/3 + 753*a**2. Factor i(k).
-4*(11*k - 2)**2*(11*k - 1)
Let m(s) = -s**4 + s**3 - s + 3. Let f(z) = 7*z**4 - 3*z**3 - 6*z**2 + 3*z - 11. Let l(r) = 2*f(r) + 10*m(r). Factor l(a).
4*(a - 1)**2*(a + 1)*(a + 2)
Let t be (-10)/(-20)*(-6 + 8). Let n(i) be the first derivative of -t - 2/15*i**6 + 8/15*i**3 + 3/5*i**4 + 0*i**5 + 0*i + 0*i**2. Solve n(m) = 0.
-1, 0, 2
Suppose -5*b = -2*b. Let r(y) = -y**3 - y**2 + y + 27. Let j be r(b). Suppose -a**3 - 20*a**3 - j*a**5 - 45*a**4 + 18*a - 18*a - 3*a**2 = 0. What is a?
-1, -1/3, 0
Let y(x) be the third derivative of x**7/630 + x**6/90 - x**5/180 - x**4/18 + 10*x**2 - x. Factor y(f).
f*(f - 1)*(f + 1)*(f + 4)/3
Let k = -9 + 11. Let o(l) = -8*l**3 - 4*l**2 + 4*l - 5*l + 14*l**k. Let m(c) = -1. Let p(y) = -m(y) - o(y). Factor p(b).
(b - 1)*(2*b - 1)*(4*b + 1)
Let b(n) be the first derivative of 0*n**2 + 7 + 2/7*n - 2/21*n**3. Factor b(u).
-2*(u - 1)*(u + 1)/7
Suppose -3*s + q - 1181 = 0, 5*q - q - 1196 = 3*s. Let o be (-210)/s + (-6)/21. Determine v, given that 0*v + 3/4*v**2 + o*v**3 + 0 = 0.
-3, 0
Let z(f) = 2*f + 2. Let t be z(-1). Suppose -5*w + 0*w + 15 = t. Find p, given that -3*p**5 + 0*p**3 + 9*p**3 - 6*p - 2*p**2 + 5*p**2 - w*p**4 = 0.
-2, -1, 0, 1
Factor 3642*a**4 - 3647*a**4 - 10*a**3 + 5 - 2*a + 12*a.
-5*(a - 1)*(a + 1)**3
Let v(k) be the first derivative of -16*k**5/5 - 11*k**4/2 + 10*k**3/3 + 11*k**2 + 6*k - 182. Solve v(t) = 0.
-1, -3/8, 1
Suppose -2*o + 4 = -2*t, -19*t = -22*t + 2*o. Solve 0*l - l**2 + 0 + 1/2*l**3 + 1/2*l**t = 0 for l.
-2, 0, 1
Let r(q) be the first derivative of q**6/51 - 2*q**5/85 - 5*q**4/34 - 2*q**3/17 + 118. Suppose r(v) = 0. What is v?
-1, 0, 3
Let n(f) be the third derivative of f**7/5040 + f**6/1440 - 5*f**4/12 - 5*f**2. Let r(i) be the second derivative of n(i). Factor r(u).
u*(u + 1)/2
Let d be -128*((-1)/3)/((-12)/72). Let f = d + 256. Factor 7/4*o**4 + f*o - 5/4*o**5 + 0*o**2 + 0 - 1/2*o**3.
-o**3*(o - 1)*(5*o - 2)/4
Suppose 0 = -0*j - 5*j - 5*x + 75, -4*j + x = -70. Let w = 17 - j. Suppose w + 0*p + 0*p**2 - 1/2*p**5 + 1/4*p**3 + 1/4*p**4 = 0. What is p?
-1/2, 0, 1
Let r(b) = -40*b**4 - 172*b**3 + 317*b**2. Let g(o) = 7*o**4 + 29*o**3 - 53*o**2. Let f(x) = 34*g(x) + 6*r(x). Determine d, given that f(d) = 0.
-25, 0, 2
Let x(u) be the first derivative of u**6/12 + u**5/10 - 9*u**4/4 + 7*u**3/3 + 17*u**2/4 - 15*u/2 - 31. Determine m so that x(m) = 0.
-5, -1, 1, 3
Suppose -2048*x + 5 = -2047*x. Factor -2/7*g**2 + 6/7*g**3 + 0*g - 6/7*g**4 + 0 + 2/7*g**x.
2*g**2*(g - 1)**3/7
Let a be -7 + ((-1170)/(-189) - (-20)/12). What is k in 4/7 + 2/7*k**2 - a*k = 0?
