4
Suppose -3*b + 1/2*b**2 + 9/2 = 0. What is b?
3
Suppose -6075*f**2 - 23691*f - 3*f**4 + 23691*f - 270*f**3 = 0. What is f?
-45, 0
Let u(q) be the first derivative of 3/10*q**2 + 2/5*q**3 - 19 - 6/5*q - 3/20*q**4. Factor u(k).
-3*(k - 2)*(k - 1)*(k + 1)/5
Let t be 6/10 - (-5)/((-50)/(-84)). Let j(p) = -p + 12. Let m be j(t). Factor 0 - 7/5*c**m - 2/5*c**2 + 0*c.
-c**2*(7*c + 2)/5
Suppose -12/5*u + 24/5*u**2 - 4/5*u**3 - 8 = 0. Calculate u.
-1, 2, 5
Let q(w) = 3*w**4 - 11*w**3 - 10*w**2. Let p(o) = -7*o**4 + 34*o**3 + 30*o**2. Let a(d) = -4*p(d) - 11*q(d). Let a(i) = 0. What is i?
-2, -1, 0
Determine n so that -101*n + 5*n**2 + 61 + 36*n - 1 = 0.
1, 12
Suppose -2*z = -4, 282 - 278 = -4*w + 2*z. Let m(u) be the third derivative of -1/960*u**6 + 0*u**4 + 0*u**5 + 0 + 0*u + w*u**3 - 6*u**2. Solve m(t) = 0 for t.
0
Let n(p) be the third derivative of p**5/20 + 9*p**4/8 + 3*p**2 - 2*p. Solve n(f) = 0.
-9, 0
Let p be (-63)/(-294) - (1 + (-18)/14). Let v(j) be the second derivative of p*j**3 + 0 + 3*j + 1/4*j**4 + 1/2*j**2 + 1/20*j**5. Factor v(b).
(b + 1)**3
Suppose -10*f = -8 - 12. Factor -2*c**f + 2*c**2 + 2*c - 6*c**2 + 4*c**2.
-2*c*(c - 1)
Let k(d) be the first derivative of -11 + 1/20*d**5 + 1/4*d**3 - 1/4*d**4 - d + 1/2*d**2. Factor k(r).
(r - 2)**2*(r - 1)*(r + 1)/4
Let n(z) be the first derivative of 0*z - 1/15*z**3 + 1/5*z**2 + 11. Factor n(g).
-g*(g - 2)/5
Let s(d) be the first derivative of d**5/100 + d**4/20 - 2*d**2/5 - 25*d - 15. Let v(a) be the first derivative of s(a). Suppose v(j) = 0. Calculate j.
-2, 1
Let x = -1/19 + 22/57. Let c(r) = 5*r**3 + 91*r**2 + 23*r + 94. Let b be c(-18). Factor 0*j**2 + x*j**5 + 1/3*j**3 - 2/3*j**b + 0*j + 0.
j**3*(j - 1)**2/3
Let h(k) be the second derivative of 0 - 1/15*k**4 + 0*k**3 - 11*k + 0*k**2 - 1/75*k**6 + 3/50*k**5. Solve h(a) = 0.
0, 1, 2
Suppose 19 = -3*w + 10. Let v(k) = -4*k - 12. Let m be v(w). Determine z so that 2/5*z + m + 16/5*z**3 - 7/5*z**4 - 11/5*z**2 = 0.
0, 2/7, 1
What is g in -5/4*g - 1/4*g**2 - 3/2 = 0?
-3, -2
Suppose 4*o + 5*d = 38 + 3, -3*o + 37 = 5*d. Determine l so that -3/2*l**2 - 3/4*l**5 - 9/2*l**o + 9*l + 6 - 33/4*l**3 = 0.
-2, -1, 1
Let p = -1267/79285 + -3/785. Let n = 188/707 - p. Determine r so that -2/7*r**3 - 4/7 + n*r + 4/7*r**2 = 0.
-1, 1, 2
Suppose b + 33 = 5*b - 5*d, 25 = -5*d. Factor 1/2*j**b - 2 - 3/2*j.
(j - 4)*(j + 1)/2
Let u(v) = v**3 - 4*v**2 - 4*v + 3. Let y be u(5). Factor 2*h**3 - y*h**2 + 6*h**2 + 1 - 1.
2*h**2*(h - 1)
Let l(v) be the second derivative of 2*v**6/15 - 2*v**5/5 - v**4/3 + 4*v**3/3 - 22*v. Factor l(w).
4*w*(w - 2)*(w - 1)*(w + 1)
Let 2/9*i**4 + 2/3*i**3 - 4/9*i + 0 - 2/9*i**5 - 2/9*i**2 = 0. Calculate i.
-1, 0, 1, 2
Let c(x) be the second derivative of -x**7/252 + x**6/36 - x**5/30 + 51*x - 2. Factor c(m).
