 d. Find i such that h(i) = 0.
-1, 1
Suppose 14*i - 3*i + 154 = 0. Let f be 0 + i/(-16) + (-177)/354. Determine z so that -f*z**2 + 3/8*z + 3/4 = 0.
-1, 2
Let b = 192 - 186. Let v(s) = -12*s**2 - 78*s - 5. Let z(x) = -15*x**2 - 78*x - 6. Let n(c) = b*v(c) - 5*z(c). Find r such that n(r) = 0.
0, 26
Let y = -486 + 480. Let x be (-5)/y*(6/(-10) - -7). Suppose 4/3*i**2 + 16/3*i + x = 0. Calculate i.
-2
Let o(i) = 28*i + 125. Let w be o(0). Suppose 135*a - 20 = w*a. Factor 5/4*c**a + 0 + c**3 + 1/4*c**4 + 1/2*c.
c*(c + 1)**2*(c + 2)/4
Let q(r) be the third derivative of -44/3*r**3 + 97/6*r**4 + 0 - 174*r**2 + 0*r + 3/5*r**5. Factor q(y).
4*(y + 11)*(9*y - 2)
Suppose 3*s - q - 56 = -73, 51 = 5*s + 3*q. Factor 2/7*f**2 + 16/7*f + s.
2*f*(f + 8)/7
Let f(a) = a**3 + a**2 + a + 3. Let i = 9 + -56. Let n = i - -51. Let z(t) = 3*t**3 + 3*t**2 + 2*t + 7. Let o(y) = n*z(y) - 10*f(y). Solve o(g) = 0 for g.
-1, 1
Let f = -403 + 413. Factor -22*d**2 - 8*d + 22*d**3 - f*d**4 + 2*d**3 + 15*d + d**5.
d*(d - 7)*(d - 1)**3
Let -112*q**2 + 720 - 120*q - 1925 + 705 - 4*q**4 + 120*q**3 + 616 = 0. What is q?
-1, 1, 29
Let g(z) be the third derivative of z**5/60 - 163*z**4/24 + 620*z**3/3 + 92*z**2. Factor g(m).
(m - 155)*(m - 8)
Suppose s + s = 6. Let b = s - -1. Factor -3*c**4 + 2 + 83*c**2 + c - 81*c**2 + c**5 - b*c + 2*c**3 - 1.
(c - 1)**4*(c + 1)
Let p(w) be the second derivative of -w**4/6 - 46*w**3/3 - 168*w**2 - 6*w + 6. Factor p(b).
-2*(b + 4)*(b + 42)
Let u(j) be the third derivative of j**5/210 + 141*j**4/28 + 422*j**3/21 - 450*j**2 + j - 3. Factor u(r).
2*(r + 1)*(r + 422)/7
Let s(o) be the second derivative of 71*o**7/126 - o**6/45 - 3729*o. Suppose s(l) = 0. What is l?
0, 2/71
Let u(v) = v**2 + 8*v - 5. Let o be u(-9). Suppose 4*p = -2*h + o, 0 = -0*h - 2*h - 4. Find i, given that 8*i**2 - i**2 + 4 + 0*i**p - 8*i - 3*i**2 = 0.
1
Let i(t) be the second derivative of -64/3*t**3 - 49/40*t**5 + 469/24*t**4 + 9*t**2 - 4*t - 8. Factor i(k).
-(k - 9)*(7*k - 2)**2/2
Let s(k) = -45*k**3 + 25*k**2 + 20*k - 50. Let a = -525 + 500. Let t(n) = 11*n**3 - 6*n**2 - 5*n + 12. Let r(f) = a*t(f) - 6*s(f). Factor r(l).
-5*l*(l - 1)*(l + 1)
Let a(x) be the second derivative of -7*x**5/100 - 17*x**4/4 - 24*x**3/5 - 79*x**2/2 + 9*x + 2. Let j(g) be the first derivative of a(g). Factor j(m).
-3*(m + 24)*(7*m + 2)/5
Let g(m) be the second derivative of -1/126*m**4 + 16/9*m**3 - 448/3*m**2 + 93*m - 1. Factor g(d).
-2*(d - 56)**2/21
Let r = 93 + -91. Suppose -4*y + r*b + 67 = -59, b - 82 = -3*y. Factor -2 - y*z**3 - 2*z + 11*z**2 + 3*z + 15*z**4 + 4*z.
(z - 1)**2*(3*z - 1)*(5*z + 2)
Let c(a) be the third derivative of 365*a**8/1176 + 367*a**7/735 - 26*a**6/15 - 2*a**5/105 + a**2 - 268*a - 1. Find l, given that c(l) = 0.