1, 2
Let u(v) be the first derivative of v**6/360 + v**5/90 - 10*v**2 - 29. Let j(i) be the second derivative of u(i). Factor j(x).
x**2*(x + 2)/3
Let y be (2/6)/(2/454). Let o = -75 + y. Find d, given that -4/3*d - o*d**2 + 0 = 0.
-2, 0
Let o(s) be the third derivative of -s**6/24 - s**5 - 15*s**4/2 - s**2 + 88. Factor o(v).
-5*v*(v + 6)**2
Factor 1/4*x**4 - 5/4*x**3 + 0 + 0*x + x**2.
x**2*(x - 4)*(x - 1)/4
Let u = -26 - -20. Let q = u + 11. Let -p**3 - q*p**3 + 4*p**3 - 2*p**4 = 0. What is p?
-1, 0
Let v = 100661/268472 + 2/33559. Factor v*l**2 + 9/4*l + 0.
3*l*(l + 6)/8
Let s(v) = -v**2 - 8*v + 11. Let y be s(-8). Let t(h) = -h + 15. Let m be t(y). Find g, given that -g**4 - 6*g**3 + 8*g + g**4 + 2*g**m = 0.
-1, 0, 2
Find x such that -12 + 32/3*x - 5/3*x**2 - 1/3*x**3 = 0.
-9, 2
Solve -1/3*s**4 - 13/3*s + 7/3*s**2 + 2 + 1/3*s**3 = 0.
-3, 1, 2
Let a(x) be the second derivative of -x**2 - 1/3*x**4 - 1/20*x**5 - 5/6*x**3 - 12*x + 0. Find n, given that a(n) = 0.
-2, -1
Let f be (-4)/(-12) + (680/3)/4. Let q = f - 113/2. Suppose -q*n + 1/2*n**3 + 0 + 0*n**2 = 0. Calculate n.
-1, 0, 1
Suppose 4*z + 4 + 0 = 0. Let n be (3/(-2))/(z*(-2 - -5)). Factor 0*t**2 - n*t**3 + 0 + 1/2*t.
-t*(t - 1)*(t + 1)/2
Let u(r) be the second derivative of -2*r**7/105 + r**5/5 + r**4/3 - 33*r**2/2 + 26*r. Let c(j) be the first derivative of u(j). Factor c(h).
-4*h*(h - 2)*(h + 1)**2
Let d(x) be the first derivative of -x**6/12 - 9*x**5/10 + 11*x**4/4 - x**3/3 - 21*x**2/4 + 11*x/2 - 66. Factor d(j).
-(j - 1)**3*(j + 1)*(j + 11)/2
Let s be -20*(-2)/(-25)*5. Let f be 1*4/s*-4. Determine w so that 6*w**3 + 0 - f*w**5 + 2*w**4 + 0 - 856*w - 10*w**2 + 860*w = 0.
-2, 0, 1
Let p = 11 + -1. Factor m + 0*m - 16 + m + p*m + 4*m**2.
4*(m - 1)*(m + 4)
Let w(k) = 11*k**2 + 9*k - 24. Let j(m) = 21*m**2 + 18*m - 54. Let y(b) = -4*j(b) + 9*w(b). Factor y(q).
3*q*(5*q + 3)
Solve -1/5*z**3 + 0 + 2*z + 3/5*z**2 = 0.
-2, 0, 5
Let z(x) be the second derivative of -x**5/190 - 2*x**4/57 - 5*x**3/57 - 2*x**2/19 - 14*x - 3. Let z(d) = 0. Calculate d.
-2, -1
Determine q, given that -39*q - 3*q + 5*q**3 - 5*q**3 + 3*q**3 - 15*q**2 = 0.
-2, 0, 7
Let c(n) be the third derivative of 1/120*n**6 + 8*n**2 + 0*n**3 + 0*n + 0 + 1/30*n**5 + 0*n**4. Suppose c(j) = 0. Calculate j.
-2, 0
Let m(a) be the second derivative of -a**4/36 - 46*a**3/9 - 1058*a**2/3 + 205*a. Find k, given that m(k) = 0.
-46
Suppose -5*q - t = 46, 0*t = -2*q + t - 17. Let l be (q/3)/((-6)/8). Factor 3*y**l + y**5 - y**4 - y**4.
y**4*(y + 1)
Suppose y - 8 = -o, -y - 4 = -3*y + o. Let u(v) be the first derivative of 4*v**2 - 4*v**3 - 2*v - 2/5*v**5 - 3 + 2*v**y. Factor u(x).