-m**3*(m - 4)*(m - 1)/6
Factor 1767*q**5 - 16*q**4 - 1760*q**5 - 14*q**2 - 23*q**3 + 8*q - 20*q**3 - 2*q**3.
q*(q - 4)*(q + 1)**2*(7*q - 2)
Let c(p) be the third derivative of 0*p - 4*p**2 - 2/27*p**4 + 16/27*p**3 + 0 + 1/270*p**5. Factor c(x).
2*(x - 4)**2/9
Let r(h) = 2*h - 2. Let d be r(5). Let k = 13 - d. Factor v**2 + v**5 + 7*v**2 - k*v**3 - 3*v**5 - 2*v - 7*v**3 + 8*v**4.
-2*v*(v - 1)**4
Let a(f) = 2*f**4 - 43*f**3 - 19*f**2 + 65*f. Let v(n) = n**4 - 2*n**3 + n**2 + n. Let u(i) = a(i) - 5*v(i). Suppose u(t) = 0. Calculate t.
-10, -2, 0, 1
Let a(t) be the third derivative of t**8/672 + t**7/420 - t**6/240 - t**5/120 - 53*t**2 + 4. Factor a(y).
y**2*(y - 1)*(y + 1)**2/2
Let s(o) be the third derivative of -o**5/5 + 7*o**4/6 + 4*o**3 - 80*o**2 - 2. Let s(q) = 0. What is q?
-2/3, 3
Let u(c) be the first derivative of 7*c**3/3 + c**2/6 - 2*c/3 + 17. Factor u(x).
(3*x + 1)*(7*x - 2)/3
Let h(u) be the first derivative of u**4/10 - 2*u**3/15 - 4*u**2 - 713. Factor h(i).
2*i*(i - 5)*(i + 4)/5
Let a(h) be the third derivative of h**6/324 - h**5/45 + h**4/27 + h**3/3 - 17*h**2. Let u(k) be the first derivative of a(k). Let u(g) = 0. What is g?
2/5, 2
Let k be (140/80)/(1/(-24)). Let x be ((-7)/k)/(2/16). Solve -2/3*h**4 + 0 + x*h**3 + 1/6*h - 5/6*h**2 = 0.
0, 1/2, 1
Solve -3/4*m**5 + 15/4*m**3 + 4*m**2 + 0 - 4*m**4 - 3*m = 0 for m.
-6, -1, 0, 2/3, 1
Let j(c) = -c**3 - 2*c**2 - c + 2. Let k be j(0). Suppose 0 + 2310*y**2 + 8*y - 2308*y**2 - 8 - k = 0. Calculate y.
-5, 1
What is u in -5/6*u + 1/6*u**2 + 2/3 = 0?
1, 4
Let q(r) = r**3 - 7*r**2 + 10*r - 20. Let j be 5/2 - (-7)/2. Let s be q(j). Factor -1/7*x + 1/7*x**3 - 1/7*x**s - 2/7 + 3/7*x**2.
-(x - 2)*(x - 1)*(x + 1)**2/7
Let m be -1*(0 - -3 - 6). Suppose -4*n - 6*f - m = -3*f, 2*n - 3*f - 21 = 0. Find c, given that -2*c - 3*c**2 + c - n*c**3 - 35*c**4 + 34*c**4 = 0.
-1, 0
Let c = -1417/2 - -55265/78. Let k(f) be the first derivative of 0*f**5 - 1 - 1/26*f**4 + 0*f**3 + 0*f**2 + c*f**6 + 0*f. Factor k(o).
2*o**3*(o - 1)*(o + 1)/13
Let f be (0/(-1))/(17 + -23). Let o(x) be the third derivative of x**2 - 1/120*x**5 - 1/96*x**4 + 0 + f*x - 1/480*x**6 + 0*x**3. Factor o(i).
-i*(i + 1)**2/4
Factor -114*j + 350*j**3 - 100*j**4 + 354*j + 5*j**5 - 80 - 500*j**2 + 85*j.
5*(j - 16)*(j - 1)**4
Let r = -56 - -52. Let k be 15/(0 - 5)*r/6. Suppose -2/5 - k*x - 8/5*x**2 = 0. What is x?
-1, -1/4
Let v(a) = a**2 + 2*a + 1. Let m(t) = 2*t**3 - 89*t**2 - 12*t + 79. Let u(x) = -2*m(x) - 10*v(x). Solve u(z) = 0.
-1, 1, 42
Let y = -3905 - -3905. Factor -1/2 + y*i + 1/8*i**2.
(i - 2)*(i + 2)/8
Factor -85*a**3 - 6*a**4 - 1884*a**2 - 3888 + 58*a**3 + 90*a**3 + 97*a**3 + 5616*a + 2*a**4.