-2, -2/365, 0, 1
Let c(l) be the first derivative of -l**4/2 + 1026*l**3 - 592899*l**2 + 1182722*l - 4363. Find a, given that c(a) = 0.
1, 769
Suppose 416226*j**2 - 39*j - 416410*j**2 + 36*j - 44*j**4 + 154*j**3 + 75*j + 2*j**5 = 0. Calculate j.
0, 1, 2, 18
Suppose 110 = 4*o - 6. Suppose 8*d + o = 9*d. Factor -25*f - d*f + 50*f - 4*f**5 + 8*f**3.
-4*f*(f - 1)**2*(f + 1)**2
Suppose -32 - 321 = -202*h + 417 + 240. Suppose 0 - 1/2*y**2 - h*y = 0. Calculate y.
-10, 0
Let i be 9 + -1 + -4*(6 - 5). Factor 2*m - 1/2*m**3 + 2*m**4 - 5*m**2 + i - 1/2*m**5.
-(m - 2)**3*(m + 1)**2/2
Suppose 0*r - r - 5*p = 5, 5 = -3*r - 5*p. Suppose 0 = 4*s + y + 6 - 14, 5*s - y - 10 = r. Find u, given that 6/7 + 9/7*u**s + 3*u = 0.
-2, -1/3
Factor -2260*w**3 - 32451*w - 4*w**4 - w**4 + w**4 + 11895*w + 332849*w**2 - 319181*w**2.
-4*w*(w - 3)**2*(w + 571)
Let d(g) be the first derivative of 2*g**2 - 44*g + 34/3*g**3 - 18 + 289/12*g**4. Let w(v) be the first derivative of d(v). Let w(z) = 0. Calculate z.
-2/17
Let p(v) be the second derivative of 16*v**6/5 + 68*v**5/5 + 17*v**4/2 - 18*v**3 + 8*v**2 - 1745*v. Solve p(o) = 0.
-2, -4/3, 1/4
Let b = 6/209 - -8342/627. Let a be 1 + 1*-3*2/(-3). Let -140/3*z + 190/3*z**2 + 40/3*z**4 + b - 125/3*z**a - 5/3*z**5 = 0. Calculate z.
1, 2
Suppose 2*d + 17 = 2*s + 15, -15 = -3*s - 3*d. Let i(r) be the second derivative of r**s + 1/2*r**5 - 1/15*r**6 - 12*r - 7/6*r**4 + 0 + 0*r**2. Factor i(x).
-2*x*(x - 3)*(x - 1)**2
Let s(y) be the first derivative of 5*y**4/24 - 385*y**3/9 + 33725*y**2/12 - 50410*y - 3908. Solve s(g) = 0.
12, 71
Let k = -836/107 - -2207/214. Let n(j) = 2*j**2. Let s be n(-1). Factor 0*f - k + 5/2*f**s.
5*(f - 1)*(f + 1)/2
Suppose -100*y + 49*y = -43*y - 39*y + 93. Suppose 2 - 2/3*v - 2/9*v**y - 10/9*v**2 = 0. What is v?
-3, 1
Let m(g) = g**3 + 2*g**2 - 4*g - 3. Let q be 1*(3 + -2)*-2. Let k be m(q). Suppose 12*p + 3*p**k - 12*p**2 + 42 + 6*p**4 - 42 - 9*p**3 = 0. Calculate p.
-2, 0, 1
Suppose -2/7*y**2 - 110/7*y - 212/7 = 0. Calculate y.
-53, -2
Let y(c) be the third derivative of 0 + 0*c**5 + 0*c - 2/27*c**3 + 1/36*c**4 - 1/540*c**6 - 142*c**2. Factor y(i).
-2*(i - 1)**2*(i + 2)/9
Let c = -1075 - -1075. Let u(s) be the first derivative of 14 - 4/15*s**5 + 0*s**2 + 8/9*s**3 - 1/3*s**4 + c*s. Let u(a) = 0. What is a?
-2, 0, 1
Let b(g) = 14*g - 208. Let p be b(15). Let i be (p*12/(-44))/((-14)/77). Suppose -12/5*r - 16/5*r**2 + 4/5*r**i + 72/5 = 0. Calculate r.
-2, 3
Let d(z) be the second derivative of -z**5/120 - 223*z**4/18 - 66007*z**3/12 + 66603*z**2/2 + 4*z - 220. Factor d(f).
-(f - 2)*(f + 447)**2/6
Let k(a) be the third derivative of a**8/2016 + 4*a**7/315 - 3*a**6/80 - 299*a**5/180 + 44*a**4/9 + 280*a**3/3 + 14022*a**2. Determine s, given that k(s) = 0.