-2*(x - 1)**4
Let m(s) = -12*s**3 - 2*s**2 - 14*s - 6. Let c(g) = -4*g**3 + g**3 - g**2 - 1 + 4*g**3 - g. Let h(b) = -20*c(b) - 2*m(b). Determine p so that h(p) = 0.
-2
Let h(j) be the third derivative of -2*j**5/15 - j**4/6 - j**3 - 25*j**2. Let q(k) = -1 - 4 - 7*k**2 - k - 3*k. Let u(z) = 5*h(z) - 6*q(z). Factor u(g).
2*g*(g + 2)
Let t(p) = 6*p**3 + 3*p**2 - 24*p + 12. Let h(o) = 17*o**3 + 8*o**2 - 71*o + 38. Let v(m) = -3*h(m) + 8*t(m). Find r, given that v(r) = 0.
-3, 1, 2
Let -1/6*w**2 - 2*w - 10/3 = 0. What is w?
-10, -2
Let b(o) = o**3 - 5*o**2 - 39*o + 230. Let m be b(6). Find i, given that -1/2*i**4 + 0 - 6*i**3 - m*i - 24*i**2 = 0.
-4, 0
Let w = -1139 + 1145. Let c(k) be the first derivative of 8 - 1/5*k**3 + 0*k + 0*k**2 - 7/20*k**4 - 1/5*k**5 - 1/30*k**w. Factor c(t).
-t**2*(t + 1)**2*(t + 3)/5
Let i(o) = 12*o + o**2 - 5*o + 4 - 7*o. Let j(l) = 3. Let v(b) = 3*i(b) - 4*j(b). Find f, given that v(f) = 0.
0
Let a(c) = -698*c**4 + 4*c**3 + 32*c**2 - 16*c - 8. Let s(i) = 233*i**4 - i**3 - 12*i**2 + 6*i + 3. Let t(o) = 3*a(o) + 8*s(o). Factor t(f).
-2*f**3*(115*f - 2)
Let k(f) be the second derivative of f**4/2 + 2*f**3/3 - f**2 + 32*f. Solve k(w) = 0 for w.
-1, 1/3
Let v(i) be the second derivative of -i**4/12 - i**3/6 + 15*i. Let t be v(-1). Factor o + 1/2*o**2 + t.
o*(o + 2)/2
Factor 18*v**2 - 18 - 3/4*v**3 + 3/4*v.
-3*(v - 24)*(v - 1)*(v + 1)/4
Let t(n) be the first derivative of n**2/2 + 2. Let f be t(4). Factor 0*d**5 - 4*d**5 + 4*d**5 - 3*d**f - 3*d**5.
-3*d**4*(d + 1)
Factor -8/3 + 12*p + 2/3*p**2 - 3*p**3.
-(p - 2)*(p + 2)*(9*p - 2)/3
Suppose -25*k - 6 = -5*i - 22*k, 4*k - 12 = 0. Factor 2/3*w**i + 8/3 + 0*w - 2*w**2.
2*(w - 2)**2*(w + 1)/3
Let c = 306 - 306. Let h(k) be the second derivative of -16/15*k**6 + 5*k - k**2 - 2*k**3 + c - 1/6*k**4 + 12/5*k**5. Factor h(n).
-2*(n - 1)**2*(4*n + 1)**2
Solve -270/11 - 108/11*j - 116/11*j**3 + 14/11*j**4 + 288/11*j**2 = 0.
-5/7, 3
Let d(m) be the third derivative of -m**5/360 - 49*m**4/36 - 2401*m**3/9 - 27*m**2 - 2. Let d(r) = 0. What is r?
-98
Let w(q) be the second derivative of 0 - q**3 + 20*q + 5/3*q**4 + 0*q**2. Determine p so that w(p) = 0.
0, 3/10
Let a(t) = -20*t**3 + 3 - 1 - 4*t**2 + 5*t**3 + 11*t**3. Let z(g) = g**3 - 1. Let r(i) = a(i) + 2*z(i). Factor r(x).
-2*x**2*(x + 2)
Factor 163 - 14 - 6*v**4 - 48*v**2 + 5*v**4 - 14*v + 14*v**3 - 57 - 43.
-(v - 7)**2*(v - 1)*(v + 1)
Let a(s) be the second derivative of 3*s**5/20 - 5*s**4/2 + 25*s**3/2 + 518*s. Factor a(w).
3*w*(w - 5)**2
Let n(x) = 12*x**4 + 12*x**3 + 12*x**2 + 4*x - 8. Let c(f) = -f**4 - f**