-4*(a - 18)**2*(a - 3)*(a - 1)
Let c(j) be the first derivative of j**4/14 + 34*j**3/21 + 75*j**2/7 + 198*j/7 + 142. Factor c(q).
2*(q + 3)**2*(q + 11)/7
Let g(i) be the first derivative of i**4/2 - 17*i**3/6 + 5*i**2 - 2*i - 101. Suppose g(f) = 0. What is f?
1/4, 2
Suppose -199*g + 7 + 590 = 0. Solve 3/2*z**5 - 11/2*z**g + 1/2*z**4 - 9/2*z**2 + 2 + 2*z = 0 for z.
-1, 2/3, 2
Let b = 54812/9 - 6090. Factor -b*n**2 + 4/9*n - 2/9.
-2*(n - 1)**2/9
Factor 15/4*u**3 + 9/4*u**4 + 0 + 0*u + 1/4*u**5 + 7/4*u**2.
u**2*(u + 1)**2*(u + 7)/4
Let f be ((-108)/(-702) + 4/(-26))*1. Solve f - 6/5*q - 2/5*q**2 = 0.
-3, 0
Let i(w) = 2*w**5 - 4*w**4 + 9*w**2 - 7*w - 5. Let k(d) = -2*d**5 + 4*d**4 - 10*d**2 + 8*d + 6. Let o be 3 + (-4)/8*-6. Let y(b) = o*i(b) + 5*k(b). Factor y(h).
2*h*(h - 1)**3*(h + 1)
Let h(w) = -w**4 - 31*w**3 + 65*w**2 - 37*w - 2. Let z(v) = -v**4 - 31*v**3 + 65*v**2 - 39*v - 3. Let s(t) = 3*h(t) - 2*z(t). Factor s(f).
-f*(f - 1)**2*(f + 33)
Let d(x) = x**2 + 40*x + 359. Let s(m) = -5*m**2 - 201*m - 1794. Let r(q) = 11*d(q) + 2*s(q). Factor r(b).
(b + 19)**2
Let f(m) be the third derivative of 0 - 1/30*m**5 + 0*m**3 + 1/35*m**7 - 1/6*m**4 + 1/15*m**6 - 2*m**2 + 0*m. Suppose f(a) = 0. What is a?
-1, 0, 2/3
Let x(d) = 8*d**2 - 57*d - 62. Let r be x(-1). Find p such that 0*p - 2/13*p**4 - 2/13*p**2 + 4/13*p**r + 0 = 0.
0, 1
Suppose -277*q - 215 = -769. Determine a so that -243/2*a**3 + 0 - 24*a - 108*a**q = 0.
-4/9, 0
Let d(t) be the third derivative of 0 + 1/70*t**5 - 1/420*t**6 + 0*t + 14*t**2 + 0*t**4 + 0*t**3. Factor d(v).
-2*v**2*(v - 3)/7
Let m(s) be the third derivative of s**5/90 + 53*s**4/6 + 2809*s**3 - 158*s**2 - 1. Find y such that m(y) = 0.
-159
Let h(s) = -s**5 - 2*s**4 - 2*s**3 + 4*s**2 + s. Let b(u) = -u**5 + 1. Let l(q) = -10*b(q) + 5*h(q). Determine g, given that l(g) = 0.
-1, 1, 2
Factor -12*d**3 + 48 - 199*d - d**5 - 2*d**5 - 15*d**4 + 295*d + 48*d**2.
-3*(d - 2)*(d + 1)*(d + 2)**3
Let i be 6/(-81)*-33 + -2. Let r = 313/288 + 15/32. Factor -2*y - r*y**2 - i.
-2*(y + 1)*(7*y + 2)/9
Let v = 1 - 0. Let t be (1/v)/((4 + 1)/10). Factor 4/13*d + 2/13*d**t + 2/13.
2*(d + 1)**2/13
Let o(y) be the second derivative of y**6/210 - 23*y**5/140 + 143*y**4/84 - 121*y**3/42 - y - 1. Determine t, given that o(t) = 0.
0, 1, 11
Factor -26*t + t**4 - 12*t**3 - 30 - 126*t**2 - 38 - 106*t + 49*t**2.
(t - 17)*(t + 1)*(t + 2)**2
Suppose 1/2*c**2 + 0 + 5*c = 0. What is c?
-10, 0
Factor 10*w**2 + w + w**3 - 2*w + 16*w + w.
w*(w + 2)*(w + 8)
Factor -237*w**2 + 235*w**2 + 96*w + 13*w + 93*w - 172 - 28*w.
-2*(w - 86)*(w - 1)
What is n in 320/7*n - 50/7*n**2 - 512/7 = 0?
16/5
Let d(a) = -a**3 - a - 1. Let i(g) be the second derivative of 3*g**5/10 - 5*g**4/12 + g**3/6 + g**2/2 + 12*g. Let t(q) = -d(q) - i(q). Factor t(c).
-5*c**2*(c - 1