-15, -7, -2, 4
Let v(k) be the first derivative of k**7/84 - 3*k**5/40 + k**4/12 + 61*k + 103. Let a(b) be the first derivative of v(b). Suppose a(m) = 0. What is m?
-2, 0, 1
Let y(n) be the third derivative of 1/672*n**8 + 6*n - 1/120*n**5 - 1/3*n**3 + 0 + 1/84*n**7 + 2*n**2 + 7/240*n**6 - 1/6*n**4. What is t in y(t) = 0?
-2, -1, 1
Let h(d) be the first derivative of -50 + 0*d**2 - 2/27*d**3 + 0*d. Solve h(i) = 0.
0
Let v be (14432/260)/41 - 6/39. Let 2/5 + v*j**3 + 2/5*j**2 - 4/5*j**4 - 6/5*j = 0. What is j?
-1, 1/2, 1
Let k(g) be the second derivative of 4/21*g**3 + 11/2*g**2 - 43*g + 5/84*g**4 + 1/210*g**5 + 0. Let n(m) be the first derivative of k(m). What is x in n(x) = 0?
-4, -1
Let i(p) be the second derivative of -177*p**4/20 - 533*p**3/10 - 9*p**2/5 + 350*p - 1. Factor i(l).
-3*(l + 3)*(177*l + 2)/5
Suppose 14*w - 530 - 100 = 0. What is n in 4*n**2 + w + 21 - n**2 + 43*n - 4*n = 0?
-11, -2
Let o be (-384)/(-18) - (0 - 2/(-6)). Suppose 5*u + 7 + 22 = 2*q, -2*q - 5*u - o = 0. Factor 14*y**q + y**2 - 4 + y**2.
4*(2*y - 1)*(2*y + 1)
Solve 96*d**2 - 257 - 4132*d - 177 + 606 = 0 for d.
1/24, 43
Let u(o) = 21*o**3 + 126*o**2 + 258*o + 99. Let f(i) = 3*i**3 + 18*i**2 + 37*i + 14. Let s = -15 + -12. Let k(x) = s*f(x) + 4*u(x). Factor k(m).
3*(m + 1)*(m + 2)*(m + 3)
Let m(g) = 34*g**3 + 7*g**2 - 420*g - 261. Let y(x) = -37*x**3 - 6*x**2 + 419*x + 264. Let z(j) = 4*m(j) + 3*y(j). Suppose z(d) = 0. Calculate d.
-4, -3/5, 21/5
Let k be 18 + (-186)/(-42) + (-20)/(-35). Factor 12*b**2 - k*b**2 + 4*b**2 + 8*b**2 - 3*b + 2.
(b - 2)*(b - 1)
Let r(l) be the second derivative of 8*l + 0*l**3 + 4 + 1/40*l**5 + 0*l**2 + 1/24*l**4. Determine w, given that r(w) = 0.
-1, 0
Let a(l) be the first derivative of 2*l**5/55 - 29*l**4/11 - 362*l**3/33 - 122*l**2/11 - 1330. Suppose a(z) = 0. Calculate z.
-2, -1, 0, 61
Let c(p) be the third derivative of -p**7/1260 + p**6/180 + p**5/18 - 11*p**3/6 - 10*p**2 + 3. Let a(s) be the first derivative of c(s). Factor a(z).
-2*z*(z - 5)*(z + 2)/3
Let p(z) be the second derivative of 2 - 5/6*z**3 + 3*z + 1/4*z**5 + 55/12*z**4 - 55/2*z**2. Suppose p(w) = 0. Calculate w.
-11, -1, 1
Suppose 11*l - 6*l - 31 = -3*s, 3*l = -4*s + 34. Factor 7*y**2 - 3 - y**3 + 4*y**3 - 2*y**3 - 12*y**2 + s*y.
(y - 3)*(y - 1)**2
Let a(z) = 10*z**2 - 395*z + 1765. Let t(b) = -7*b**2 + 197*b - 883. Let k(u) = -3*a(u) - 5*t(u). Factor k(d).
5*(d - 4)*(d + 44)
Suppose -264 = -4*g - 312. Let q(m) = 41*m + 495. Let l be q(g). Factor 0*w + 2/7*w**4 + 0 + 2/7*w**2 + 4/7*w**l.
2*w**2*(w + 1)**2/7
Let b(t) be the first derivative of -28 + 1/5*t**2 - 2/15*t**3 + 0*t. What is a in b(a) = 0?
0, 1
Let g(i) be the third derivative of -i**7/1365 + 11*i**6/390 - 47*i**5/130 + 82*i**4/39 - 16*i**3/3 + 